YES After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, it remains to prove termination of the 95-rule system { 0 0 1 2 1 0 3 2 -> 0 2 0 1 1 0 3 2 , 1 0 4 1 2 5 2 4 -> 1 0 4 1 5 2 2 4 , 1 4 4 0 4 1 5 2 5 -> 1 4 4 1 4 5 0 2 5 , 4 4 1 3 0 5 5 5 3 -> 4 1 4 3 5 0 5 5 3 , 1 1 3 1 2 1 1 1 0 0 -> 2 0 3 3 2 0 3 5 0 1 , 1 3 0 5 5 1 1 1 2 2 -> 1 3 5 5 1 0 1 1 2 2 , 3 0 1 4 4 2 0 2 2 4 -> 1 1 1 4 4 0 5 3 5 3 , 0 0 5 4 0 4 2 3 5 2 2 -> 1 5 0 2 4 4 4 0 4 2 , 0 1 0 1 0 3 2 3 5 5 1 -> 3 2 2 3 4 4 3 1 3 4 , 0 1 0 2 4 2 1 2 5 1 5 -> 1 5 3 1 3 1 1 5 2 1 , 0 2 0 4 4 2 4 1 0 3 3 -> 4 5 2 3 1 4 1 3 5 2 , 0 2 2 4 1 5 3 0 0 0 1 -> 4 1 1 3 1 0 5 1 2 0 , 0 3 1 0 3 2 4 2 2 1 2 -> 1 3 3 1 3 4 0 1 0 3 , 0 5 2 5 2 5 1 4 4 4 2 -> 2 2 1 5 4 4 4 5 5 0 2 , 1 0 0 3 4 2 5 4 2 1 1 -> 2 4 5 4 4 3 3 4 2 2 , 1 2 2 0 2 0 4 4 1 1 5 -> 5 2 5 2 1 2 1 0 0 0 , 1 3 1 3 2 4 5 0 2 2 1 -> 2 5 1 1 2 2 3 1 4 2 , 1 3 1 4 1 2 2 1 1 1 5 -> 3 1 3 0 1 1 5 2 5 0 , 1 3 5 1 2 3 5 0 1 5 3 -> 2 0 5 1 1 3 2 3 5 3 , 1 4 2 5 0 0 4 2 3 5 3 -> 1 2 5 5 2 0 2 1 1 2 , 1 5 2 0 4 1 0 2 1 3 2 -> 5 0 2 1 2 1 5 2 0 1 , 1 5 3 2 1 3 0 2 1 0 3 -> 5 0 5 3 4 0 4 4 1 2 , 2 1 0 1 4 2 3 5 2 4 4 -> 1 0 1 5 4 4 2 1 1 3 , 2 3 5 0 0 4 5 0 3 0 5 -> 2 5 0 3 5 2 3 4 1 4 , 2 4 3 5 2 1 5 4 1 2 4 -> 1 3 1 4 3 1 3 0 5 3 , 2 5 1 3 2 3 2 4 1 1 4 -> 1 0 4 1 5 5 3 5 3 3 , 2 5 3 2 5 1 2 1 1 5 4 -> 5 5 1 2 2 1 2 5 4 3 , 2 5 4 0 3 1 4 1 1 1 0 -> 2 5 4 0 1 3 4 1 1 1 0 , 2 5 4 1 5 1 5 2 3 2 4 -> 2 1 2 0 5 1 4 4 0 5 , 3 3 0 0 1 1 5 0 2 4 3 -> 5 3 3 0 3 0 3 4 5 4 , 3 5 2 3 3 2 2 1 4 2 1 -> 3 5 4 3 2 5 3 3 2 4 , 4 1 4 4 0 3 0 0 4 2 5 -> 3 4 2 5 0 2 5 1 1 0 , 4 2 5 3 2 4 1 2 3 0 1 -> 3 0 4 1 3 0 4 0 1 2 , 4 4 0 0 2 1 4 3 5 0 5 -> 3 4 2 3 2 1 0 4 1 1 , 4 4 4 3 3 5 4 4 4 5 1 -> 0 3 0 3 2 1 2 2 3 1 , 4 5 1 2 0 1 0 5 4 2 2 -> 1 0 5 4 2 1 0 5 5 4 , 4 5 1 2 2 0 1 4 1 3 1 -> 2 3 3 4 1 0 0 1 5 2 , 4 5 4 5 5 0 4 3 3 2 4 -> 3 1 2 3 0 2 1 4 3 5 , 5 1 2 0 1 0 5 3 2 0 3 -> 5 1 3 1 0 2 2 1 4 2 , 5 2 1 1 0 1 4 4 1 1 1 -> 4 0 3 1 2 3 1 3 0 1 , 5 2 4 3 5 4 4 0 2 2 1 -> 5 3 4 5 0 1 4 5 0 3 , 0 0 2 5 1 2 4 1 4 4 4 5 -> 4 1 0 4 0 3 2 4 3 0 , 0 2 5 3 3 2 3 5 0 0 3 2 -> 5 0 2 0 1 3 1 2 5 1 , 1 0 2 5 2 1 2 0 1 0 2 2 -> 1 0 2 5 1 2 2 0 1 0 2 2 , 1 4 4 1 5 5 5 4 3 5 5 3 -> 4 5 5 1 1 4 1 2 4 4 , 2 0 5 2 2 3 0 1 0 5 4 3 -> 5 3 4 0 1 3 2 1 5 2 , 2 1 1 1 5 4 1 5 0 1 4 2 -> 4 4 0 5 0 4 3 1 2 5 , 2 2 2 1 5 5 5 0 5 4 5 3 -> 4 0 3 5 0 5 2 4 2 5 , 2 5 3 0 0 5 1 2 5 5 2 1 -> 0 0 0 2 0 2 3 2 1 4 , 2 5 3 4 2 3 1 2 5 3 2 0 -> 0 1 2 5 4 1 0 0 0 4 , 3 3 3 4 2 0 4 1 5 0 1 5 -> 4 0 0 3 1 3 3 4 3 0 , 5 0 1 2 1 4 4 0 5 0 5 4 -> 5 0 1 2 1 4 0 4 5 0 5 4 , 5 1 3 3 4 1 2 2 5 1 5 0 -> 4 2 0 3 0 1 4 0 4 4 , 5 2 2 3 5 4 3 3 3 0 0 3 -> 4 0 5 3 5 0 0 4 0 4 , 5 2 3 0 3 5 4 3 0 1 0 3 -> 5 0 4 5 5 2 2 0 1 4 , 5 3 3 2 2 3 0 2 0 0 1 2 -> 4 4 2 4 0 3 2 1 1 3 , 5 3 5 0 4 2 0 0 0 4 3 2 -> 0 3 4 5 4 2 3 2 5 0 , 5 5 5 1 0 0 3 5 5 3 4 1 -> 1 3 2 0 2 2 2 5 2 2 , 2 5 0 5 4 4 5 5 1 3 1 0 1 -> 2 5 0 4 5 5 4 5 1 3 1 0 1 , 2 5 1 0 5 3 3 5 2 2 1 2 3 -> 2 5 1 0 5 3 5 3 2 2 1 2 3 , 4 0 1 4 1 4 4 3 1 3 1 4 4 -> 4 0 1 4 1 4 3 4 1 3 1 4 4 , 4 2 2 2 2 2 3 2 5 3 1 2 4 -> 4 2 3 2 2 2 2 3 2 5 1 2 4 , 4 3 5 2 2 3 5 3 3 3 3 5 0 -> 3 4 4 2 2 2 0 0 1 0 , 5 2 3 5 2 4 2 1 0 4 2 0 5 -> 5 2 2 3 2 1 0 5 4 4 2 0 5 , 1 5 0 2 1 0 3 5 5 2 0 3 0 5 -> 1 5 0 2 1 0 5 3 5 2 0 3 0 5 , 3 5 3 4 2 2 2 5 4 4 3 4 0 4 -> 3 5 3 4 2 2 2 4 5 4 3 4 0 4 , 4 0 2 4 1 4 4 5 1 0 0 4 0 5 -> 4 0 2 4 1 4 5 4 1 0 0 4 0 5 , 1 1 0 3 0 3 4 4 4 4 4 0 0 1 1 -> 1 1 0 3 0 4 3 4 4 4 4 0 0 1 1 , 1 2 4 4 2 3 0 0 4 3 3 0 5 5 3 -> 1 2 4 4 3 2 0 3 5 0 0 5 3 4 3 , 1 3 2 5 3 1 5 3 3 5 3 2 0 4 4 -> 1 3 2 5 3 5 1 3 3 5 3 2 0 4 4 , 5 5 3 3 0 3 4 2 1 2 3 1 1 4 1 -> 5 5 0 3 3 3 4 2 2 1 3 1 1 4 1 , 0 5 3 4 3 5 2 2 2 0 2 1 0 1 4 2 -> 0 5 3 4 3 5 2 2 2 0 1 2 0 1 4 2 , 0 0 0 3 5 0 0 5 4 3 5 4 5 4 3 2 4 -> 0 0 0 3 5 0 5 0 4 3 5 4 5 4 3 2 4 , 5 4 0 2 4 4 5 2 1 3 3 0 4 1 2 1 0 -> 5 4 0 2 4 4 5 2 1 3 3 0 1 4 2 1 0 , 3 1 4 4 3 3 1 3 0 2 0 2 5 3 5 0 3 1 -> 3 1 4 4 3 1 3 3 0 2 2 0 5 3 5 3 0 1 , 5 5 5 0 2 1 1 5 4 4 0 4 4 3 1 4 4 3 -> 5 5 5 0 2 1 1 5 4 4 0 4 4 3 4 1 4 3 , 3 1 2 2 1 5 2 1 2 5 3 1 1 5 1 2 5 3 4 -> 3 5 1 1 3 4 1 2 2 2 1 5 1 2 2 1 5 3 5 , 3 5 2 4 0 2 1 0 0 5 3 0 4 1 4 2 0 0 3 -> 3 1 0 5 1 4 2 2 3 0 4 0 2 0 4 5 0 0 3 , 0 2 5 1 4 2 5 3 1 4 1 0 3 2 3 4 3 0 1 1 3 -> 0 2 5 1 4 2 5 1 3 4 1 0 3 2 3 4 3 0 1 1 3 , 1 0 5 2 4 3 5 0 0 5 2 5 5 4 5 4 0 0 5 5 4 -> 1 0 5 2 4 3 5 0 0 5 2 5 5 4 4 5 0 0 5 5 4 , 1 2 1 4 2 1 3 4 2 5 1 4 5 1 3 0 4 1 0 4 4 -> 1 2 1 4 2 1 3 2 4 5 1 4 5 1 3 0 4 1 0 4 4 , 3 4 0 0 2 0 4 1 5 5 0 0 4 3 5 2 1 0 2 4 4 -> 3 4 0 0 2 0 4 1 5 0 5 0 4 3 5 2 1 0 2 4 4 , 5 1 4 3 3 3 4 1 1 4 0 0 0 3 2 3 1 3 5 5 1 0 -> 5 1 4 3 3 3 4 1 1 4 0 0 0 3 2 3 3 1 5 5 1 0 , 2 0 3 3 0 5 3 1 4 3 0 1 1 4 0 5 5 3 1 2 1 2 4 2 5 -> 2 0 3 3 0 5 1 3 4 3 0 1 1 4 0 5 5 3 1 2 1 2 4 2 5 , 2 1 1 1 4 4 1 4 4 4 5 3 2 2 1 4 4 4 4 1 2 2 3 1 1 -> 2 1 1 4 1 4 1 4 4 4 5 3 2 2 1 4 4 4 4 1 2 2 3 1 1 , 2 1 2 1 1 4 1 3 2 0 2 2 1 5 3 2 3 5 0 2 0 0 5 0 2 -> 2 1 2 1 1 4 1 3 2 0 2 2 1 5 3 3 2 5 0 2 0 0 5 0 2 , 0 4 0 2 5 4 5 1 3 5 2 0 1 1 0 4 1 3 0 4 2 3 4 5 5 1 4 -> 0 4 0 2 5 4 5 1 3 5 0 2 1 1 0 4 1 3 0 4 2 3 4 5 5 1 4 , 4 5 3 1 0 2 2 2 4 5 3 5 5 5 0 2 1 2 4 0 4 4 1 3 0 0 2 -> 4 5 3 1 0 2 2 2 4 5 3 5 5 5 0 2 1 2 4 4 0 4 1 3 0 0 2 , 5 1 2 3 2 3 4 2 4 2 1 0 4 4 0 3 0 3 2 5 3 1 5 2 3 1 0 -> 5 1 2 3 2 3 4 2 4 2 1 0 4 4 0 3 0 3 2 5 3 1 5 3 2 1 0 , 2 0 4 5 3 3 2 4 3 4 4 4 1 5 1 5 5 0 2 4 4 1 0 5 0 5 3 3 -> 2 0 4 5 3 3 2 4 3 4 4 1 4 5 1 5 5 0 2 4 4 1 0 5 0 5 3 3 , 2 0 0 0 0 0 5 4 5 1 2 3 2 3 4 3 5 5 5 0 1 3 3 1 4 1 4 0 2 -> 2 0 0 0 0 0 5 4 5 1 2 3 2 3 3 4 5 5 5 0 1 3 3 1 4 1 4 0 2 , 2 0 3 0 4 2 1 1 4 5 0 1 2 1 4 3 1 3 0 1 1 0 5 4 4 2 3 3 3 -> 2 0 3 0 4 2 1 1 4 5 0 1 2 1 4 3 1 3 0 1 1 0 4 5 4 2 3 3 3 , 2 2 5 3 2 2 0 4 4 4 4 0 5 0 5 3 4 4 4 0 0 5 0 5 0 2 0 1 3 -> 2 2 5 3 2 2 0 4 4 4 4 0 5 0 5 3 4 4 4 0 5 0 0 5 0 2 0 1 3 , 4 5 5 0 5 5 5 2 1 2 3 0 3 2 1 1 2 1 3 0 1 1 5 1 1 5 0 0 4 4 -> 4 5 5 5 0 5 5 2 1 2 3 0 3 1 1 2 2 1 0 1 3 1 5 1 5 1 0 0 4 4 , 5 5 0 5 0 0 3 4 4 0 0 0 0 4 0 4 5 3 1 1 1 3 1 1 2 1 0 1 2 4 -> 5 5 0 5 0 0 4 3 4 0 0 0 0 4 0 4 5 3 1 1 1 3 1 1 2 1 0 1 2 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 47-rule system { 0 0 1 2 1 0 3 2 -> 0 2 0 1 1 0 3 2 , 1 0 4 1 2 5 2 4 -> 1 0 4 1 5 2 2 4 , 1 4 4 0 4 1 5 2 5 -> 1 4 4 1 4 5 0 2 5 , 4 4 1 3 0 5 5 5 3 -> 4 1 4 3 5 0 5 5 3 , 1 1 3 1 2 1 1 1 0 0 -> 2 0 3 3 2 0 3 5 0 1 , 1 3 0 5 5 1 1 1 2 2 -> 1 3 5 5 1 0 1 1 2 2 , 3 0 1 4 4 2 0 2 2 4 -> 1 1 1 4 4 0 5 3 5 3 , 0 5 2 5 2 5 1 4 4 4 2 -> 2 2 1 5 4 4 4 5 5 0 2 , 2 5 4 0 3 1 4 1 1 1 0 -> 2 5 4 0 1 3 4 1 1 1 0 , 1 0 2 5 2 1 2 0 1 0 2 2 -> 1 0 2 5 1 2 2 0 1 0 2 2 , 5 0 1 2 1 4 4 0 5 0 5 4 -> 5 0 1 2 1 4 0 4 5 0 5 4 , 2 5 0 5 4 4 5 5 1 3 1 0 1 -> 2 5 0 4 5 5 4 5 1 3 1 0 1 , 2 5 1 0 5 3 3 5 2 2 1 2 3 -> 2 5 1 0 5 3 5 3 2 2 1 2 3 , 4 0 1 4 1 4 4 3 1 3 1 4 4 -> 4 0 1 4 1 4 3 4 1 3 1 4 4 , 4 2 2 2 2 2 3 2 5 3 1 2 4 -> 4 2 3 2 2 2 2 3 2 5 1 2 4 , 5 2 3 5 2 4 2 1 0 4 2 0 5 -> 5 2 2 3 2 1 0 5 4 4 2 0 5 , 1 5 0 2 1 0 3 5 5 2 0 3 0 5 -> 1 5 0 2 1 0 5 3 5 2 0 3 0 5 , 3 5 3 4 2 2 2 5 4 4 3 4 0 4 -> 3 5 3 4 2 2 2 4 5 4 3 4 0 4 , 4 0 2 4 1 4 4 5 1 0 0 4 0 5 -> 4 0 2 4 1 4 5 4 1 0 0 4 0 5 , 1 1 0 3 0 3 4 4 4 4 4 0 0 1 1 -> 1 1 0 3 0 4 3 4 4 4 4 0 0 1 1 , 1 2 4 4 2 3 0 0 4 3 3 0 5 5 3 -> 1 2 4 4 3 2 0 3 5 0 0 5 3 4 3 , 1 3 2 5 3 1 5 3 3 5 3 2 0 4 4 -> 1 3 2 5 3 5 1 3 3 5 3 2 0 4 4 , 5 5 3 3 0 3 4 2 1 2 3 1 1 4 1 -> 5 5 0 3 3 3 4 2 2 1 3 1 1 4 1 , 0 5 3 4 3 5 2 2 2 0 2 1 0 1 4 2 -> 0 5 3 4 3 5 2 2 2 0 1 2 0 1 4 2 , 0 0 0 3 5 0 0 5 4 3 5 4 5 4 3 2 4 -> 0 0 0 3 5 0 5 0 4 3 5 4 5 4 3 2 4 , 5 4 0 2 4 4 5 2 1 3 3 0 4 1 2 1 0 -> 5 4 0 2 4 4 5 2 1 3 3 0 1 4 2 1 0 , 3 1 4 4 3 3 1 3 0 2 0 2 5 3 5 0 3 1 -> 3 1 4 4 3 1 3 3 0 2 2 0 5 3 5 3 0 1 , 5 5 5 0 2 1 1 5 4 4 0 4 4 3 1 4 4 3 -> 5 5 5 0 2 1 1 5 4 4 0 4 4 3 4 1 4 3 , 3 1 2 2 1 5 2 1 2 5 3 1 1 5 1 2 5 3 4 -> 3 5 1 1 3 4 1 2 2 2 1 5 1 2 2 1 5 3 5 , 3 5 2 4 0 2 1 0 0 5 3 0 4 1 4 2 0 0 3 -> 3 1 0 5 1 4 2 2 3 0 4 0 2 0 4 5 0 0 3 , 0 2 5 1 4 2 5 3 1 4 1 0 3 2 3 4 3 0 1 1 3 -> 0 2 5 1 4 2 5 1 3 4 1 0 3 2 3 4 3 0 1 1 3 , 1 0 5 2 4 3 5 0 0 5 2 5 5 4 5 4 0 0 5 5 4 -> 1 0 5 2 4 3 5 0 0 5 2 5 5 4 4 5 0 0 5 5 4 , 1 2 1 4 2 1 3 4 2 5 1 4 5 1 3 0 4 1 0 4 4 -> 1 2 1 4 2 1 3 2 4 5 1 4 5 1 3 0 4 1 0 4 4 , 3 4 0 0 2 0 4 1 5 5 0 0 4 3 5 2 1 0 2 4 4 -> 3 4 0 0 2 0 4 1 5 0 5 0 4 3 5 2 1 0 2 4 4 , 5 1 4 3 3 3 4 1 1 4 0 0 0 3 2 3 1 3 5 5 1 0 -> 5 1 4 3 3 3 4 1 1 4 0 0 0 3 2 3 3 1 5 5 1 0 , 2 0 3 3 0 5 3 1 4 3 0 1 1 4 0 5 5 3 1 2 1 2 4 2 5 -> 2 0 3 3 0 5 1 3 4 3 0 1 1 4 0 5 5 3 1 2 1 2 4 2 5 , 2 1 1 1 4 4 1 4 4 4 5 3 2 2 1 4 4 4 4 1 2 2 3 1 1 -> 2 1 1 4 1 4 1 4 4 4 5 3 2 2 1 4 4 4 4 1 2 2 3 1 1 , 2 1 2 1 1 4 1 3 2 0 2 2 1 5 3 2 3 5 0 2 0 0 5 0 2 -> 2 1 2 1 1 4 1 3 2 0 2 2 1 5 3 3 2 5 0 2 0 0 5 0 2 , 0 4 0 2 5 4 5 1 3 5 2 0 1 1 0 4 1 3 0 4 2 3 4 5 5 1 4 -> 0 4 0 2 5 4 5 1 3 5 0 2 1 1 0 4 1 3 0 4 2 3 4 5 5 1 4 , 4 5 3 1 0 2 2 2 4 5 3 5 5 5 0 2 1 2 4 0 4 4 1 3 0 0 2 -> 4 5 3 1 0 2 2 2 4 5 3 5 5 5 0 2 1 2 4 4 0 4 1 3 0 0 2 , 5 1 2 3 2 3 4 2 4 2 1 0 4 4 0 3 0 3 2 5 3 1 5 2 3 1 0 -> 5 1 2 3 2 3 4 2 4 2 1 0 4 4 0 3 0 3 2 5 3 1 5 3 2 1 0 , 2 0 4 5 3 3 2 4 3 4 4 4 1 5 1 5 5 0 2 4 4 1 0 5 0 5 3 3 -> 2 0 4 5 3 3 2 4 3 4 4 1 4 5 1 5 5 0 2 4 4 1 0 5 0 5 3 3 , 2 0 0 0 0 0 5 4 5 1 2 3 2 3 4 3 5 5 5 0 1 3 3 1 4 1 4 0 2 -> 2 0 0 0 0 0 5 4 5 1 2 3 2 3 3 4 5 5 5 0 1 3 3 1 4 1 4 0 2 , 2 0 3 0 4 2 1 1 4 5 0 1 2 1 4 3 1 3 0 1 1 0 5 4 4 2 3 3 3 -> 2 0 3 0 4 2 1 1 4 5 0 1 2 1 4 3 1 3 0 1 1 0 4 5 4 2 3 3 3 , 2 2 5 3 2 2 0 4 4 4 4 0 5 0 5 3 4 4 4 0 0 5 0 5 0 2 0 1 3 -> 2 2 5 3 2 2 0 4 4 4 4 0 5 0 5 3 4 4 4 0 5 0 0 5 0 2 0 1 3 , 4 5 5 0 5 5 5 2 1 2 3 0 3 2 1 1 2 1 3 0 1 1 5 1 1 5 0 0 4 4 -> 4 5 5 5 0 5 5 2 1 2 3 0 3 1 1 2 2 1 0 1 3 1 5 1 5 1 0 0 4 4 , 5 5 0 5 0 0 3 4 4 0 0 0 0 4 0 4 5 3 1 1 1 3 1 1 2 1 0 1 2 4 -> 5 5 0 5 0 0 4 3 4 0 0 0 0 4 0 4 5 3 1 1 1 3 1 1 2 1 0 1 2 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 0 | | 0 1 | \ / 4 is interpreted by / \ | 1 1 | | 0 1 | \ / 5 is interpreted by / \ | 1 0 | | 0 1 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, it remains to prove termination of the 45-rule system { 0 0 1 2 1 0 3 2 -> 0 2 0 1 1 0 3 2 , 1 0 4 1 2 5 2 4 -> 1 0 4 1 5 2 2 4 , 1 4 4 0 4 1 5 2 5 -> 1 4 4 1 4 5 0 2 5 , 4 4 1 3 0 5 5 5 3 -> 4 1 4 3 5 0 5 5 3 , 1 3 0 5 5 1 1 1 2 2 -> 1 3 5 5 1 0 1 1 2 2 , 0 5 2 5 2 5 1 4 4 4 2 -> 2 2 1 5 4 4 4 5 5 0 2 , 2 5 4 0 3 1 4 1 1 1 0 -> 2 5 4 0 1 3 4 1 1 1 0 , 1 0 2 5 2 1 2 0 1 0 2 2 -> 1 0 2 5 1 2 2 0 1 0 2 2 , 5 0 1 2 1 4 4 0 5 0 5 4 -> 5 0 1 2 1 4 0 4 5 0 5 4 , 2 5 0 5 4 4 5 5 1 3 1 0 1 -> 2 5 0 4 5 5 4 5 1 3 1 0 1 , 2 5 1 0 5 3 3 5 2 2 1 2 3 -> 2 5 1 0 5 3 5 3 2 2 1 2 3 , 4 0 1 4 1 4 4 3 1 3 1 4 4 -> 4 0 1 4 1 4 3 4 1 3 1 4 4 , 4 2 2 2 2 2 3 2 5 3 1 2 4 -> 4 2 3 2 2 2 2 3 2 5 1 2 4 , 5 2 3 5 2 4 2 1 0 4 2 0 5 -> 5 2 2 3 2 1 0 5 4 4 2 0 5 , 1 5 0 2 1 0 3 5 5 2 0 3 0 5 -> 1 5 0 2 1 0 5 3 5 2 0 3 0 5 , 3 5 3 4 2 2 2 5 4 4 3 4 0 4 -> 3 5 3 4 2 2 2 4 5 4 3 4 0 4 , 4 0 2 4 1 4 4 5 1 0 0 4 0 5 -> 4 0 2 4 1 4 5 4 1 0 0 4 0 5 , 1 1 0 3 0 3 4 4 4 4 4 0 0 1 1 -> 1 1 0 3 0 4 3 4 4 4 4 0 0 1 1 , 1 2 4 4 2 3 0 0 4 3 3 0 5 5 3 -> 1 2 4 4 3 2 0 3 5 0 0 5 3 4 3 , 1 3 2 5 3 1 5 3 3 5 3 2 0 4 4 -> 1 3 2 5 3 5 1 3 3 5 3 2 0 4 4 , 5 5 3 3 0 3 4 2 1 2 3 1 1 4 1 -> 5 5 0 3 3 3 4 2 2 1 3 1 1 4 1 , 0 5 3 4 3 5 2 2 2 0 2 1 0 1 4 2 -> 0 5 3 4 3 5 2 2 2 0 1 2 0 1 4 2 , 0 0 0 3 5 0 0 5 4 3 5 4 5 4 3 2 4 -> 0 0 0 3 5 0 5 0 4 3 5 4 5 4 3 2 4 , 5 4 0 2 4 4 5 2 1 3 3 0 4 1 2 1 0 -> 5 4 0 2 4 4 5 2 1 3 3 0 1 4 2 1 0 , 3 1 4 4 3 3 1 3 0 2 0 2 5 3 5 0 3 1 -> 3 1 4 4 3 1 3 3 0 2 2 0 5 3 5 3 0 1 , 5 5 5 0 2 1 1 5 4 4 0 4 4 3 1 4 4 3 -> 5 5 5 0 2 1 1 5 4 4 0 4 4 3 4 1 4 3 , 3 1 2 2 1 5 2 1 2 5 3 1 1 5 1 2 5 3 4 -> 3 5 1 1 3 4 1 2 2 2 1 5 1 2 2 1 5 3 5 , 3 5 2 4 0 2 1 0 0 5 3 0 4 1 4 2 0 0 3 -> 3 1 0 5 1 4 2 2 3 0 4 0 2 0 4 5 0 0 3 , 0 2 5 1 4 2 5 3 1 4 1 0 3 2 3 4 3 0 1 1 3 -> 0 2 5 1 4 2 5 1 3 4 1 0 3 2 3 4 3 0 1 1 3 , 1 0 5 2 4 3 5 0 0 5 2 5 5 4 5 4 0 0 5 5 4 -> 1 0 5 2 4 3 5 0 0 5 2 5 5 4 4 5 0 0 5 5 4 , 1 2 1 4 2 1 3 4 2 5 1 4 5 1 3 0 4 1 0 4 4 -> 1 2 1 4 2 1 3 2 4 5 1 4 5 1 3 0 4 1 0 4 4 , 3 4 0 0 2 0 4 1 5 5 0 0 4 3 5 2 1 0 2 4 4 -> 3 4 0 0 2 0 4 1 5 0 5 0 4 3 5 2 1 0 2 4 4 , 5 1 4 3 3 3 4 1 1 4 0 0 0 3 2 3 1 3 5 5 1 0 -> 5 1 4 3 3 3 4 1 1 4 0 0 0 3 2 3 3 1 5 5 1 0 , 2 0 3 3 0 5 3 1 4 3 0 1 1 4 0 5 5 3 1 2 1 2 4 2 5 -> 2 0 3 3 0 5 1 3 4 3 0 1 1 4 0 5 5 3 1 2 1 2 4 2 5 , 2 1 1 1 4 4 1 4 4 4 5 3 2 2 1 4 4 4 4 1 2 2 3 1 1 -> 2 1 1 4 1 4 1 4 4 4 5 3 2 2 1 4 4 4 4 1 2 2 3 1 1 , 2 1 2 1 1 4 1 3 2 0 2 2 1 5 3 2 3 5 0 2 0 0 5 0 2 -> 2 1 2 1 1 4 1 3 2 0 2 2 1 5 3 3 2 5 0 2 0 0 5 0 2 , 0 4 0 2 5 4 5 1 3 5 2 0 1 1 0 4 1 3 0 4 2 3 4 5 5 1 4 -> 0 4 0 2 5 4 5 1 3 5 0 2 1 1 0 4 1 3 0 4 2 3 4 5 5 1 4 , 4 5 3 1 0 2 2 2 4 5 3 5 5 5 0 2 1 2 4 0 4 4 1 3 0 0 2 -> 4 5 3 1 0 2 2 2 4 5 3 5 5 5 0 2 1 2 4 4 0 4 1 3 0 0 2 , 5 1 2 3 2 3 4 2 4 2 1 0 4 4 0 3 0 3 2 5 3 1 5 2 3 1 0 -> 5 1 2 3 2 3 4 2 4 2 1 0 4 4 0 3 0 3 2 5 3 1 5 3 2 1 0 , 2 0 4 5 3 3 2 4 3 4 4 4 1 5 1 5 5 0 2 4 4 1 0 5 0 5 3 3 -> 2 0 4 5 3 3 2 4 3 4 4 1 4 5 1 5 5 0 2 4 4 1 0 5 0 5 3 3 , 2 0 0 0 0 0 5 4 5 1 2 3 2 3 4 3 5 5 5 0 1 3 3 1 4 1 4 0 2 -> 2 0 0 0 0 0 5 4 5 1 2 3 2 3 3 4 5 5 5 0 1 3 3 1 4 1 4 0 2 , 2 0 3 0 4 2 1 1 4 5 0 1 2 1 4 3 1 3 0 1 1 0 5 4 4 2 3 3 3 -> 2 0 3 0 4 2 1 1 4 5 0 1 2 1 4 3 1 3 0 1 1 0 4 5 4 2 3 3 3 , 2 2 5 3 2 2 0 4 4 4 4 0 5 0 5 3 4 4 4 0 0 5 0 5 0 2 0 1 3 -> 2 2 5 3 2 2 0 4 4 4 4 0 5 0 5 3 4 4 4 0 5 0 0 5 0 2 0 1 3 , 4 5 5 0 5 5 5 2 1 2 3 0 3 2 1 1 2 1 3 0 1 1 5 1 1 5 0 0 4 4 -> 4 5 5 5 0 5 5 2 1 2 3 0 3 1 1 2 2 1 0 1 3 1 5 1 5 1 0 0 4 4 , 5 5 0 5 0 0 3 4 4 0 0 0 0 4 0 4 5 3 1 1 1 3 1 1 2 1 0 1 2 4 -> 5 5 0 5 0 0 4 3 4 0 0 0 0 4 0 4 5 3 1 1 1 3 1 1 2 1 0 1 2 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 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 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 1 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 44-rule system { 0 0 1 2 1 0 3 2 -> 0 2 0 1 1 0 3 2 , 1 4 4 0 4 1 5 2 5 -> 1 4 4 1 4 5 0 2 5 , 4 4 1 3 0 5 5 5 3 -> 4 1 4 3 5 0 5 5 3 , 1 3 0 5 5 1 1 1 2 2 -> 1 3 5 5 1 0 1 1 2 2 , 0 5 2 5 2 5 1 4 4 4 2 -> 2 2 1 5 4 4 4 5 5 0 2 , 2 5 4 0 3 1 4 1 1 1 0 -> 2 5 4 0 1 3 4 1 1 1 0 , 1 0 2 5 2 1 2 0 1 0 2 2 -> 1 0 2 5 1 2 2 0 1 0 2 2 , 5 0 1 2 1 4 4 0 5 0 5 4 -> 5 0 1 2 1 4 0 4 5 0 5 4 , 2 5 0 5 4 4 5 5 1 3 1 0 1 -> 2 5 0 4 5 5 4 5 1 3 1 0 1 , 2 5 1 0 5 3 3 5 2 2 1 2 3 -> 2 5 1 0 5 3 5 3 2 2 1 2 3 , 4 0 1 4 1 4 4 3 1 3 1 4 4 -> 4 0 1 4 1 4 3 4 1 3 1 4 4 , 4 2 2 2 2 2 3 2 5 3 1 2 4 -> 4 2 3 2 2 2 2 3 2 5 1 2 4 , 5 2 3 5 2 4 2 1 0 4 2 0 5 -> 5 2 2 3 2 1 0 5 4 4 2 0 5 , 1 5 0 2 1 0 3 5 5 2 0 3 0 5 -> 1 5 0 2 1 0 5 3 5 2 0 3 0 5 , 3 5 3 4 2 2 2 5 4 4 3 4 0 4 -> 3 5 3 4 2 2 2 4 5 4 3 4 0 4 , 4 0 2 4 1 4 4 5 1 0 0 4 0 5 -> 4 0 2 4 1 4 5 4 1 0 0 4 0 5 , 1 1 0 3 0 3 4 4 4 4 4 0 0 1 1 -> 1 1 0 3 0 4 3 4 4 4 4 0 0 1 1 , 1 2 4 4 2 3 0 0 4 3 3 0 5 5 3 -> 1 2 4 4 3 2 0 3 5 0 0 5 3 4 3 , 1 3 2 5 3 1 5 3 3 5 3 2 0 4 4 -> 1 3 2 5 3 5 1 3 3 5 3 2 0 4 4 , 5 5 3 3 0 3 4 2 1 2 3 1 1 4 1 -> 5 5 0 3 3 3 4 2 2 1 3 1 1 4 1 , 0 5 3 4 3 5 2 2 2 0 2 1 0 1 4 2 -> 0 5 3 4 3 5 2 2 2 0 1 2 0 1 4 2 , 0 0 0 3 5 0 0 5 4 3 5 4 5 4 3 2 4 -> 0 0 0 3 5 0 5 0 4 3 5 4 5 4 3 2 4 , 5 4 0 2 4 4 5 2 1 3 3 0 4 1 2 1 0 -> 5 4 0 2 4 4 5 2 1 3 3 0 1 4 2 1 0 , 3 1 4 4 3 3 1 3 0 2 0 2 5 3 5 0 3 1 -> 3 1 4 4 3 1 3 3 0 2 2 0 5 3 5 3 0 1 , 5 5 5 0 2 1 1 5 4 4 0 4 4 3 1 4 4 3 -> 5 5 5 0 2 1 1 5 4 4 0 4 4 3 4 1 4 3 , 3 1 2 2 1 5 2 1 2 5 3 1 1 5 1 2 5 3 4 -> 3 5 1 1 3 4 1 2 2 2 1 5 1 2 2 1 5 3 5 , 3 5 2 4 0 2 1 0 0 5 3 0 4 1 4 2 0 0 3 -> 3 1 0 5 1 4 2 2 3 0 4 0 2 0 4 5 0 0 3 , 0 2 5 1 4 2 5 3 1 4 1 0 3 2 3 4 3 0 1 1 3 -> 0 2 5 1 4 2 5 1 3 4 1 0 3 2 3 4 3 0 1 1 3 , 1 0 5 2 4 3 5 0 0 5 2 5 5 4 5 4 0 0 5 5 4 -> 1 0 5 2 4 3 5 0 0 5 2 5 5 4 4 5 0 0 5 5 4 , 1 2 1 4 2 1 3 4 2 5 1 4 5 1 3 0 4 1 0 4 4 -> 1 2 1 4 2 1 3 2 4 5 1 4 5 1 3 0 4 1 0 4 4 , 3 4 0 0 2 0 4 1 5 5 0 0 4 3 5 2 1 0 2 4 4 -> 3 4 0 0 2 0 4 1 5 0 5 0 4 3 5 2 1 0 2 4 4 , 5 1 4 3 3 3 4 1 1 4 0 0 0 3 2 3 1 3 5 5 1 0 -> 5 1 4 3 3 3 4 1 1 4 0 0 0 3 2 3 3 1 5 5 1 0 , 2 0 3 3 0 5 3 1 4 3 0 1 1 4 0 5 5 3 1 2 1 2 4 2 5 -> 2 0 3 3 0 5 1 3 4 3 0 1 1 4 0 5 5 3 1 2 1 2 4 2 5 , 2 1 1 1 4 4 1 4 4 4 5 3 2 2 1 4 4 4 4 1 2 2 3 1 1 -> 2 1 1 4 1 4 1 4 4 4 5 3 2 2 1 4 4 4 4 1 2 2 3 1 1 , 2 1 2 1 1 4 1 3 2 0 2 2 1 5 3 2 3 5 0 2 0 0 5 0 2 -> 2 1 2 1 1 4 1 3 2 0 2 2 1 5 3 3 2 5 0 2 0 0 5 0 2 , 0 4 0 2 5 4 5 1 3 5 2 0 1 1 0 4 1 3 0 4 2 3 4 5 5 1 4 -> 0 4 0 2 5 4 5 1 3 5 0 2 1 1 0 4 1 3 0 4 2 3 4 5 5 1 4 , 4 5 3 1 0 2 2 2 4 5 3 5 5 5 0 2 1 2 4 0 4 4 1 3 0 0 2 -> 4 5 3 1 0 2 2 2 4 5 3 5 5 5 0 2 1 2 4 4 0 4 1 3 0 0 2 , 5 1 2 3 2 3 4 2 4 2 1 0 4 4 0 3 0 3 2 5 3 1 5 2 3 1 0 -> 5 1 2 3 2 3 4 2 4 2 1 0 4 4 0 3 0 3 2 5 3 1 5 3 2 1 0 , 2 0 4 5 3 3 2 4 3 4 4 4 1 5 1 5 5 0 2 4 4 1 0 5 0 5 3 3 -> 2 0 4 5 3 3 2 4 3 4 4 1 4 5 1 5 5 0 2 4 4 1 0 5 0 5 3 3 , 2 0 0 0 0 0 5 4 5 1 2 3 2 3 4 3 5 5 5 0 1 3 3 1 4 1 4 0 2 -> 2 0 0 0 0 0 5 4 5 1 2 3 2 3 3 4 5 5 5 0 1 3 3 1 4 1 4 0 2 , 2 0 3 0 4 2 1 1 4 5 0 1 2 1 4 3 1 3 0 1 1 0 5 4 4 2 3 3 3 -> 2 0 3 0 4 2 1 1 4 5 0 1 2 1 4 3 1 3 0 1 1 0 4 5 4 2 3 3 3 , 2 2 5 3 2 2 0 4 4 4 4 0 5 0 5 3 4 4 4 0 0 5 0 5 0 2 0 1 3 -> 2 2 5 3 2 2 0 4 4 4 4 0 5 0 5 3 4 4 4 0 5 0 0 5 0 2 0 1 3 , 4 5 5 0 5 5 5 2 1 2 3 0 3 2 1 1 2 1 3 0 1 1 5 1 1 5 0 0 4 4 -> 4 5 5 5 0 5 5 2 1 2 3 0 3 1 1 2 2 1 0 1 3 1 5 1 5 1 0 0 4 4 , 5 5 0 5 0 0 3 4 4 0 0 0 0 4 0 4 5 3 1 1 1 3 1 1 2 1 0 1 2 4 -> 5 5 0 5 0 0 4 3 4 0 0 0 0 4 0 4 5 3 1 1 1 3 1 1 2 1 0 1 2 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 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 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 1 | | 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 1 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 43-rule system { 0 0 1 2 1 0 3 2 -> 0 2 0 1 1 0 3 2 , 4 4 1 3 0 5 5 5 3 -> 4 1 4 3 5 0 5 5 3 , 1 3 0 5 5 1 1 1 2 2 -> 1 3 5 5 1 0 1 1 2 2 , 0 5 2 5 2 5 1 4 4 4 2 -> 2 2 1 5 4 4 4 5 5 0 2 , 2 5 4 0 3 1 4 1 1 1 0 -> 2 5 4 0 1 3 4 1 1 1 0 , 1 0 2 5 2 1 2 0 1 0 2 2 -> 1 0 2 5 1 2 2 0 1 0 2 2 , 5 0 1 2 1 4 4 0 5 0 5 4 -> 5 0 1 2 1 4 0 4 5 0 5 4 , 2 5 0 5 4 4 5 5 1 3 1 0 1 -> 2 5 0 4 5 5 4 5 1 3 1 0 1 , 2 5 1 0 5 3 3 5 2 2 1 2 3 -> 2 5 1 0 5 3 5 3 2 2 1 2 3 , 4 0 1 4 1 4 4 3 1 3 1 4 4 -> 4 0 1 4 1 4 3 4 1 3 1 4 4 , 4 2 2 2 2 2 3 2 5 3 1 2 4 -> 4 2 3 2 2 2 2 3 2 5 1 2 4 , 5 2 3 5 2 4 2 1 0 4 2 0 5 -> 5 2 2 3 2 1 0 5 4 4 2 0 5 , 1 5 0 2 1 0 3 5 5 2 0 3 0 5 -> 1 5 0 2 1 0 5 3 5 2 0 3 0 5 , 3 5 3 4 2 2 2 5 4 4 3 4 0 4 -> 3 5 3 4 2 2 2 4 5 4 3 4 0 4 , 4 0 2 4 1 4 4 5 1 0 0 4 0 5 -> 4 0 2 4 1 4 5 4 1 0 0 4 0 5 , 1 1 0 3 0 3 4 4 4 4 4 0 0 1 1 -> 1 1 0 3 0 4 3 4 4 4 4 0 0 1 1 , 1 2 4 4 2 3 0 0 4 3 3 0 5 5 3 -> 1 2 4 4 3 2 0 3 5 0 0 5 3 4 3 , 1 3 2 5 3 1 5 3 3 5 3 2 0 4 4 -> 1 3 2 5 3 5 1 3 3 5 3 2 0 4 4 , 5 5 3 3 0 3 4 2 1 2 3 1 1 4 1 -> 5 5 0 3 3 3 4 2 2 1 3 1 1 4 1 , 0 5 3 4 3 5 2 2 2 0 2 1 0 1 4 2 -> 0 5 3 4 3 5 2 2 2 0 1 2 0 1 4 2 , 0 0 0 3 5 0 0 5 4 3 5 4 5 4 3 2 4 -> 0 0 0 3 5 0 5 0 4 3 5 4 5 4 3 2 4 , 5 4 0 2 4 4 5 2 1 3 3 0 4 1 2 1 0 -> 5 4 0 2 4 4 5 2 1 3 3 0 1 4 2 1 0 , 3 1 4 4 3 3 1 3 0 2 0 2 5 3 5 0 3 1 -> 3 1 4 4 3 1 3 3 0 2 2 0 5 3 5 3 0 1 , 5 5 5 0 2 1 1 5 4 4 0 4 4 3 1 4 4 3 -> 5 5 5 0 2 1 1 5 4 4 0 4 4 3 4 1 4 3 , 3 1 2 2 1 5 2 1 2 5 3 1 1 5 1 2 5 3 4 -> 3 5 1 1 3 4 1 2 2 2 1 5 1 2 2 1 5 3 5 , 3 5 2 4 0 2 1 0 0 5 3 0 4 1 4 2 0 0 3 -> 3 1 0 5 1 4 2 2 3 0 4 0 2 0 4 5 0 0 3 , 0 2 5 1 4 2 5 3 1 4 1 0 3 2 3 4 3 0 1 1 3 -> 0 2 5 1 4 2 5 1 3 4 1 0 3 2 3 4 3 0 1 1 3 , 1 0 5 2 4 3 5 0 0 5 2 5 5 4 5 4 0 0 5 5 4 -> 1 0 5 2 4 3 5 0 0 5 2 5 5 4 4 5 0 0 5 5 4 , 1 2 1 4 2 1 3 4 2 5 1 4 5 1 3 0 4 1 0 4 4 -> 1 2 1 4 2 1 3 2 4 5 1 4 5 1 3 0 4 1 0 4 4 , 3 4 0 0 2 0 4 1 5 5 0 0 4 3 5 2 1 0 2 4 4 -> 3 4 0 0 2 0 4 1 5 0 5 0 4 3 5 2 1 0 2 4 4 , 5 1 4 3 3 3 4 1 1 4 0 0 0 3 2 3 1 3 5 5 1 0 -> 5 1 4 3 3 3 4 1 1 4 0 0 0 3 2 3 3 1 5 5 1 0 , 2 0 3 3 0 5 3 1 4 3 0 1 1 4 0 5 5 3 1 2 1 2 4 2 5 -> 2 0 3 3 0 5 1 3 4 3 0 1 1 4 0 5 5 3 1 2 1 2 4 2 5 , 2 1 1 1 4 4 1 4 4 4 5 3 2 2 1 4 4 4 4 1 2 2 3 1 1 -> 2 1 1 4 1 4 1 4 4 4 5 3 2 2 1 4 4 4 4 1 2 2 3 1 1 , 2 1 2 1 1 4 1 3 2 0 2 2 1 5 3 2 3 5 0 2 0 0 5 0 2 -> 2 1 2 1 1 4 1 3 2 0 2 2 1 5 3 3 2 5 0 2 0 0 5 0 2 , 0 4 0 2 5 4 5 1 3 5 2 0 1 1 0 4 1 3 0 4 2 3 4 5 5 1 4 -> 0 4 0 2 5 4 5 1 3 5 0 2 1 1 0 4 1 3 0 4 2 3 4 5 5 1 4 , 4 5 3 1 0 2 2 2 4 5 3 5 5 5 0 2 1 2 4 0 4 4 1 3 0 0 2 -> 4 5 3 1 0 2 2 2 4 5 3 5 5 5 0 2 1 2 4 4 0 4 1 3 0 0 2 , 5 1 2 3 2 3 4 2 4 2 1 0 4 4 0 3 0 3 2 5 3 1 5 2 3 1 0 -> 5 1 2 3 2 3 4 2 4 2 1 0 4 4 0 3 0 3 2 5 3 1 5 3 2 1 0 , 2 0 4 5 3 3 2 4 3 4 4 4 1 5 1 5 5 0 2 4 4 1 0 5 0 5 3 3 -> 2 0 4 5 3 3 2 4 3 4 4 1 4 5 1 5 5 0 2 4 4 1 0 5 0 5 3 3 , 2 0 0 0 0 0 5 4 5 1 2 3 2 3 4 3 5 5 5 0 1 3 3 1 4 1 4 0 2 -> 2 0 0 0 0 0 5 4 5 1 2 3 2 3 3 4 5 5 5 0 1 3 3 1 4 1 4 0 2 , 2 0 3 0 4 2 1 1 4 5 0 1 2 1 4 3 1 3 0 1 1 0 5 4 4 2 3 3 3 -> 2 0 3 0 4 2 1 1 4 5 0 1 2 1 4 3 1 3 0 1 1 0 4 5 4 2 3 3 3 , 2 2 5 3 2 2 0 4 4 4 4 0 5 0 5 3 4 4 4 0 0 5 0 5 0 2 0 1 3 -> 2 2 5 3 2 2 0 4 4 4 4 0 5 0 5 3 4 4 4 0 5 0 0 5 0 2 0 1 3 , 4 5 5 0 5 5 5 2 1 2 3 0 3 2 1 1 2 1 3 0 1 1 5 1 1 5 0 0 4 4 -> 4 5 5 5 0 5 5 2 1 2 3 0 3 1 1 2 2 1 0 1 3 1 5 1 5 1 0 0 4 4 , 5 5 0 5 0 0 3 4 4 0 0 0 0 4 0 4 5 3 1 1 1 3 1 1 2 1 0 1 2 4 -> 5 5 0 5 0 0 4 3 4 0 0 0 0 4 0 4 5 3 1 1 1 3 1 1 2 1 0 1 2 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | \ / 4 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 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 5->4, 4->5 }, it remains to prove termination of the 42-rule system { 0 0 1 2 1 0 3 2 -> 0 2 0 1 1 0 3 2 , 1 3 0 4 4 1 1 1 2 2 -> 1 3 4 4 1 0 1 1 2 2 , 0 4 2 4 2 4 1 5 5 5 2 -> 2 2 1 4 5 5 5 4 4 0 2 , 2 4 5 0 3 1 5 1 1 1 0 -> 2 4 5 0 1 3 5 1 1 1 0 , 1 0 2 4 2 1 2 0 1 0 2 2 -> 1 0 2 4 1 2 2 0 1 0 2 2 , 4 0 1 2 1 5 5 0 4 0 4 5 -> 4 0 1 2 1 5 0 5 4 0 4 5 , 2 4 0 4 5 5 4 4 1 3 1 0 1 -> 2 4 0 5 4 4 5 4 1 3 1 0 1 , 2 4 1 0 4 3 3 4 2 2 1 2 3 -> 2 4 1 0 4 3 4 3 2 2 1 2 3 , 5 0 1 5 1 5 5 3 1 3 1 5 5 -> 5 0 1 5 1 5 3 5 1 3 1 5 5 , 5 2 2 2 2 2 3 2 4 3 1 2 5 -> 5 2 3 2 2 2 2 3 2 4 1 2 5 , 4 2 3 4 2 5 2 1 0 5 2 0 4 -> 4 2 2 3 2 1 0 4 5 5 2 0 4 , 1 4 0 2 1 0 3 4 4 2 0 3 0 4 -> 1 4 0 2 1 0 4 3 4 2 0 3 0 4 , 3 4 3 5 2 2 2 4 5 5 3 5 0 5 -> 3 4 3 5 2 2 2 5 4 5 3 5 0 5 , 5 0 2 5 1 5 5 4 1 0 0 5 0 4 -> 5 0 2 5 1 5 4 5 1 0 0 5 0 4 , 1 1 0 3 0 3 5 5 5 5 5 0 0 1 1 -> 1 1 0 3 0 5 3 5 5 5 5 0 0 1 1 , 1 2 5 5 2 3 0 0 5 3 3 0 4 4 3 -> 1 2 5 5 3 2 0 3 4 0 0 4 3 5 3 , 1 3 2 4 3 1 4 3 3 4 3 2 0 5 5 -> 1 3 2 4 3 4 1 3 3 4 3 2 0 5 5 , 4 4 3 3 0 3 5 2 1 2 3 1 1 5 1 -> 4 4 0 3 3 3 5 2 2 1 3 1 1 5 1 , 0 4 3 5 3 4 2 2 2 0 2 1 0 1 5 2 -> 0 4 3 5 3 4 2 2 2 0 1 2 0 1 5 2 , 0 0 0 3 4 0 0 4 5 3 4 5 4 5 3 2 5 -> 0 0 0 3 4 0 4 0 5 3 4 5 4 5 3 2 5 , 4 5 0 2 5 5 4 2 1 3 3 0 5 1 2 1 0 -> 4 5 0 2 5 5 4 2 1 3 3 0 1 5 2 1 0 , 3 1 5 5 3 3 1 3 0 2 0 2 4 3 4 0 3 1 -> 3 1 5 5 3 1 3 3 0 2 2 0 4 3 4 3 0 1 , 4 4 4 0 2 1 1 4 5 5 0 5 5 3 1 5 5 3 -> 4 4 4 0 2 1 1 4 5 5 0 5 5 3 5 1 5 3 , 3 1 2 2 1 4 2 1 2 4 3 1 1 4 1 2 4 3 5 -> 3 4 1 1 3 5 1 2 2 2 1 4 1 2 2 1 4 3 4 , 3 4 2 5 0 2 1 0 0 4 3 0 5 1 5 2 0 0 3 -> 3 1 0 4 1 5 2 2 3 0 5 0 2 0 5 4 0 0 3 , 0 2 4 1 5 2 4 3 1 5 1 0 3 2 3 5 3 0 1 1 3 -> 0 2 4 1 5 2 4 1 3 5 1 0 3 2 3 5 3 0 1 1 3 , 1 0 4 2 5 3 4 0 0 4 2 4 4 5 4 5 0 0 4 4 5 -> 1 0 4 2 5 3 4 0 0 4 2 4 4 5 5 4 0 0 4 4 5 , 1 2 1 5 2 1 3 5 2 4 1 5 4 1 3 0 5 1 0 5 5 -> 1 2 1 5 2 1 3 2 5 4 1 5 4 1 3 0 5 1 0 5 5 , 3 5 0 0 2 0 5 1 4 4 0 0 5 3 4 2 1 0 2 5 5 -> 3 5 0 0 2 0 5 1 4 0 4 0 5 3 4 2 1 0 2 5 5 , 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 1 3 4 4 1 0 -> 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 3 1 4 4 1 0 , 2 0 3 3 0 4 3 1 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 -> 2 0 3 3 0 4 1 3 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 , 2 1 1 1 5 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 -> 2 1 1 5 1 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 , 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 2 3 4 0 2 0 0 4 0 2 -> 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 3 2 4 0 2 0 0 4 0 2 , 0 5 0 2 4 5 4 1 3 4 2 0 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 -> 0 5 0 2 4 5 4 1 3 4 0 2 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 , 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 0 5 5 1 3 0 0 2 -> 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 5 0 5 1 3 0 0 2 , 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 2 3 1 0 -> 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 3 2 1 0 , 2 0 5 4 3 3 2 5 3 5 5 5 1 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 -> 2 0 5 4 3 3 2 5 3 5 5 1 5 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 , 2 0 0 0 0 0 4 5 4 1 2 3 2 3 5 3 4 4 4 0 1 3 3 1 5 1 5 0 2 -> 2 0 0 0 0 0 4 5 4 1 2 3 2 3 3 5 4 4 4 0 1 3 3 1 5 1 5 0 2 , 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 4 5 5 2 3 3 3 -> 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 5 4 5 2 3 3 3 , 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 0 4 0 4 0 2 0 1 3 -> 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 4 0 0 4 0 2 0 1 3 , 5 4 4 0 4 4 4 2 1 2 3 0 3 2 1 1 2 1 3 0 1 1 4 1 1 4 0 0 5 5 -> 5 4 4 4 0 4 4 2 1 2 3 0 3 1 1 2 2 1 0 1 3 1 4 1 4 1 0 0 5 5 , 4 4 0 4 0 0 3 5 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 -> 4 4 0 4 0 0 5 3 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 12: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 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 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 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 | \ / 2 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 | \ / 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 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 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 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 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 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 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 0 1 2 1 0 3 2 -> 0 2 0 1 1 0 3 2 , 1 3 0 4 4 1 1 1 2 2 -> 1 3 4 4 1 0 1 1 2 2 , 0 4 2 4 2 4 1 5 5 5 2 -> 2 2 1 4 5 5 5 4 4 0 2 , 1 0 2 4 2 1 2 0 1 0 2 2 -> 1 0 2 4 1 2 2 0 1 0 2 2 , 4 0 1 2 1 5 5 0 4 0 4 5 -> 4 0 1 2 1 5 0 5 4 0 4 5 , 2 4 0 4 5 5 4 4 1 3 1 0 1 -> 2 4 0 5 4 4 5 4 1 3 1 0 1 , 2 4 1 0 4 3 3 4 2 2 1 2 3 -> 2 4 1 0 4 3 4 3 2 2 1 2 3 , 5 0 1 5 1 5 5 3 1 3 1 5 5 -> 5 0 1 5 1 5 3 5 1 3 1 5 5 , 5 2 2 2 2 2 3 2 4 3 1 2 5 -> 5 2 3 2 2 2 2 3 2 4 1 2 5 , 4 2 3 4 2 5 2 1 0 5 2 0 4 -> 4 2 2 3 2 1 0 4 5 5 2 0 4 , 1 4 0 2 1 0 3 4 4 2 0 3 0 4 -> 1 4 0 2 1 0 4 3 4 2 0 3 0 4 , 3 4 3 5 2 2 2 4 5 5 3 5 0 5 -> 3 4 3 5 2 2 2 5 4 5 3 5 0 5 , 5 0 2 5 1 5 5 4 1 0 0 5 0 4 -> 5 0 2 5 1 5 4 5 1 0 0 5 0 4 , 1 1 0 3 0 3 5 5 5 5 5 0 0 1 1 -> 1 1 0 3 0 5 3 5 5 5 5 0 0 1 1 , 1 2 5 5 2 3 0 0 5 3 3 0 4 4 3 -> 1 2 5 5 3 2 0 3 4 0 0 4 3 5 3 , 1 3 2 4 3 1 4 3 3 4 3 2 0 5 5 -> 1 3 2 4 3 4 1 3 3 4 3 2 0 5 5 , 4 4 3 3 0 3 5 2 1 2 3 1 1 5 1 -> 4 4 0 3 3 3 5 2 2 1 3 1 1 5 1 , 0 4 3 5 3 4 2 2 2 0 2 1 0 1 5 2 -> 0 4 3 5 3 4 2 2 2 0 1 2 0 1 5 2 , 0 0 0 3 4 0 0 4 5 3 4 5 4 5 3 2 5 -> 0 0 0 3 4 0 4 0 5 3 4 5 4 5 3 2 5 , 4 5 0 2 5 5 4 2 1 3 3 0 5 1 2 1 0 -> 4 5 0 2 5 5 4 2 1 3 3 0 1 5 2 1 0 , 3 1 5 5 3 3 1 3 0 2 0 2 4 3 4 0 3 1 -> 3 1 5 5 3 1 3 3 0 2 2 0 4 3 4 3 0 1 , 4 4 4 0 2 1 1 4 5 5 0 5 5 3 1 5 5 3 -> 4 4 4 0 2 1 1 4 5 5 0 5 5 3 5 1 5 3 , 3 1 2 2 1 4 2 1 2 4 3 1 1 4 1 2 4 3 5 -> 3 4 1 1 3 5 1 2 2 2 1 4 1 2 2 1 4 3 4 , 3 4 2 5 0 2 1 0 0 4 3 0 5 1 5 2 0 0 3 -> 3 1 0 4 1 5 2 2 3 0 5 0 2 0 5 4 0 0 3 , 0 2 4 1 5 2 4 3 1 5 1 0 3 2 3 5 3 0 1 1 3 -> 0 2 4 1 5 2 4 1 3 5 1 0 3 2 3 5 3 0 1 1 3 , 1 0 4 2 5 3 4 0 0 4 2 4 4 5 4 5 0 0 4 4 5 -> 1 0 4 2 5 3 4 0 0 4 2 4 4 5 5 4 0 0 4 4 5 , 1 2 1 5 2 1 3 5 2 4 1 5 4 1 3 0 5 1 0 5 5 -> 1 2 1 5 2 1 3 2 5 4 1 5 4 1 3 0 5 1 0 5 5 , 3 5 0 0 2 0 5 1 4 4 0 0 5 3 4 2 1 0 2 5 5 -> 3 5 0 0 2 0 5 1 4 0 4 0 5 3 4 2 1 0 2 5 5 , 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 1 3 4 4 1 0 -> 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 3 1 4 4 1 0 , 2 0 3 3 0 4 3 1 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 -> 2 0 3 3 0 4 1 3 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 , 2 1 1 1 5 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 -> 2 1 1 5 1 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 , 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 2 3 4 0 2 0 0 4 0 2 -> 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 3 2 4 0 2 0 0 4 0 2 , 0 5 0 2 4 5 4 1 3 4 2 0 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 -> 0 5 0 2 4 5 4 1 3 4 0 2 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 , 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 0 5 5 1 3 0 0 2 -> 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 5 0 5 1 3 0 0 2 , 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 2 3 1 0 -> 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 3 2 1 0 , 2 0 5 4 3 3 2 5 3 5 5 5 1 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 -> 2 0 5 4 3 3 2 5 3 5 5 1 5 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 , 2 0 0 0 0 0 4 5 4 1 2 3 2 3 5 3 4 4 4 0 1 3 3 1 5 1 5 0 2 -> 2 0 0 0 0 0 4 5 4 1 2 3 2 3 3 5 4 4 4 0 1 3 3 1 5 1 5 0 2 , 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 4 5 5 2 3 3 3 -> 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 5 4 5 2 3 3 3 , 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 0 4 0 4 0 2 0 1 3 -> 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 4 0 0 4 0 2 0 1 3 , 5 4 4 0 4 4 4 2 1 2 3 0 3 2 1 1 2 1 3 0 1 1 4 1 1 4 0 0 5 5 -> 5 4 4 4 0 4 4 2 1 2 3 0 3 1 1 2 2 1 0 1 3 1 4 1 4 1 0 0 5 5 , 4 4 0 4 0 0 3 5 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 -> 4 4 0 4 0 0 5 3 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 14: 0 is interpreted by / \ | 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 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 is interpreted by / \ | 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 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 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 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 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 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 40-rule system { 0 0 1 2 1 0 3 2 -> 0 2 0 1 1 0 3 2 , 1 3 0 4 4 1 1 1 2 2 -> 1 3 4 4 1 0 1 1 2 2 , 0 4 2 4 2 4 1 5 5 5 2 -> 2 2 1 4 5 5 5 4 4 0 2 , 1 0 2 4 2 1 2 0 1 0 2 2 -> 1 0 2 4 1 2 2 0 1 0 2 2 , 4 0 1 2 1 5 5 0 4 0 4 5 -> 4 0 1 2 1 5 0 5 4 0 4 5 , 2 4 1 0 4 3 3 4 2 2 1 2 3 -> 2 4 1 0 4 3 4 3 2 2 1 2 3 , 5 0 1 5 1 5 5 3 1 3 1 5 5 -> 5 0 1 5 1 5 3 5 1 3 1 5 5 , 5 2 2 2 2 2 3 2 4 3 1 2 5 -> 5 2 3 2 2 2 2 3 2 4 1 2 5 , 4 2 3 4 2 5 2 1 0 5 2 0 4 -> 4 2 2 3 2 1 0 4 5 5 2 0 4 , 1 4 0 2 1 0 3 4 4 2 0 3 0 4 -> 1 4 0 2 1 0 4 3 4 2 0 3 0 4 , 3 4 3 5 2 2 2 4 5 5 3 5 0 5 -> 3 4 3 5 2 2 2 5 4 5 3 5 0 5 , 5 0 2 5 1 5 5 4 1 0 0 5 0 4 -> 5 0 2 5 1 5 4 5 1 0 0 5 0 4 , 1 1 0 3 0 3 5 5 5 5 5 0 0 1 1 -> 1 1 0 3 0 5 3 5 5 5 5 0 0 1 1 , 1 2 5 5 2 3 0 0 5 3 3 0 4 4 3 -> 1 2 5 5 3 2 0 3 4 0 0 4 3 5 3 , 1 3 2 4 3 1 4 3 3 4 3 2 0 5 5 -> 1 3 2 4 3 4 1 3 3 4 3 2 0 5 5 , 4 4 3 3 0 3 5 2 1 2 3 1 1 5 1 -> 4 4 0 3 3 3 5 2 2 1 3 1 1 5 1 , 0 4 3 5 3 4 2 2 2 0 2 1 0 1 5 2 -> 0 4 3 5 3 4 2 2 2 0 1 2 0 1 5 2 , 0 0 0 3 4 0 0 4 5 3 4 5 4 5 3 2 5 -> 0 0 0 3 4 0 4 0 5 3 4 5 4 5 3 2 5 , 4 5 0 2 5 5 4 2 1 3 3 0 5 1 2 1 0 -> 4 5 0 2 5 5 4 2 1 3 3 0 1 5 2 1 0 , 3 1 5 5 3 3 1 3 0 2 0 2 4 3 4 0 3 1 -> 3 1 5 5 3 1 3 3 0 2 2 0 4 3 4 3 0 1 , 4 4 4 0 2 1 1 4 5 5 0 5 5 3 1 5 5 3 -> 4 4 4 0 2 1 1 4 5 5 0 5 5 3 5 1 5 3 , 3 1 2 2 1 4 2 1 2 4 3 1 1 4 1 2 4 3 5 -> 3 4 1 1 3 5 1 2 2 2 1 4 1 2 2 1 4 3 4 , 3 4 2 5 0 2 1 0 0 4 3 0 5 1 5 2 0 0 3 -> 3 1 0 4 1 5 2 2 3 0 5 0 2 0 5 4 0 0 3 , 0 2 4 1 5 2 4 3 1 5 1 0 3 2 3 5 3 0 1 1 3 -> 0 2 4 1 5 2 4 1 3 5 1 0 3 2 3 5 3 0 1 1 3 , 1 0 4 2 5 3 4 0 0 4 2 4 4 5 4 5 0 0 4 4 5 -> 1 0 4 2 5 3 4 0 0 4 2 4 4 5 5 4 0 0 4 4 5 , 1 2 1 5 2 1 3 5 2 4 1 5 4 1 3 0 5 1 0 5 5 -> 1 2 1 5 2 1 3 2 5 4 1 5 4 1 3 0 5 1 0 5 5 , 3 5 0 0 2 0 5 1 4 4 0 0 5 3 4 2 1 0 2 5 5 -> 3 5 0 0 2 0 5 1 4 0 4 0 5 3 4 2 1 0 2 5 5 , 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 1 3 4 4 1 0 -> 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 3 1 4 4 1 0 , 2 0 3 3 0 4 3 1 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 -> 2 0 3 3 0 4 1 3 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 , 2 1 1 1 5 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 -> 2 1 1 5 1 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 , 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 2 3 4 0 2 0 0 4 0 2 -> 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 3 2 4 0 2 0 0 4 0 2 , 0 5 0 2 4 5 4 1 3 4 2 0 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 -> 0 5 0 2 4 5 4 1 3 4 0 2 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 , 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 0 5 5 1 3 0 0 2 -> 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 5 0 5 1 3 0 0 2 , 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 2 3 1 0 -> 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 3 2 1 0 , 2 0 5 4 3 3 2 5 3 5 5 5 1 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 -> 2 0 5 4 3 3 2 5 3 5 5 1 5 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 , 2 0 0 0 0 0 4 5 4 1 2 3 2 3 5 3 4 4 4 0 1 3 3 1 5 1 5 0 2 -> 2 0 0 0 0 0 4 5 4 1 2 3 2 3 3 5 4 4 4 0 1 3 3 1 5 1 5 0 2 , 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 4 5 5 2 3 3 3 -> 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 5 4 5 2 3 3 3 , 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 0 4 0 4 0 2 0 1 3 -> 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 4 0 0 4 0 2 0 1 3 , 5 4 4 0 4 4 4 2 1 2 3 0 3 2 1 1 2 1 3 0 1 1 4 1 1 4 0 0 5 5 -> 5 4 4 4 0 4 4 2 1 2 3 0 3 1 1 2 2 1 0 1 3 1 4 1 4 1 0 0 5 5 , 4 4 0 4 0 0 3 5 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 -> 4 4 0 4 0 0 5 3 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 14: 0 is interpreted by / \ | 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 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 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 1 | | 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 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 | | 0 0 0 0 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 0 | | 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 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 0 1 2 1 0 3 2 -> 0 2 0 1 1 0 3 2 , 1 3 0 4 4 1 1 1 2 2 -> 1 3 4 4 1 0 1 1 2 2 , 0 4 2 4 2 4 1 5 5 5 2 -> 2 2 1 4 5 5 5 4 4 0 2 , 1 0 2 4 2 1 2 0 1 0 2 2 -> 1 0 2 4 1 2 2 0 1 0 2 2 , 4 0 1 2 1 5 5 0 4 0 4 5 -> 4 0 1 2 1 5 0 5 4 0 4 5 , 5 0 1 5 1 5 5 3 1 3 1 5 5 -> 5 0 1 5 1 5 3 5 1 3 1 5 5 , 5 2 2 2 2 2 3 2 4 3 1 2 5 -> 5 2 3 2 2 2 2 3 2 4 1 2 5 , 4 2 3 4 2 5 2 1 0 5 2 0 4 -> 4 2 2 3 2 1 0 4 5 5 2 0 4 , 1 4 0 2 1 0 3 4 4 2 0 3 0 4 -> 1 4 0 2 1 0 4 3 4 2 0 3 0 4 , 3 4 3 5 2 2 2 4 5 5 3 5 0 5 -> 3 4 3 5 2 2 2 5 4 5 3 5 0 5 , 5 0 2 5 1 5 5 4 1 0 0 5 0 4 -> 5 0 2 5 1 5 4 5 1 0 0 5 0 4 , 1 1 0 3 0 3 5 5 5 5 5 0 0 1 1 -> 1 1 0 3 0 5 3 5 5 5 5 0 0 1 1 , 1 2 5 5 2 3 0 0 5 3 3 0 4 4 3 -> 1 2 5 5 3 2 0 3 4 0 0 4 3 5 3 , 1 3 2 4 3 1 4 3 3 4 3 2 0 5 5 -> 1 3 2 4 3 4 1 3 3 4 3 2 0 5 5 , 4 4 3 3 0 3 5 2 1 2 3 1 1 5 1 -> 4 4 0 3 3 3 5 2 2 1 3 1 1 5 1 , 0 4 3 5 3 4 2 2 2 0 2 1 0 1 5 2 -> 0 4 3 5 3 4 2 2 2 0 1 2 0 1 5 2 , 0 0 0 3 4 0 0 4 5 3 4 5 4 5 3 2 5 -> 0 0 0 3 4 0 4 0 5 3 4 5 4 5 3 2 5 , 4 5 0 2 5 5 4 2 1 3 3 0 5 1 2 1 0 -> 4 5 0 2 5 5 4 2 1 3 3 0 1 5 2 1 0 , 3 1 5 5 3 3 1 3 0 2 0 2 4 3 4 0 3 1 -> 3 1 5 5 3 1 3 3 0 2 2 0 4 3 4 3 0 1 , 4 4 4 0 2 1 1 4 5 5 0 5 5 3 1 5 5 3 -> 4 4 4 0 2 1 1 4 5 5 0 5 5 3 5 1 5 3 , 3 1 2 2 1 4 2 1 2 4 3 1 1 4 1 2 4 3 5 -> 3 4 1 1 3 5 1 2 2 2 1 4 1 2 2 1 4 3 4 , 3 4 2 5 0 2 1 0 0 4 3 0 5 1 5 2 0 0 3 -> 3 1 0 4 1 5 2 2 3 0 5 0 2 0 5 4 0 0 3 , 0 2 4 1 5 2 4 3 1 5 1 0 3 2 3 5 3 0 1 1 3 -> 0 2 4 1 5 2 4 1 3 5 1 0 3 2 3 5 3 0 1 1 3 , 1 0 4 2 5 3 4 0 0 4 2 4 4 5 4 5 0 0 4 4 5 -> 1 0 4 2 5 3 4 0 0 4 2 4 4 5 5 4 0 0 4 4 5 , 1 2 1 5 2 1 3 5 2 4 1 5 4 1 3 0 5 1 0 5 5 -> 1 2 1 5 2 1 3 2 5 4 1 5 4 1 3 0 5 1 0 5 5 , 3 5 0 0 2 0 5 1 4 4 0 0 5 3 4 2 1 0 2 5 5 -> 3 5 0 0 2 0 5 1 4 0 4 0 5 3 4 2 1 0 2 5 5 , 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 1 3 4 4 1 0 -> 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 3 1 4 4 1 0 , 2 0 3 3 0 4 3 1 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 -> 2 0 3 3 0 4 1 3 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 , 2 1 1 1 5 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 -> 2 1 1 5 1 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 , 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 2 3 4 0 2 0 0 4 0 2 -> 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 3 2 4 0 2 0 0 4 0 2 , 0 5 0 2 4 5 4 1 3 4 2 0 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 -> 0 5 0 2 4 5 4 1 3 4 0 2 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 , 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 0 5 5 1 3 0 0 2 -> 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 5 0 5 1 3 0 0 2 , 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 2 3 1 0 -> 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 3 2 1 0 , 2 0 5 4 3 3 2 5 3 5 5 5 1 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 -> 2 0 5 4 3 3 2 5 3 5 5 1 5 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 , 2 0 0 0 0 0 4 5 4 1 2 3 2 3 5 3 4 4 4 0 1 3 3 1 5 1 5 0 2 -> 2 0 0 0 0 0 4 5 4 1 2 3 2 3 3 5 4 4 4 0 1 3 3 1 5 1 5 0 2 , 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 4 5 5 2 3 3 3 -> 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 5 4 5 2 3 3 3 , 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 0 4 0 4 0 2 0 1 3 -> 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 4 0 0 4 0 2 0 1 3 , 5 4 4 0 4 4 4 2 1 2 3 0 3 2 1 1 2 1 3 0 1 1 4 1 1 4 0 0 5 5 -> 5 4 4 4 0 4 4 2 1 2 3 0 3 1 1 2 2 1 0 1 3 1 4 1 4 1 0 0 5 5 , 4 4 0 4 0 0 3 5 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 -> 4 4 0 4 0 0 5 3 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 14: 0 is interpreted by / \ | 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 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 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 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 | \ / 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 0 1 2 1 0 3 2 -> 0 2 0 1 1 0 3 2 , 1 3 0 4 4 1 1 1 2 2 -> 1 3 4 4 1 0 1 1 2 2 , 0 4 2 4 2 4 1 5 5 5 2 -> 2 2 1 4 5 5 5 4 4 0 2 , 1 0 2 4 2 1 2 0 1 0 2 2 -> 1 0 2 4 1 2 2 0 1 0 2 2 , 4 0 1 2 1 5 5 0 4 0 4 5 -> 4 0 1 2 1 5 0 5 4 0 4 5 , 5 2 2 2 2 2 3 2 4 3 1 2 5 -> 5 2 3 2 2 2 2 3 2 4 1 2 5 , 4 2 3 4 2 5 2 1 0 5 2 0 4 -> 4 2 2 3 2 1 0 4 5 5 2 0 4 , 1 4 0 2 1 0 3 4 4 2 0 3 0 4 -> 1 4 0 2 1 0 4 3 4 2 0 3 0 4 , 3 4 3 5 2 2 2 4 5 5 3 5 0 5 -> 3 4 3 5 2 2 2 5 4 5 3 5 0 5 , 5 0 2 5 1 5 5 4 1 0 0 5 0 4 -> 5 0 2 5 1 5 4 5 1 0 0 5 0 4 , 1 1 0 3 0 3 5 5 5 5 5 0 0 1 1 -> 1 1 0 3 0 5 3 5 5 5 5 0 0 1 1 , 1 2 5 5 2 3 0 0 5 3 3 0 4 4 3 -> 1 2 5 5 3 2 0 3 4 0 0 4 3 5 3 , 1 3 2 4 3 1 4 3 3 4 3 2 0 5 5 -> 1 3 2 4 3 4 1 3 3 4 3 2 0 5 5 , 4 4 3 3 0 3 5 2 1 2 3 1 1 5 1 -> 4 4 0 3 3 3 5 2 2 1 3 1 1 5 1 , 0 4 3 5 3 4 2 2 2 0 2 1 0 1 5 2 -> 0 4 3 5 3 4 2 2 2 0 1 2 0 1 5 2 , 0 0 0 3 4 0 0 4 5 3 4 5 4 5 3 2 5 -> 0 0 0 3 4 0 4 0 5 3 4 5 4 5 3 2 5 , 4 5 0 2 5 5 4 2 1 3 3 0 5 1 2 1 0 -> 4 5 0 2 5 5 4 2 1 3 3 0 1 5 2 1 0 , 3 1 5 5 3 3 1 3 0 2 0 2 4 3 4 0 3 1 -> 3 1 5 5 3 1 3 3 0 2 2 0 4 3 4 3 0 1 , 4 4 4 0 2 1 1 4 5 5 0 5 5 3 1 5 5 3 -> 4 4 4 0 2 1 1 4 5 5 0 5 5 3 5 1 5 3 , 3 1 2 2 1 4 2 1 2 4 3 1 1 4 1 2 4 3 5 -> 3 4 1 1 3 5 1 2 2 2 1 4 1 2 2 1 4 3 4 , 3 4 2 5 0 2 1 0 0 4 3 0 5 1 5 2 0 0 3 -> 3 1 0 4 1 5 2 2 3 0 5 0 2 0 5 4 0 0 3 , 0 2 4 1 5 2 4 3 1 5 1 0 3 2 3 5 3 0 1 1 3 -> 0 2 4 1 5 2 4 1 3 5 1 0 3 2 3 5 3 0 1 1 3 , 1 0 4 2 5 3 4 0 0 4 2 4 4 5 4 5 0 0 4 4 5 -> 1 0 4 2 5 3 4 0 0 4 2 4 4 5 5 4 0 0 4 4 5 , 1 2 1 5 2 1 3 5 2 4 1 5 4 1 3 0 5 1 0 5 5 -> 1 2 1 5 2 1 3 2 5 4 1 5 4 1 3 0 5 1 0 5 5 , 3 5 0 0 2 0 5 1 4 4 0 0 5 3 4 2 1 0 2 5 5 -> 3 5 0 0 2 0 5 1 4 0 4 0 5 3 4 2 1 0 2 5 5 , 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 1 3 4 4 1 0 -> 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 3 1 4 4 1 0 , 2 0 3 3 0 4 3 1 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 -> 2 0 3 3 0 4 1 3 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 , 2 1 1 1 5 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 -> 2 1 1 5 1 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 , 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 2 3 4 0 2 0 0 4 0 2 -> 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 3 2 4 0 2 0 0 4 0 2 , 0 5 0 2 4 5 4 1 3 4 2 0 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 -> 0 5 0 2 4 5 4 1 3 4 0 2 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 , 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 0 5 5 1 3 0 0 2 -> 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 5 0 5 1 3 0 0 2 , 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 2 3 1 0 -> 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 3 2 1 0 , 2 0 5 4 3 3 2 5 3 5 5 5 1 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 -> 2 0 5 4 3 3 2 5 3 5 5 1 5 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 , 2 0 0 0 0 0 4 5 4 1 2 3 2 3 5 3 4 4 4 0 1 3 3 1 5 1 5 0 2 -> 2 0 0 0 0 0 4 5 4 1 2 3 2 3 3 5 4 4 4 0 1 3 3 1 5 1 5 0 2 , 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 4 5 5 2 3 3 3 -> 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 5 4 5 2 3 3 3 , 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 0 4 0 4 0 2 0 1 3 -> 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 4 0 0 4 0 2 0 1 3 , 5 4 4 0 4 4 4 2 1 2 3 0 3 2 1 1 2 1 3 0 1 1 4 1 1 4 0 0 5 5 -> 5 4 4 4 0 4 4 2 1 2 3 0 3 1 1 2 2 1 0 1 3 1 4 1 4 1 0 0 5 5 , 4 4 0 4 0 0 3 5 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 -> 4 4 0 4 0 0 5 3 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 14: 0 is interpreted by / \ | 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 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 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 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 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 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 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 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 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 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 0 1 2 1 0 3 2 -> 0 2 0 1 1 0 3 2 , 1 3 0 4 4 1 1 1 2 2 -> 1 3 4 4 1 0 1 1 2 2 , 0 4 2 4 2 4 1 5 5 5 2 -> 2 2 1 4 5 5 5 4 4 0 2 , 1 0 2 4 2 1 2 0 1 0 2 2 -> 1 0 2 4 1 2 2 0 1 0 2 2 , 4 0 1 2 1 5 5 0 4 0 4 5 -> 4 0 1 2 1 5 0 5 4 0 4 5 , 4 2 3 4 2 5 2 1 0 5 2 0 4 -> 4 2 2 3 2 1 0 4 5 5 2 0 4 , 1 4 0 2 1 0 3 4 4 2 0 3 0 4 -> 1 4 0 2 1 0 4 3 4 2 0 3 0 4 , 3 4 3 5 2 2 2 4 5 5 3 5 0 5 -> 3 4 3 5 2 2 2 5 4 5 3 5 0 5 , 5 0 2 5 1 5 5 4 1 0 0 5 0 4 -> 5 0 2 5 1 5 4 5 1 0 0 5 0 4 , 1 1 0 3 0 3 5 5 5 5 5 0 0 1 1 -> 1 1 0 3 0 5 3 5 5 5 5 0 0 1 1 , 1 2 5 5 2 3 0 0 5 3 3 0 4 4 3 -> 1 2 5 5 3 2 0 3 4 0 0 4 3 5 3 , 1 3 2 4 3 1 4 3 3 4 3 2 0 5 5 -> 1 3 2 4 3 4 1 3 3 4 3 2 0 5 5 , 4 4 3 3 0 3 5 2 1 2 3 1 1 5 1 -> 4 4 0 3 3 3 5 2 2 1 3 1 1 5 1 , 0 4 3 5 3 4 2 2 2 0 2 1 0 1 5 2 -> 0 4 3 5 3 4 2 2 2 0 1 2 0 1 5 2 , 0 0 0 3 4 0 0 4 5 3 4 5 4 5 3 2 5 -> 0 0 0 3 4 0 4 0 5 3 4 5 4 5 3 2 5 , 4 5 0 2 5 5 4 2 1 3 3 0 5 1 2 1 0 -> 4 5 0 2 5 5 4 2 1 3 3 0 1 5 2 1 0 , 3 1 5 5 3 3 1 3 0 2 0 2 4 3 4 0 3 1 -> 3 1 5 5 3 1 3 3 0 2 2 0 4 3 4 3 0 1 , 4 4 4 0 2 1 1 4 5 5 0 5 5 3 1 5 5 3 -> 4 4 4 0 2 1 1 4 5 5 0 5 5 3 5 1 5 3 , 3 1 2 2 1 4 2 1 2 4 3 1 1 4 1 2 4 3 5 -> 3 4 1 1 3 5 1 2 2 2 1 4 1 2 2 1 4 3 4 , 3 4 2 5 0 2 1 0 0 4 3 0 5 1 5 2 0 0 3 -> 3 1 0 4 1 5 2 2 3 0 5 0 2 0 5 4 0 0 3 , 0 2 4 1 5 2 4 3 1 5 1 0 3 2 3 5 3 0 1 1 3 -> 0 2 4 1 5 2 4 1 3 5 1 0 3 2 3 5 3 0 1 1 3 , 1 0 4 2 5 3 4 0 0 4 2 4 4 5 4 5 0 0 4 4 5 -> 1 0 4 2 5 3 4 0 0 4 2 4 4 5 5 4 0 0 4 4 5 , 1 2 1 5 2 1 3 5 2 4 1 5 4 1 3 0 5 1 0 5 5 -> 1 2 1 5 2 1 3 2 5 4 1 5 4 1 3 0 5 1 0 5 5 , 3 5 0 0 2 0 5 1 4 4 0 0 5 3 4 2 1 0 2 5 5 -> 3 5 0 0 2 0 5 1 4 0 4 0 5 3 4 2 1 0 2 5 5 , 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 1 3 4 4 1 0 -> 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 3 1 4 4 1 0 , 2 0 3 3 0 4 3 1 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 -> 2 0 3 3 0 4 1 3 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 , 2 1 1 1 5 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 -> 2 1 1 5 1 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 , 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 2 3 4 0 2 0 0 4 0 2 -> 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 3 2 4 0 2 0 0 4 0 2 , 0 5 0 2 4 5 4 1 3 4 2 0 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 -> 0 5 0 2 4 5 4 1 3 4 0 2 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 , 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 0 5 5 1 3 0 0 2 -> 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 5 0 5 1 3 0 0 2 , 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 2 3 1 0 -> 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 3 2 1 0 , 2 0 5 4 3 3 2 5 3 5 5 5 1 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 -> 2 0 5 4 3 3 2 5 3 5 5 1 5 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 , 2 0 0 0 0 0 4 5 4 1 2 3 2 3 5 3 4 4 4 0 1 3 3 1 5 1 5 0 2 -> 2 0 0 0 0 0 4 5 4 1 2 3 2 3 3 5 4 4 4 0 1 3 3 1 5 1 5 0 2 , 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 4 5 5 2 3 3 3 -> 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 5 4 5 2 3 3 3 , 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 0 4 0 4 0 2 0 1 3 -> 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 4 0 0 4 0 2 0 1 3 , 5 4 4 0 4 4 4 2 1 2 3 0 3 2 1 1 2 1 3 0 1 1 4 1 1 4 0 0 5 5 -> 5 4 4 4 0 4 4 2 1 2 3 0 3 1 1 2 2 1 0 1 3 1 4 1 4 1 0 0 5 5 , 4 4 0 4 0 0 3 5 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 -> 4 4 0 4 0 0 5 3 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 15: 0 is interpreted by / \ | 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 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 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 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 1 2 1 0 3 2 -> 0 2 0 1 1 0 3 2 , 1 3 0 4 4 1 1 1 2 2 -> 1 3 4 4 1 0 1 1 2 2 , 0 4 2 4 2 4 1 5 5 5 2 -> 2 2 1 4 5 5 5 4 4 0 2 , 1 0 2 4 2 1 2 0 1 0 2 2 -> 1 0 2 4 1 2 2 0 1 0 2 2 , 4 0 1 2 1 5 5 0 4 0 4 5 -> 4 0 1 2 1 5 0 5 4 0 4 5 , 4 2 3 4 2 5 2 1 0 5 2 0 4 -> 4 2 2 3 2 1 0 4 5 5 2 0 4 , 3 4 3 5 2 2 2 4 5 5 3 5 0 5 -> 3 4 3 5 2 2 2 5 4 5 3 5 0 5 , 5 0 2 5 1 5 5 4 1 0 0 5 0 4 -> 5 0 2 5 1 5 4 5 1 0 0 5 0 4 , 1 1 0 3 0 3 5 5 5 5 5 0 0 1 1 -> 1 1 0 3 0 5 3 5 5 5 5 0 0 1 1 , 1 2 5 5 2 3 0 0 5 3 3 0 4 4 3 -> 1 2 5 5 3 2 0 3 4 0 0 4 3 5 3 , 1 3 2 4 3 1 4 3 3 4 3 2 0 5 5 -> 1 3 2 4 3 4 1 3 3 4 3 2 0 5 5 , 4 4 3 3 0 3 5 2 1 2 3 1 1 5 1 -> 4 4 0 3 3 3 5 2 2 1 3 1 1 5 1 , 0 4 3 5 3 4 2 2 2 0 2 1 0 1 5 2 -> 0 4 3 5 3 4 2 2 2 0 1 2 0 1 5 2 , 0 0 0 3 4 0 0 4 5 3 4 5 4 5 3 2 5 -> 0 0 0 3 4 0 4 0 5 3 4 5 4 5 3 2 5 , 4 5 0 2 5 5 4 2 1 3 3 0 5 1 2 1 0 -> 4 5 0 2 5 5 4 2 1 3 3 0 1 5 2 1 0 , 3 1 5 5 3 3 1 3 0 2 0 2 4 3 4 0 3 1 -> 3 1 5 5 3 1 3 3 0 2 2 0 4 3 4 3 0 1 , 4 4 4 0 2 1 1 4 5 5 0 5 5 3 1 5 5 3 -> 4 4 4 0 2 1 1 4 5 5 0 5 5 3 5 1 5 3 , 3 1 2 2 1 4 2 1 2 4 3 1 1 4 1 2 4 3 5 -> 3 4 1 1 3 5 1 2 2 2 1 4 1 2 2 1 4 3 4 , 3 4 2 5 0 2 1 0 0 4 3 0 5 1 5 2 0 0 3 -> 3 1 0 4 1 5 2 2 3 0 5 0 2 0 5 4 0 0 3 , 0 2 4 1 5 2 4 3 1 5 1 0 3 2 3 5 3 0 1 1 3 -> 0 2 4 1 5 2 4 1 3 5 1 0 3 2 3 5 3 0 1 1 3 , 1 0 4 2 5 3 4 0 0 4 2 4 4 5 4 5 0 0 4 4 5 -> 1 0 4 2 5 3 4 0 0 4 2 4 4 5 5 4 0 0 4 4 5 , 1 2 1 5 2 1 3 5 2 4 1 5 4 1 3 0 5 1 0 5 5 -> 1 2 1 5 2 1 3 2 5 4 1 5 4 1 3 0 5 1 0 5 5 , 3 5 0 0 2 0 5 1 4 4 0 0 5 3 4 2 1 0 2 5 5 -> 3 5 0 0 2 0 5 1 4 0 4 0 5 3 4 2 1 0 2 5 5 , 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 1 3 4 4 1 0 -> 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 3 1 4 4 1 0 , 2 0 3 3 0 4 3 1 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 -> 2 0 3 3 0 4 1 3 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 , 2 1 1 1 5 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 -> 2 1 1 5 1 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 , 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 2 3 4 0 2 0 0 4 0 2 -> 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 3 2 4 0 2 0 0 4 0 2 , 0 5 0 2 4 5 4 1 3 4 2 0 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 -> 0 5 0 2 4 5 4 1 3 4 0 2 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 , 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 0 5 5 1 3 0 0 2 -> 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 5 0 5 1 3 0 0 2 , 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 2 3 1 0 -> 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 3 2 1 0 , 2 0 5 4 3 3 2 5 3 5 5 5 1 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 -> 2 0 5 4 3 3 2 5 3 5 5 1 5 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 , 2 0 0 0 0 0 4 5 4 1 2 3 2 3 5 3 4 4 4 0 1 3 3 1 5 1 5 0 2 -> 2 0 0 0 0 0 4 5 4 1 2 3 2 3 3 5 4 4 4 0 1 3 3 1 5 1 5 0 2 , 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 4 5 5 2 3 3 3 -> 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 5 4 5 2 3 3 3 , 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 0 4 0 4 0 2 0 1 3 -> 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 4 0 0 4 0 2 0 1 3 , 5 4 4 0 4 4 4 2 1 2 3 0 3 2 1 1 2 1 3 0 1 1 4 1 1 4 0 0 5 5 -> 5 4 4 4 0 4 4 2 1 2 3 0 3 1 1 2 2 1 0 1 3 1 4 1 4 1 0 0 5 5 , 4 4 0 4 0 0 3 5 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 -> 4 4 0 4 0 0 5 3 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 15: 0 is interpreted by / \ | 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 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 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 1 | | 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 | | 0 0 0 0 0 0 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 0 1 2 1 0 3 2 -> 0 2 0 1 1 0 3 2 , 1 3 0 4 4 1 1 1 2 2 -> 1 3 4 4 1 0 1 1 2 2 , 0 4 2 4 2 4 1 5 5 5 2 -> 2 2 1 4 5 5 5 4 4 0 2 , 1 0 2 4 2 1 2 0 1 0 2 2 -> 1 0 2 4 1 2 2 0 1 0 2 2 , 4 0 1 2 1 5 5 0 4 0 4 5 -> 4 0 1 2 1 5 0 5 4 0 4 5 , 4 2 3 4 2 5 2 1 0 5 2 0 4 -> 4 2 2 3 2 1 0 4 5 5 2 0 4 , 3 4 3 5 2 2 2 4 5 5 3 5 0 5 -> 3 4 3 5 2 2 2 5 4 5 3 5 0 5 , 1 1 0 3 0 3 5 5 5 5 5 0 0 1 1 -> 1 1 0 3 0 5 3 5 5 5 5 0 0 1 1 , 1 2 5 5 2 3 0 0 5 3 3 0 4 4 3 -> 1 2 5 5 3 2 0 3 4 0 0 4 3 5 3 , 1 3 2 4 3 1 4 3 3 4 3 2 0 5 5 -> 1 3 2 4 3 4 1 3 3 4 3 2 0 5 5 , 4 4 3 3 0 3 5 2 1 2 3 1 1 5 1 -> 4 4 0 3 3 3 5 2 2 1 3 1 1 5 1 , 0 4 3 5 3 4 2 2 2 0 2 1 0 1 5 2 -> 0 4 3 5 3 4 2 2 2 0 1 2 0 1 5 2 , 0 0 0 3 4 0 0 4 5 3 4 5 4 5 3 2 5 -> 0 0 0 3 4 0 4 0 5 3 4 5 4 5 3 2 5 , 4 5 0 2 5 5 4 2 1 3 3 0 5 1 2 1 0 -> 4 5 0 2 5 5 4 2 1 3 3 0 1 5 2 1 0 , 3 1 5 5 3 3 1 3 0 2 0 2 4 3 4 0 3 1 -> 3 1 5 5 3 1 3 3 0 2 2 0 4 3 4 3 0 1 , 4 4 4 0 2 1 1 4 5 5 0 5 5 3 1 5 5 3 -> 4 4 4 0 2 1 1 4 5 5 0 5 5 3 5 1 5 3 , 3 1 2 2 1 4 2 1 2 4 3 1 1 4 1 2 4 3 5 -> 3 4 1 1 3 5 1 2 2 2 1 4 1 2 2 1 4 3 4 , 3 4 2 5 0 2 1 0 0 4 3 0 5 1 5 2 0 0 3 -> 3 1 0 4 1 5 2 2 3 0 5 0 2 0 5 4 0 0 3 , 0 2 4 1 5 2 4 3 1 5 1 0 3 2 3 5 3 0 1 1 3 -> 0 2 4 1 5 2 4 1 3 5 1 0 3 2 3 5 3 0 1 1 3 , 1 0 4 2 5 3 4 0 0 4 2 4 4 5 4 5 0 0 4 4 5 -> 1 0 4 2 5 3 4 0 0 4 2 4 4 5 5 4 0 0 4 4 5 , 1 2 1 5 2 1 3 5 2 4 1 5 4 1 3 0 5 1 0 5 5 -> 1 2 1 5 2 1 3 2 5 4 1 5 4 1 3 0 5 1 0 5 5 , 3 5 0 0 2 0 5 1 4 4 0 0 5 3 4 2 1 0 2 5 5 -> 3 5 0 0 2 0 5 1 4 0 4 0 5 3 4 2 1 0 2 5 5 , 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 1 3 4 4 1 0 -> 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 3 1 4 4 1 0 , 2 0 3 3 0 4 3 1 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 -> 2 0 3 3 0 4 1 3 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 , 2 1 1 1 5 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 -> 2 1 1 5 1 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 , 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 2 3 4 0 2 0 0 4 0 2 -> 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 3 2 4 0 2 0 0 4 0 2 , 0 5 0 2 4 5 4 1 3 4 2 0 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 -> 0 5 0 2 4 5 4 1 3 4 0 2 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 , 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 0 5 5 1 3 0 0 2 -> 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 5 0 5 1 3 0 0 2 , 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 2 3 1 0 -> 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 3 2 1 0 , 2 0 5 4 3 3 2 5 3 5 5 5 1 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 -> 2 0 5 4 3 3 2 5 3 5 5 1 5 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 , 2 0 0 0 0 0 4 5 4 1 2 3 2 3 5 3 4 4 4 0 1 3 3 1 5 1 5 0 2 -> 2 0 0 0 0 0 4 5 4 1 2 3 2 3 3 5 4 4 4 0 1 3 3 1 5 1 5 0 2 , 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 4 5 5 2 3 3 3 -> 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 5 4 5 2 3 3 3 , 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 0 4 0 4 0 2 0 1 3 -> 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 4 0 0 4 0 2 0 1 3 , 5 4 4 0 4 4 4 2 1 2 3 0 3 2 1 1 2 1 3 0 1 1 4 1 1 4 0 0 5 5 -> 5 4 4 4 0 4 4 2 1 2 3 0 3 1 1 2 2 1 0 1 3 1 4 1 4 1 0 0 5 5 , 4 4 0 4 0 0 3 5 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 -> 4 4 0 4 0 0 5 3 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 16: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 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 1 | | 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 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 0 1 2 1 0 3 2 -> 0 2 0 1 1 0 3 2 , 1 3 0 4 4 1 1 1 2 2 -> 1 3 4 4 1 0 1 1 2 2 , 0 4 2 4 2 4 1 5 5 5 2 -> 2 2 1 4 5 5 5 4 4 0 2 , 1 0 2 4 2 1 2 0 1 0 2 2 -> 1 0 2 4 1 2 2 0 1 0 2 2 , 4 0 1 2 1 5 5 0 4 0 4 5 -> 4 0 1 2 1 5 0 5 4 0 4 5 , 4 2 3 4 2 5 2 1 0 5 2 0 4 -> 4 2 2 3 2 1 0 4 5 5 2 0 4 , 3 4 3 5 2 2 2 4 5 5 3 5 0 5 -> 3 4 3 5 2 2 2 5 4 5 3 5 0 5 , 1 2 5 5 2 3 0 0 5 3 3 0 4 4 3 -> 1 2 5 5 3 2 0 3 4 0 0 4 3 5 3 , 1 3 2 4 3 1 4 3 3 4 3 2 0 5 5 -> 1 3 2 4 3 4 1 3 3 4 3 2 0 5 5 , 4 4 3 3 0 3 5 2 1 2 3 1 1 5 1 -> 4 4 0 3 3 3 5 2 2 1 3 1 1 5 1 , 0 4 3 5 3 4 2 2 2 0 2 1 0 1 5 2 -> 0 4 3 5 3 4 2 2 2 0 1 2 0 1 5 2 , 0 0 0 3 4 0 0 4 5 3 4 5 4 5 3 2 5 -> 0 0 0 3 4 0 4 0 5 3 4 5 4 5 3 2 5 , 4 5 0 2 5 5 4 2 1 3 3 0 5 1 2 1 0 -> 4 5 0 2 5 5 4 2 1 3 3 0 1 5 2 1 0 , 3 1 5 5 3 3 1 3 0 2 0 2 4 3 4 0 3 1 -> 3 1 5 5 3 1 3 3 0 2 2 0 4 3 4 3 0 1 , 4 4 4 0 2 1 1 4 5 5 0 5 5 3 1 5 5 3 -> 4 4 4 0 2 1 1 4 5 5 0 5 5 3 5 1 5 3 , 3 1 2 2 1 4 2 1 2 4 3 1 1 4 1 2 4 3 5 -> 3 4 1 1 3 5 1 2 2 2 1 4 1 2 2 1 4 3 4 , 3 4 2 5 0 2 1 0 0 4 3 0 5 1 5 2 0 0 3 -> 3 1 0 4 1 5 2 2 3 0 5 0 2 0 5 4 0 0 3 , 0 2 4 1 5 2 4 3 1 5 1 0 3 2 3 5 3 0 1 1 3 -> 0 2 4 1 5 2 4 1 3 5 1 0 3 2 3 5 3 0 1 1 3 , 1 0 4 2 5 3 4 0 0 4 2 4 4 5 4 5 0 0 4 4 5 -> 1 0 4 2 5 3 4 0 0 4 2 4 4 5 5 4 0 0 4 4 5 , 1 2 1 5 2 1 3 5 2 4 1 5 4 1 3 0 5 1 0 5 5 -> 1 2 1 5 2 1 3 2 5 4 1 5 4 1 3 0 5 1 0 5 5 , 3 5 0 0 2 0 5 1 4 4 0 0 5 3 4 2 1 0 2 5 5 -> 3 5 0 0 2 0 5 1 4 0 4 0 5 3 4 2 1 0 2 5 5 , 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 1 3 4 4 1 0 -> 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 3 1 4 4 1 0 , 2 0 3 3 0 4 3 1 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 -> 2 0 3 3 0 4 1 3 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 , 2 1 1 1 5 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 -> 2 1 1 5 1 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 , 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 2 3 4 0 2 0 0 4 0 2 -> 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 3 2 4 0 2 0 0 4 0 2 , 0 5 0 2 4 5 4 1 3 4 2 0 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 -> 0 5 0 2 4 5 4 1 3 4 0 2 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 , 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 0 5 5 1 3 0 0 2 -> 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 5 0 5 1 3 0 0 2 , 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 2 3 1 0 -> 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 3 2 1 0 , 2 0 5 4 3 3 2 5 3 5 5 5 1 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 -> 2 0 5 4 3 3 2 5 3 5 5 1 5 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 , 2 0 0 0 0 0 4 5 4 1 2 3 2 3 5 3 4 4 4 0 1 3 3 1 5 1 5 0 2 -> 2 0 0 0 0 0 4 5 4 1 2 3 2 3 3 5 4 4 4 0 1 3 3 1 5 1 5 0 2 , 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 4 5 5 2 3 3 3 -> 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 5 4 5 2 3 3 3 , 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 0 4 0 4 0 2 0 1 3 -> 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 4 0 0 4 0 2 0 1 3 , 5 4 4 0 4 4 4 2 1 2 3 0 3 2 1 1 2 1 3 0 1 1 4 1 1 4 0 0 5 5 -> 5 4 4 4 0 4 4 2 1 2 3 0 3 1 1 2 2 1 0 1 3 1 4 1 4 1 0 0 5 5 , 4 4 0 4 0 0 3 5 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 -> 4 4 0 4 0 0 5 3 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 16: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 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 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 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 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 0 1 2 1 0 3 2 -> 0 2 0 1 1 0 3 2 , 1 3 0 4 4 1 1 1 2 2 -> 1 3 4 4 1 0 1 1 2 2 , 0 4 2 4 2 4 1 5 5 5 2 -> 2 2 1 4 5 5 5 4 4 0 2 , 1 0 2 4 2 1 2 0 1 0 2 2 -> 1 0 2 4 1 2 2 0 1 0 2 2 , 4 0 1 2 1 5 5 0 4 0 4 5 -> 4 0 1 2 1 5 0 5 4 0 4 5 , 4 2 3 4 2 5 2 1 0 5 2 0 4 -> 4 2 2 3 2 1 0 4 5 5 2 0 4 , 3 4 3 5 2 2 2 4 5 5 3 5 0 5 -> 3 4 3 5 2 2 2 5 4 5 3 5 0 5 , 1 3 2 4 3 1 4 3 3 4 3 2 0 5 5 -> 1 3 2 4 3 4 1 3 3 4 3 2 0 5 5 , 4 4 3 3 0 3 5 2 1 2 3 1 1 5 1 -> 4 4 0 3 3 3 5 2 2 1 3 1 1 5 1 , 0 4 3 5 3 4 2 2 2 0 2 1 0 1 5 2 -> 0 4 3 5 3 4 2 2 2 0 1 2 0 1 5 2 , 0 0 0 3 4 0 0 4 5 3 4 5 4 5 3 2 5 -> 0 0 0 3 4 0 4 0 5 3 4 5 4 5 3 2 5 , 4 5 0 2 5 5 4 2 1 3 3 0 5 1 2 1 0 -> 4 5 0 2 5 5 4 2 1 3 3 0 1 5 2 1 0 , 3 1 5 5 3 3 1 3 0 2 0 2 4 3 4 0 3 1 -> 3 1 5 5 3 1 3 3 0 2 2 0 4 3 4 3 0 1 , 4 4 4 0 2 1 1 4 5 5 0 5 5 3 1 5 5 3 -> 4 4 4 0 2 1 1 4 5 5 0 5 5 3 5 1 5 3 , 3 1 2 2 1 4 2 1 2 4 3 1 1 4 1 2 4 3 5 -> 3 4 1 1 3 5 1 2 2 2 1 4 1 2 2 1 4 3 4 , 3 4 2 5 0 2 1 0 0 4 3 0 5 1 5 2 0 0 3 -> 3 1 0 4 1 5 2 2 3 0 5 0 2 0 5 4 0 0 3 , 0 2 4 1 5 2 4 3 1 5 1 0 3 2 3 5 3 0 1 1 3 -> 0 2 4 1 5 2 4 1 3 5 1 0 3 2 3 5 3 0 1 1 3 , 1 0 4 2 5 3 4 0 0 4 2 4 4 5 4 5 0 0 4 4 5 -> 1 0 4 2 5 3 4 0 0 4 2 4 4 5 5 4 0 0 4 4 5 , 1 2 1 5 2 1 3 5 2 4 1 5 4 1 3 0 5 1 0 5 5 -> 1 2 1 5 2 1 3 2 5 4 1 5 4 1 3 0 5 1 0 5 5 , 3 5 0 0 2 0 5 1 4 4 0 0 5 3 4 2 1 0 2 5 5 -> 3 5 0 0 2 0 5 1 4 0 4 0 5 3 4 2 1 0 2 5 5 , 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 1 3 4 4 1 0 -> 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 3 1 4 4 1 0 , 2 0 3 3 0 4 3 1 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 -> 2 0 3 3 0 4 1 3 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 , 2 1 1 1 5 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 -> 2 1 1 5 1 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 , 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 2 3 4 0 2 0 0 4 0 2 -> 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 3 2 4 0 2 0 0 4 0 2 , 0 5 0 2 4 5 4 1 3 4 2 0 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 -> 0 5 0 2 4 5 4 1 3 4 0 2 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 , 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 0 5 5 1 3 0 0 2 -> 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 5 0 5 1 3 0 0 2 , 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 2 3 1 0 -> 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 3 2 1 0 , 2 0 5 4 3 3 2 5 3 5 5 5 1 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 -> 2 0 5 4 3 3 2 5 3 5 5 1 5 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 , 2 0 0 0 0 0 4 5 4 1 2 3 2 3 5 3 4 4 4 0 1 3 3 1 5 1 5 0 2 -> 2 0 0 0 0 0 4 5 4 1 2 3 2 3 3 5 4 4 4 0 1 3 3 1 5 1 5 0 2 , 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 4 5 5 2 3 3 3 -> 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 5 4 5 2 3 3 3 , 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 0 4 0 4 0 2 0 1 3 -> 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 4 0 0 4 0 2 0 1 3 , 5 4 4 0 4 4 4 2 1 2 3 0 3 2 1 1 2 1 3 0 1 1 4 1 1 4 0 0 5 5 -> 5 4 4 4 0 4 4 2 1 2 3 0 3 1 1 2 2 1 0 1 3 1 4 1 4 1 0 0 5 5 , 4 4 0 4 0 0 3 5 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 -> 4 4 0 4 0 0 5 3 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 16: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 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 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 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 | \ / 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 0 1 2 1 0 3 2 -> 0 2 0 1 1 0 3 2 , 1 3 0 4 4 1 1 1 2 2 -> 1 3 4 4 1 0 1 1 2 2 , 0 4 2 4 2 4 1 5 5 5 2 -> 2 2 1 4 5 5 5 4 4 0 2 , 1 0 2 4 2 1 2 0 1 0 2 2 -> 1 0 2 4 1 2 2 0 1 0 2 2 , 4 0 1 2 1 5 5 0 4 0 4 5 -> 4 0 1 2 1 5 0 5 4 0 4 5 , 4 2 3 4 2 5 2 1 0 5 2 0 4 -> 4 2 2 3 2 1 0 4 5 5 2 0 4 , 3 4 3 5 2 2 2 4 5 5 3 5 0 5 -> 3 4 3 5 2 2 2 5 4 5 3 5 0 5 , 4 4 3 3 0 3 5 2 1 2 3 1 1 5 1 -> 4 4 0 3 3 3 5 2 2 1 3 1 1 5 1 , 0 4 3 5 3 4 2 2 2 0 2 1 0 1 5 2 -> 0 4 3 5 3 4 2 2 2 0 1 2 0 1 5 2 , 0 0 0 3 4 0 0 4 5 3 4 5 4 5 3 2 5 -> 0 0 0 3 4 0 4 0 5 3 4 5 4 5 3 2 5 , 4 5 0 2 5 5 4 2 1 3 3 0 5 1 2 1 0 -> 4 5 0 2 5 5 4 2 1 3 3 0 1 5 2 1 0 , 3 1 5 5 3 3 1 3 0 2 0 2 4 3 4 0 3 1 -> 3 1 5 5 3 1 3 3 0 2 2 0 4 3 4 3 0 1 , 4 4 4 0 2 1 1 4 5 5 0 5 5 3 1 5 5 3 -> 4 4 4 0 2 1 1 4 5 5 0 5 5 3 5 1 5 3 , 3 1 2 2 1 4 2 1 2 4 3 1 1 4 1 2 4 3 5 -> 3 4 1 1 3 5 1 2 2 2 1 4 1 2 2 1 4 3 4 , 3 4 2 5 0 2 1 0 0 4 3 0 5 1 5 2 0 0 3 -> 3 1 0 4 1 5 2 2 3 0 5 0 2 0 5 4 0 0 3 , 0 2 4 1 5 2 4 3 1 5 1 0 3 2 3 5 3 0 1 1 3 -> 0 2 4 1 5 2 4 1 3 5 1 0 3 2 3 5 3 0 1 1 3 , 1 0 4 2 5 3 4 0 0 4 2 4 4 5 4 5 0 0 4 4 5 -> 1 0 4 2 5 3 4 0 0 4 2 4 4 5 5 4 0 0 4 4 5 , 1 2 1 5 2 1 3 5 2 4 1 5 4 1 3 0 5 1 0 5 5 -> 1 2 1 5 2 1 3 2 5 4 1 5 4 1 3 0 5 1 0 5 5 , 3 5 0 0 2 0 5 1 4 4 0 0 5 3 4 2 1 0 2 5 5 -> 3 5 0 0 2 0 5 1 4 0 4 0 5 3 4 2 1 0 2 5 5 , 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 1 3 4 4 1 0 -> 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 3 1 4 4 1 0 , 2 0 3 3 0 4 3 1 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 -> 2 0 3 3 0 4 1 3 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 , 2 1 1 1 5 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 -> 2 1 1 5 1 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 , 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 2 3 4 0 2 0 0 4 0 2 -> 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 3 2 4 0 2 0 0 4 0 2 , 0 5 0 2 4 5 4 1 3 4 2 0 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 -> 0 5 0 2 4 5 4 1 3 4 0 2 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 , 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 0 5 5 1 3 0 0 2 -> 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 5 0 5 1 3 0 0 2 , 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 2 3 1 0 -> 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 3 2 1 0 , 2 0 5 4 3 3 2 5 3 5 5 5 1 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 -> 2 0 5 4 3 3 2 5 3 5 5 1 5 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 , 2 0 0 0 0 0 4 5 4 1 2 3 2 3 5 3 4 4 4 0 1 3 3 1 5 1 5 0 2 -> 2 0 0 0 0 0 4 5 4 1 2 3 2 3 3 5 4 4 4 0 1 3 3 1 5 1 5 0 2 , 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 4 5 5 2 3 3 3 -> 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 5 4 5 2 3 3 3 , 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 0 4 0 4 0 2 0 1 3 -> 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 4 0 0 4 0 2 0 1 3 , 5 4 4 0 4 4 4 2 1 2 3 0 3 2 1 1 2 1 3 0 1 1 4 1 1 4 0 0 5 5 -> 5 4 4 4 0 4 4 2 1 2 3 0 3 1 1 2 2 1 0 1 3 1 4 1 4 1 0 0 5 5 , 4 4 0 4 0 0 3 5 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 -> 4 4 0 4 0 0 5 3 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 18: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 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 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 | \ / 1 is interpreted by / \ | 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 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 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 0 1 2 1 0 3 2 -> 0 2 0 1 1 0 3 2 , 1 3 0 4 4 1 1 1 2 2 -> 1 3 4 4 1 0 1 1 2 2 , 0 4 2 4 2 4 1 5 5 5 2 -> 2 2 1 4 5 5 5 4 4 0 2 , 1 0 2 4 2 1 2 0 1 0 2 2 -> 1 0 2 4 1 2 2 0 1 0 2 2 , 4 0 1 2 1 5 5 0 4 0 4 5 -> 4 0 1 2 1 5 0 5 4 0 4 5 , 4 2 3 4 2 5 2 1 0 5 2 0 4 -> 4 2 2 3 2 1 0 4 5 5 2 0 4 , 3 4 3 5 2 2 2 4 5 5 3 5 0 5 -> 3 4 3 5 2 2 2 5 4 5 3 5 0 5 , 4 4 3 3 0 3 5 2 1 2 3 1 1 5 1 -> 4 4 0 3 3 3 5 2 2 1 3 1 1 5 1 , 0 4 3 5 3 4 2 2 2 0 2 1 0 1 5 2 -> 0 4 3 5 3 4 2 2 2 0 1 2 0 1 5 2 , 4 5 0 2 5 5 4 2 1 3 3 0 5 1 2 1 0 -> 4 5 0 2 5 5 4 2 1 3 3 0 1 5 2 1 0 , 3 1 5 5 3 3 1 3 0 2 0 2 4 3 4 0 3 1 -> 3 1 5 5 3 1 3 3 0 2 2 0 4 3 4 3 0 1 , 4 4 4 0 2 1 1 4 5 5 0 5 5 3 1 5 5 3 -> 4 4 4 0 2 1 1 4 5 5 0 5 5 3 5 1 5 3 , 3 1 2 2 1 4 2 1 2 4 3 1 1 4 1 2 4 3 5 -> 3 4 1 1 3 5 1 2 2 2 1 4 1 2 2 1 4 3 4 , 3 4 2 5 0 2 1 0 0 4 3 0 5 1 5 2 0 0 3 -> 3 1 0 4 1 5 2 2 3 0 5 0 2 0 5 4 0 0 3 , 0 2 4 1 5 2 4 3 1 5 1 0 3 2 3 5 3 0 1 1 3 -> 0 2 4 1 5 2 4 1 3 5 1 0 3 2 3 5 3 0 1 1 3 , 1 0 4 2 5 3 4 0 0 4 2 4 4 5 4 5 0 0 4 4 5 -> 1 0 4 2 5 3 4 0 0 4 2 4 4 5 5 4 0 0 4 4 5 , 1 2 1 5 2 1 3 5 2 4 1 5 4 1 3 0 5 1 0 5 5 -> 1 2 1 5 2 1 3 2 5 4 1 5 4 1 3 0 5 1 0 5 5 , 3 5 0 0 2 0 5 1 4 4 0 0 5 3 4 2 1 0 2 5 5 -> 3 5 0 0 2 0 5 1 4 0 4 0 5 3 4 2 1 0 2 5 5 , 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 1 3 4 4 1 0 -> 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 3 1 4 4 1 0 , 2 0 3 3 0 4 3 1 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 -> 2 0 3 3 0 4 1 3 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 , 2 1 1 1 5 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 -> 2 1 1 5 1 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 , 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 2 3 4 0 2 0 0 4 0 2 -> 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 3 2 4 0 2 0 0 4 0 2 , 0 5 0 2 4 5 4 1 3 4 2 0 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 -> 0 5 0 2 4 5 4 1 3 4 0 2 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 , 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 0 5 5 1 3 0 0 2 -> 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 5 0 5 1 3 0 0 2 , 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 2 3 1 0 -> 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 3 2 1 0 , 2 0 5 4 3 3 2 5 3 5 5 5 1 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 -> 2 0 5 4 3 3 2 5 3 5 5 1 5 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 , 2 0 0 0 0 0 4 5 4 1 2 3 2 3 5 3 4 4 4 0 1 3 3 1 5 1 5 0 2 -> 2 0 0 0 0 0 4 5 4 1 2 3 2 3 3 5 4 4 4 0 1 3 3 1 5 1 5 0 2 , 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 4 5 5 2 3 3 3 -> 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 5 4 5 2 3 3 3 , 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 0 4 0 4 0 2 0 1 3 -> 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 4 0 0 4 0 2 0 1 3 , 5 4 4 0 4 4 4 2 1 2 3 0 3 2 1 1 2 1 3 0 1 1 4 1 1 4 0 0 5 5 -> 5 4 4 4 0 4 4 2 1 2 3 0 3 1 1 2 2 1 0 1 3 1 4 1 4 1 0 0 5 5 , 4 4 0 4 0 0 3 5 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 -> 4 4 0 4 0 0 5 3 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 } 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 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, it remains to prove termination of the 30-rule system { 0 0 1 2 1 0 3 2 -> 0 2 0 1 1 0 3 2 , 1 3 0 4 4 1 1 1 2 2 -> 1 3 4 4 1 0 1 1 2 2 , 0 4 2 4 2 4 1 5 5 5 2 -> 2 2 1 4 5 5 5 4 4 0 2 , 1 0 2 4 2 1 2 0 1 0 2 2 -> 1 0 2 4 1 2 2 0 1 0 2 2 , 4 0 1 2 1 5 5 0 4 0 4 5 -> 4 0 1 2 1 5 0 5 4 0 4 5 , 4 2 3 4 2 5 2 1 0 5 2 0 4 -> 4 2 2 3 2 1 0 4 5 5 2 0 4 , 3 4 3 5 2 2 2 4 5 5 3 5 0 5 -> 3 4 3 5 2 2 2 5 4 5 3 5 0 5 , 4 4 3 3 0 3 5 2 1 2 3 1 1 5 1 -> 4 4 0 3 3 3 5 2 2 1 3 1 1 5 1 , 0 4 3 5 3 4 2 2 2 0 2 1 0 1 5 2 -> 0 4 3 5 3 4 2 2 2 0 1 2 0 1 5 2 , 4 5 0 2 5 5 4 2 1 3 3 0 5 1 2 1 0 -> 4 5 0 2 5 5 4 2 1 3 3 0 1 5 2 1 0 , 3 1 5 5 3 3 1 3 0 2 0 2 4 3 4 0 3 1 -> 3 1 5 5 3 1 3 3 0 2 2 0 4 3 4 3 0 1 , 4 4 4 0 2 1 1 4 5 5 0 5 5 3 1 5 5 3 -> 4 4 4 0 2 1 1 4 5 5 0 5 5 3 5 1 5 3 , 3 4 2 5 0 2 1 0 0 4 3 0 5 1 5 2 0 0 3 -> 3 1 0 4 1 5 2 2 3 0 5 0 2 0 5 4 0 0 3 , 0 2 4 1 5 2 4 3 1 5 1 0 3 2 3 5 3 0 1 1 3 -> 0 2 4 1 5 2 4 1 3 5 1 0 3 2 3 5 3 0 1 1 3 , 1 0 4 2 5 3 4 0 0 4 2 4 4 5 4 5 0 0 4 4 5 -> 1 0 4 2 5 3 4 0 0 4 2 4 4 5 5 4 0 0 4 4 5 , 1 2 1 5 2 1 3 5 2 4 1 5 4 1 3 0 5 1 0 5 5 -> 1 2 1 5 2 1 3 2 5 4 1 5 4 1 3 0 5 1 0 5 5 , 3 5 0 0 2 0 5 1 4 4 0 0 5 3 4 2 1 0 2 5 5 -> 3 5 0 0 2 0 5 1 4 0 4 0 5 3 4 2 1 0 2 5 5 , 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 1 3 4 4 1 0 -> 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 3 1 4 4 1 0 , 2 0 3 3 0 4 3 1 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 -> 2 0 3 3 0 4 1 3 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 , 2 1 1 1 5 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 -> 2 1 1 5 1 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 , 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 2 3 4 0 2 0 0 4 0 2 -> 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 3 2 4 0 2 0 0 4 0 2 , 0 5 0 2 4 5 4 1 3 4 2 0 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 -> 0 5 0 2 4 5 4 1 3 4 0 2 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 , 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 0 5 5 1 3 0 0 2 -> 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 5 0 5 1 3 0 0 2 , 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 2 3 1 0 -> 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 3 2 1 0 , 2 0 5 4 3 3 2 5 3 5 5 5 1 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 -> 2 0 5 4 3 3 2 5 3 5 5 1 5 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 , 2 0 0 0 0 0 4 5 4 1 2 3 2 3 5 3 4 4 4 0 1 3 3 1 5 1 5 0 2 -> 2 0 0 0 0 0 4 5 4 1 2 3 2 3 3 5 4 4 4 0 1 3 3 1 5 1 5 0 2 , 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 4 5 5 2 3 3 3 -> 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 5 4 5 2 3 3 3 , 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 0 4 0 4 0 2 0 1 3 -> 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 4 0 0 4 0 2 0 1 3 , 5 4 4 0 4 4 4 2 1 2 3 0 3 2 1 1 2 1 3 0 1 1 4 1 1 4 0 0 5 5 -> 5 4 4 4 0 4 4 2 1 2 3 0 3 1 1 2 2 1 0 1 3 1 4 1 4 1 0 0 5 5 , 4 4 0 4 0 0 3 5 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 -> 4 4 0 4 0 0 5 3 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 } 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 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 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 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 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 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 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 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 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 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 1 0 0 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 0 1 2 1 0 3 2 -> 0 2 0 1 1 0 3 2 , 1 3 0 4 4 1 1 1 2 2 -> 1 3 4 4 1 0 1 1 2 2 , 0 4 2 4 2 4 1 5 5 5 2 -> 2 2 1 4 5 5 5 4 4 0 2 , 1 0 2 4 2 1 2 0 1 0 2 2 -> 1 0 2 4 1 2 2 0 1 0 2 2 , 4 2 3 4 2 5 2 1 0 5 2 0 4 -> 4 2 2 3 2 1 0 4 5 5 2 0 4 , 3 4 3 5 2 2 2 4 5 5 3 5 0 5 -> 3 4 3 5 2 2 2 5 4 5 3 5 0 5 , 4 4 3 3 0 3 5 2 1 2 3 1 1 5 1 -> 4 4 0 3 3 3 5 2 2 1 3 1 1 5 1 , 0 4 3 5 3 4 2 2 2 0 2 1 0 1 5 2 -> 0 4 3 5 3 4 2 2 2 0 1 2 0 1 5 2 , 4 5 0 2 5 5 4 2 1 3 3 0 5 1 2 1 0 -> 4 5 0 2 5 5 4 2 1 3 3 0 1 5 2 1 0 , 3 1 5 5 3 3 1 3 0 2 0 2 4 3 4 0 3 1 -> 3 1 5 5 3 1 3 3 0 2 2 0 4 3 4 3 0 1 , 4 4 4 0 2 1 1 4 5 5 0 5 5 3 1 5 5 3 -> 4 4 4 0 2 1 1 4 5 5 0 5 5 3 5 1 5 3 , 3 4 2 5 0 2 1 0 0 4 3 0 5 1 5 2 0 0 3 -> 3 1 0 4 1 5 2 2 3 0 5 0 2 0 5 4 0 0 3 , 0 2 4 1 5 2 4 3 1 5 1 0 3 2 3 5 3 0 1 1 3 -> 0 2 4 1 5 2 4 1 3 5 1 0 3 2 3 5 3 0 1 1 3 , 1 0 4 2 5 3 4 0 0 4 2 4 4 5 4 5 0 0 4 4 5 -> 1 0 4 2 5 3 4 0 0 4 2 4 4 5 5 4 0 0 4 4 5 , 1 2 1 5 2 1 3 5 2 4 1 5 4 1 3 0 5 1 0 5 5 -> 1 2 1 5 2 1 3 2 5 4 1 5 4 1 3 0 5 1 0 5 5 , 3 5 0 0 2 0 5 1 4 4 0 0 5 3 4 2 1 0 2 5 5 -> 3 5 0 0 2 0 5 1 4 0 4 0 5 3 4 2 1 0 2 5 5 , 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 1 3 4 4 1 0 -> 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 3 1 4 4 1 0 , 2 0 3 3 0 4 3 1 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 -> 2 0 3 3 0 4 1 3 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 , 2 1 1 1 5 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 -> 2 1 1 5 1 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 , 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 2 3 4 0 2 0 0 4 0 2 -> 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 3 2 4 0 2 0 0 4 0 2 , 0 5 0 2 4 5 4 1 3 4 2 0 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 -> 0 5 0 2 4 5 4 1 3 4 0 2 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 , 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 0 5 5 1 3 0 0 2 -> 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 5 0 5 1 3 0 0 2 , 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 2 3 1 0 -> 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 3 2 1 0 , 2 0 5 4 3 3 2 5 3 5 5 5 1 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 -> 2 0 5 4 3 3 2 5 3 5 5 1 5 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 , 2 0 0 0 0 0 4 5 4 1 2 3 2 3 5 3 4 4 4 0 1 3 3 1 5 1 5 0 2 -> 2 0 0 0 0 0 4 5 4 1 2 3 2 3 3 5 4 4 4 0 1 3 3 1 5 1 5 0 2 , 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 4 5 5 2 3 3 3 -> 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 5 4 5 2 3 3 3 , 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 0 4 0 4 0 2 0 1 3 -> 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 4 0 0 4 0 2 0 1 3 , 5 4 4 0 4 4 4 2 1 2 3 0 3 2 1 1 2 1 3 0 1 1 4 1 1 4 0 0 5 5 -> 5 4 4 4 0 4 4 2 1 2 3 0 3 1 1 2 2 1 0 1 3 1 4 1 4 1 0 0 5 5 , 4 4 0 4 0 0 3 5 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 -> 4 4 0 4 0 0 5 3 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 14: 0 is interpreted by / \ | 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 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 is interpreted by / \ | 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 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 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 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 0 1 2 1 0 3 2 -> 0 2 0 1 1 0 3 2 , 1 3 0 4 4 1 1 1 2 2 -> 1 3 4 4 1 0 1 1 2 2 , 0 4 2 4 2 4 1 5 5 5 2 -> 2 2 1 4 5 5 5 4 4 0 2 , 1 0 2 4 2 1 2 0 1 0 2 2 -> 1 0 2 4 1 2 2 0 1 0 2 2 , 3 4 3 5 2 2 2 4 5 5 3 5 0 5 -> 3 4 3 5 2 2 2 5 4 5 3 5 0 5 , 4 4 3 3 0 3 5 2 1 2 3 1 1 5 1 -> 4 4 0 3 3 3 5 2 2 1 3 1 1 5 1 , 0 4 3 5 3 4 2 2 2 0 2 1 0 1 5 2 -> 0 4 3 5 3 4 2 2 2 0 1 2 0 1 5 2 , 4 5 0 2 5 5 4 2 1 3 3 0 5 1 2 1 0 -> 4 5 0 2 5 5 4 2 1 3 3 0 1 5 2 1 0 , 3 1 5 5 3 3 1 3 0 2 0 2 4 3 4 0 3 1 -> 3 1 5 5 3 1 3 3 0 2 2 0 4 3 4 3 0 1 , 4 4 4 0 2 1 1 4 5 5 0 5 5 3 1 5 5 3 -> 4 4 4 0 2 1 1 4 5 5 0 5 5 3 5 1 5 3 , 3 4 2 5 0 2 1 0 0 4 3 0 5 1 5 2 0 0 3 -> 3 1 0 4 1 5 2 2 3 0 5 0 2 0 5 4 0 0 3 , 0 2 4 1 5 2 4 3 1 5 1 0 3 2 3 5 3 0 1 1 3 -> 0 2 4 1 5 2 4 1 3 5 1 0 3 2 3 5 3 0 1 1 3 , 1 0 4 2 5 3 4 0 0 4 2 4 4 5 4 5 0 0 4 4 5 -> 1 0 4 2 5 3 4 0 0 4 2 4 4 5 5 4 0 0 4 4 5 , 1 2 1 5 2 1 3 5 2 4 1 5 4 1 3 0 5 1 0 5 5 -> 1 2 1 5 2 1 3 2 5 4 1 5 4 1 3 0 5 1 0 5 5 , 3 5 0 0 2 0 5 1 4 4 0 0 5 3 4 2 1 0 2 5 5 -> 3 5 0 0 2 0 5 1 4 0 4 0 5 3 4 2 1 0 2 5 5 , 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 1 3 4 4 1 0 -> 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 3 1 4 4 1 0 , 2 0 3 3 0 4 3 1 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 -> 2 0 3 3 0 4 1 3 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 , 2 1 1 1 5 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 -> 2 1 1 5 1 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 , 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 2 3 4 0 2 0 0 4 0 2 -> 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 3 2 4 0 2 0 0 4 0 2 , 0 5 0 2 4 5 4 1 3 4 2 0 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 -> 0 5 0 2 4 5 4 1 3 4 0 2 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 , 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 0 5 5 1 3 0 0 2 -> 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 5 0 5 1 3 0 0 2 , 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 2 3 1 0 -> 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 3 2 1 0 , 2 0 5 4 3 3 2 5 3 5 5 5 1 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 -> 2 0 5 4 3 3 2 5 3 5 5 1 5 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 , 2 0 0 0 0 0 4 5 4 1 2 3 2 3 5 3 4 4 4 0 1 3 3 1 5 1 5 0 2 -> 2 0 0 0 0 0 4 5 4 1 2 3 2 3 3 5 4 4 4 0 1 3 3 1 5 1 5 0 2 , 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 4 5 5 2 3 3 3 -> 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 5 4 5 2 3 3 3 , 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 0 4 0 4 0 2 0 1 3 -> 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 4 0 0 4 0 2 0 1 3 , 5 4 4 0 4 4 4 2 1 2 3 0 3 2 1 1 2 1 3 0 1 1 4 1 1 4 0 0 5 5 -> 5 4 4 4 0 4 4 2 1 2 3 0 3 1 1 2 2 1 0 1 3 1 4 1 4 1 0 0 5 5 , 4 4 0 4 0 0 3 5 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 -> 4 4 0 4 0 0 5 3 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 15: 0 is interpreted by / \ | 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 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 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 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 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 | \ / 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 0 1 2 1 0 3 2 -> 0 2 0 1 1 0 3 2 , 1 3 0 4 4 1 1 1 2 2 -> 1 3 4 4 1 0 1 1 2 2 , 0 4 2 4 2 4 1 5 5 5 2 -> 2 2 1 4 5 5 5 4 4 0 2 , 1 0 2 4 2 1 2 0 1 0 2 2 -> 1 0 2 4 1 2 2 0 1 0 2 2 , 4 4 3 3 0 3 5 2 1 2 3 1 1 5 1 -> 4 4 0 3 3 3 5 2 2 1 3 1 1 5 1 , 0 4 3 5 3 4 2 2 2 0 2 1 0 1 5 2 -> 0 4 3 5 3 4 2 2 2 0 1 2 0 1 5 2 , 4 5 0 2 5 5 4 2 1 3 3 0 5 1 2 1 0 -> 4 5 0 2 5 5 4 2 1 3 3 0 1 5 2 1 0 , 3 1 5 5 3 3 1 3 0 2 0 2 4 3 4 0 3 1 -> 3 1 5 5 3 1 3 3 0 2 2 0 4 3 4 3 0 1 , 4 4 4 0 2 1 1 4 5 5 0 5 5 3 1 5 5 3 -> 4 4 4 0 2 1 1 4 5 5 0 5 5 3 5 1 5 3 , 3 4 2 5 0 2 1 0 0 4 3 0 5 1 5 2 0 0 3 -> 3 1 0 4 1 5 2 2 3 0 5 0 2 0 5 4 0 0 3 , 0 2 4 1 5 2 4 3 1 5 1 0 3 2 3 5 3 0 1 1 3 -> 0 2 4 1 5 2 4 1 3 5 1 0 3 2 3 5 3 0 1 1 3 , 1 0 4 2 5 3 4 0 0 4 2 4 4 5 4 5 0 0 4 4 5 -> 1 0 4 2 5 3 4 0 0 4 2 4 4 5 5 4 0 0 4 4 5 , 1 2 1 5 2 1 3 5 2 4 1 5 4 1 3 0 5 1 0 5 5 -> 1 2 1 5 2 1 3 2 5 4 1 5 4 1 3 0 5 1 0 5 5 , 3 5 0 0 2 0 5 1 4 4 0 0 5 3 4 2 1 0 2 5 5 -> 3 5 0 0 2 0 5 1 4 0 4 0 5 3 4 2 1 0 2 5 5 , 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 1 3 4 4 1 0 -> 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 3 1 4 4 1 0 , 2 0 3 3 0 4 3 1 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 -> 2 0 3 3 0 4 1 3 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 , 2 1 1 1 5 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 -> 2 1 1 5 1 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 , 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 2 3 4 0 2 0 0 4 0 2 -> 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 3 2 4 0 2 0 0 4 0 2 , 0 5 0 2 4 5 4 1 3 4 2 0 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 -> 0 5 0 2 4 5 4 1 3 4 0 2 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 , 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 0 5 5 1 3 0 0 2 -> 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 5 0 5 1 3 0 0 2 , 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 2 3 1 0 -> 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 3 2 1 0 , 2 0 5 4 3 3 2 5 3 5 5 5 1 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 -> 2 0 5 4 3 3 2 5 3 5 5 1 5 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 , 2 0 0 0 0 0 4 5 4 1 2 3 2 3 5 3 4 4 4 0 1 3 3 1 5 1 5 0 2 -> 2 0 0 0 0 0 4 5 4 1 2 3 2 3 3 5 4 4 4 0 1 3 3 1 5 1 5 0 2 , 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 4 5 5 2 3 3 3 -> 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 5 4 5 2 3 3 3 , 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 0 4 0 4 0 2 0 1 3 -> 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 4 0 0 4 0 2 0 1 3 , 5 4 4 0 4 4 4 2 1 2 3 0 3 2 1 1 2 1 3 0 1 1 4 1 1 4 0 0 5 5 -> 5 4 4 4 0 4 4 2 1 2 3 0 3 1 1 2 2 1 0 1 3 1 4 1 4 1 0 0 5 5 , 4 4 0 4 0 0 3 5 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 -> 4 4 0 4 0 0 5 3 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 16: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 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 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 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 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 0 1 2 1 0 3 2 -> 0 2 0 1 1 0 3 2 , 1 3 0 4 4 1 1 1 2 2 -> 1 3 4 4 1 0 1 1 2 2 , 0 4 2 4 2 4 1 5 5 5 2 -> 2 2 1 4 5 5 5 4 4 0 2 , 1 0 2 4 2 1 2 0 1 0 2 2 -> 1 0 2 4 1 2 2 0 1 0 2 2 , 0 4 3 5 3 4 2 2 2 0 2 1 0 1 5 2 -> 0 4 3 5 3 4 2 2 2 0 1 2 0 1 5 2 , 4 5 0 2 5 5 4 2 1 3 3 0 5 1 2 1 0 -> 4 5 0 2 5 5 4 2 1 3 3 0 1 5 2 1 0 , 3 1 5 5 3 3 1 3 0 2 0 2 4 3 4 0 3 1 -> 3 1 5 5 3 1 3 3 0 2 2 0 4 3 4 3 0 1 , 4 4 4 0 2 1 1 4 5 5 0 5 5 3 1 5 5 3 -> 4 4 4 0 2 1 1 4 5 5 0 5 5 3 5 1 5 3 , 3 4 2 5 0 2 1 0 0 4 3 0 5 1 5 2 0 0 3 -> 3 1 0 4 1 5 2 2 3 0 5 0 2 0 5 4 0 0 3 , 0 2 4 1 5 2 4 3 1 5 1 0 3 2 3 5 3 0 1 1 3 -> 0 2 4 1 5 2 4 1 3 5 1 0 3 2 3 5 3 0 1 1 3 , 1 0 4 2 5 3 4 0 0 4 2 4 4 5 4 5 0 0 4 4 5 -> 1 0 4 2 5 3 4 0 0 4 2 4 4 5 5 4 0 0 4 4 5 , 1 2 1 5 2 1 3 5 2 4 1 5 4 1 3 0 5 1 0 5 5 -> 1 2 1 5 2 1 3 2 5 4 1 5 4 1 3 0 5 1 0 5 5 , 3 5 0 0 2 0 5 1 4 4 0 0 5 3 4 2 1 0 2 5 5 -> 3 5 0 0 2 0 5 1 4 0 4 0 5 3 4 2 1 0 2 5 5 , 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 1 3 4 4 1 0 -> 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 3 1 4 4 1 0 , 2 0 3 3 0 4 3 1 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 -> 2 0 3 3 0 4 1 3 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 , 2 1 1 1 5 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 -> 2 1 1 5 1 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 , 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 2 3 4 0 2 0 0 4 0 2 -> 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 3 2 4 0 2 0 0 4 0 2 , 0 5 0 2 4 5 4 1 3 4 2 0 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 -> 0 5 0 2 4 5 4 1 3 4 0 2 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 , 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 0 5 5 1 3 0 0 2 -> 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 5 0 5 1 3 0 0 2 , 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 2 3 1 0 -> 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 3 2 1 0 , 2 0 5 4 3 3 2 5 3 5 5 5 1 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 -> 2 0 5 4 3 3 2 5 3 5 5 1 5 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 , 2 0 0 0 0 0 4 5 4 1 2 3 2 3 5 3 4 4 4 0 1 3 3 1 5 1 5 0 2 -> 2 0 0 0 0 0 4 5 4 1 2 3 2 3 3 5 4 4 4 0 1 3 3 1 5 1 5 0 2 , 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 4 5 5 2 3 3 3 -> 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 5 4 5 2 3 3 3 , 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 0 4 0 4 0 2 0 1 3 -> 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 4 0 0 4 0 2 0 1 3 , 5 4 4 0 4 4 4 2 1 2 3 0 3 2 1 1 2 1 3 0 1 1 4 1 1 4 0 0 5 5 -> 5 4 4 4 0 4 4 2 1 2 3 0 3 1 1 2 2 1 0 1 3 1 4 1 4 1 0 0 5 5 , 4 4 0 4 0 0 3 5 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 -> 4 4 0 4 0 0 5 3 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 18: 0 is interpreted by / \ | 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 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 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 | \ / 4 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 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 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 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 2 1 0 3 2 -> 0 2 0 1 1 0 3 2 , 1 3 0 4 4 1 1 1 2 2 -> 1 3 4 4 1 0 1 1 2 2 , 0 4 2 4 2 4 1 5 5 5 2 -> 2 2 1 4 5 5 5 4 4 0 2 , 1 0 2 4 2 1 2 0 1 0 2 2 -> 1 0 2 4 1 2 2 0 1 0 2 2 , 0 4 3 5 3 4 2 2 2 0 2 1 0 1 5 2 -> 0 4 3 5 3 4 2 2 2 0 1 2 0 1 5 2 , 3 1 5 5 3 3 1 3 0 2 0 2 4 3 4 0 3 1 -> 3 1 5 5 3 1 3 3 0 2 2 0 4 3 4 3 0 1 , 4 4 4 0 2 1 1 4 5 5 0 5 5 3 1 5 5 3 -> 4 4 4 0 2 1 1 4 5 5 0 5 5 3 5 1 5 3 , 3 4 2 5 0 2 1 0 0 4 3 0 5 1 5 2 0 0 3 -> 3 1 0 4 1 5 2 2 3 0 5 0 2 0 5 4 0 0 3 , 0 2 4 1 5 2 4 3 1 5 1 0 3 2 3 5 3 0 1 1 3 -> 0 2 4 1 5 2 4 1 3 5 1 0 3 2 3 5 3 0 1 1 3 , 1 0 4 2 5 3 4 0 0 4 2 4 4 5 4 5 0 0 4 4 5 -> 1 0 4 2 5 3 4 0 0 4 2 4 4 5 5 4 0 0 4 4 5 , 1 2 1 5 2 1 3 5 2 4 1 5 4 1 3 0 5 1 0 5 5 -> 1 2 1 5 2 1 3 2 5 4 1 5 4 1 3 0 5 1 0 5 5 , 3 5 0 0 2 0 5 1 4 4 0 0 5 3 4 2 1 0 2 5 5 -> 3 5 0 0 2 0 5 1 4 0 4 0 5 3 4 2 1 0 2 5 5 , 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 1 3 4 4 1 0 -> 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 3 1 4 4 1 0 , 2 0 3 3 0 4 3 1 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 -> 2 0 3 3 0 4 1 3 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 , 2 1 1 1 5 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 -> 2 1 1 5 1 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 , 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 2 3 4 0 2 0 0 4 0 2 -> 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 3 2 4 0 2 0 0 4 0 2 , 0 5 0 2 4 5 4 1 3 4 2 0 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 -> 0 5 0 2 4 5 4 1 3 4 0 2 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 , 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 0 5 5 1 3 0 0 2 -> 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 5 0 5 1 3 0 0 2 , 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 2 3 1 0 -> 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 3 2 1 0 , 2 0 5 4 3 3 2 5 3 5 5 5 1 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 -> 2 0 5 4 3 3 2 5 3 5 5 1 5 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 , 2 0 0 0 0 0 4 5 4 1 2 3 2 3 5 3 4 4 4 0 1 3 3 1 5 1 5 0 2 -> 2 0 0 0 0 0 4 5 4 1 2 3 2 3 3 5 4 4 4 0 1 3 3 1 5 1 5 0 2 , 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 4 5 5 2 3 3 3 -> 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 5 4 5 2 3 3 3 , 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 0 4 0 4 0 2 0 1 3 -> 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 4 0 0 4 0 2 0 1 3 , 5 4 4 0 4 4 4 2 1 2 3 0 3 2 1 1 2 1 3 0 1 1 4 1 1 4 0 0 5 5 -> 5 4 4 4 0 4 4 2 1 2 3 0 3 1 1 2 2 1 0 1 3 1 4 1 4 1 0 0 5 5 , 4 4 0 4 0 0 3 5 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 -> 4 4 0 4 0 0 5 3 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 } 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 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 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 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 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 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 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 1 | | 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 0 1 2 1 0 3 2 -> 0 2 0 1 1 0 3 2 , 1 3 0 4 4 1 1 1 2 2 -> 1 3 4 4 1 0 1 1 2 2 , 0 4 2 4 2 4 1 5 5 5 2 -> 2 2 1 4 5 5 5 4 4 0 2 , 1 0 2 4 2 1 2 0 1 0 2 2 -> 1 0 2 4 1 2 2 0 1 0 2 2 , 0 4 3 5 3 4 2 2 2 0 2 1 0 1 5 2 -> 0 4 3 5 3 4 2 2 2 0 1 2 0 1 5 2 , 3 1 5 5 3 3 1 3 0 2 0 2 4 3 4 0 3 1 -> 3 1 5 5 3 1 3 3 0 2 2 0 4 3 4 3 0 1 , 3 4 2 5 0 2 1 0 0 4 3 0 5 1 5 2 0 0 3 -> 3 1 0 4 1 5 2 2 3 0 5 0 2 0 5 4 0 0 3 , 0 2 4 1 5 2 4 3 1 5 1 0 3 2 3 5 3 0 1 1 3 -> 0 2 4 1 5 2 4 1 3 5 1 0 3 2 3 5 3 0 1 1 3 , 1 0 4 2 5 3 4 0 0 4 2 4 4 5 4 5 0 0 4 4 5 -> 1 0 4 2 5 3 4 0 0 4 2 4 4 5 5 4 0 0 4 4 5 , 1 2 1 5 2 1 3 5 2 4 1 5 4 1 3 0 5 1 0 5 5 -> 1 2 1 5 2 1 3 2 5 4 1 5 4 1 3 0 5 1 0 5 5 , 3 5 0 0 2 0 5 1 4 4 0 0 5 3 4 2 1 0 2 5 5 -> 3 5 0 0 2 0 5 1 4 0 4 0 5 3 4 2 1 0 2 5 5 , 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 1 3 4 4 1 0 -> 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 3 1 4 4 1 0 , 2 0 3 3 0 4 3 1 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 -> 2 0 3 3 0 4 1 3 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 , 2 1 1 1 5 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 -> 2 1 1 5 1 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 , 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 2 3 4 0 2 0 0 4 0 2 -> 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 3 2 4 0 2 0 0 4 0 2 , 0 5 0 2 4 5 4 1 3 4 2 0 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 -> 0 5 0 2 4 5 4 1 3 4 0 2 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 , 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 0 5 5 1 3 0 0 2 -> 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 5 0 5 1 3 0 0 2 , 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 2 3 1 0 -> 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 3 2 1 0 , 2 0 5 4 3 3 2 5 3 5 5 5 1 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 -> 2 0 5 4 3 3 2 5 3 5 5 1 5 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 , 2 0 0 0 0 0 4 5 4 1 2 3 2 3 5 3 4 4 4 0 1 3 3 1 5 1 5 0 2 -> 2 0 0 0 0 0 4 5 4 1 2 3 2 3 3 5 4 4 4 0 1 3 3 1 5 1 5 0 2 , 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 4 5 5 2 3 3 3 -> 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 5 4 5 2 3 3 3 , 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 0 4 0 4 0 2 0 1 3 -> 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 4 0 0 4 0 2 0 1 3 , 5 4 4 0 4 4 4 2 1 2 3 0 3 2 1 1 2 1 3 0 1 1 4 1 1 4 0 0 5 5 -> 5 4 4 4 0 4 4 2 1 2 3 0 3 1 1 2 2 1 0 1 3 1 4 1 4 1 0 0 5 5 , 4 4 0 4 0 0 3 5 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 -> 4 4 0 4 0 0 5 3 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 } 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 | \ / 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 2 1 0 3 2 -> 0 2 0 1 1 0 3 2 , 1 3 0 4 4 1 1 1 2 2 -> 1 3 4 4 1 0 1 1 2 2 , 0 4 2 4 2 4 1 5 5 5 2 -> 2 2 1 4 5 5 5 4 4 0 2 , 1 0 2 4 2 1 2 0 1 0 2 2 -> 1 0 2 4 1 2 2 0 1 0 2 2 , 0 4 3 5 3 4 2 2 2 0 2 1 0 1 5 2 -> 0 4 3 5 3 4 2 2 2 0 1 2 0 1 5 2 , 3 1 5 5 3 3 1 3 0 2 0 2 4 3 4 0 3 1 -> 3 1 5 5 3 1 3 3 0 2 2 0 4 3 4 3 0 1 , 0 2 4 1 5 2 4 3 1 5 1 0 3 2 3 5 3 0 1 1 3 -> 0 2 4 1 5 2 4 1 3 5 1 0 3 2 3 5 3 0 1 1 3 , 1 0 4 2 5 3 4 0 0 4 2 4 4 5 4 5 0 0 4 4 5 -> 1 0 4 2 5 3 4 0 0 4 2 4 4 5 5 4 0 0 4 4 5 , 1 2 1 5 2 1 3 5 2 4 1 5 4 1 3 0 5 1 0 5 5 -> 1 2 1 5 2 1 3 2 5 4 1 5 4 1 3 0 5 1 0 5 5 , 3 5 0 0 2 0 5 1 4 4 0 0 5 3 4 2 1 0 2 5 5 -> 3 5 0 0 2 0 5 1 4 0 4 0 5 3 4 2 1 0 2 5 5 , 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 1 3 4 4 1 0 -> 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 3 1 4 4 1 0 , 2 0 3 3 0 4 3 1 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 -> 2 0 3 3 0 4 1 3 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 , 2 1 1 1 5 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 -> 2 1 1 5 1 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 , 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 2 3 4 0 2 0 0 4 0 2 -> 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 3 2 4 0 2 0 0 4 0 2 , 0 5 0 2 4 5 4 1 3 4 2 0 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 -> 0 5 0 2 4 5 4 1 3 4 0 2 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 , 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 0 5 5 1 3 0 0 2 -> 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 5 0 5 1 3 0 0 2 , 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 2 3 1 0 -> 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 3 2 1 0 , 2 0 5 4 3 3 2 5 3 5 5 5 1 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 -> 2 0 5 4 3 3 2 5 3 5 5 1 5 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 , 2 0 0 0 0 0 4 5 4 1 2 3 2 3 5 3 4 4 4 0 1 3 3 1 5 1 5 0 2 -> 2 0 0 0 0 0 4 5 4 1 2 3 2 3 3 5 4 4 4 0 1 3 3 1 5 1 5 0 2 , 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 4 5 5 2 3 3 3 -> 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 5 4 5 2 3 3 3 , 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 0 4 0 4 0 2 0 1 3 -> 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 4 0 0 4 0 2 0 1 3 , 5 4 4 0 4 4 4 2 1 2 3 0 3 2 1 1 2 1 3 0 1 1 4 1 1 4 0 0 5 5 -> 5 4 4 4 0 4 4 2 1 2 3 0 3 1 1 2 2 1 0 1 3 1 4 1 4 1 0 0 5 5 , 4 4 0 4 0 0 3 5 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 -> 4 4 0 4 0 0 5 3 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 } 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 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 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 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 2 1 0 3 2 -> 0 2 0 1 1 0 3 2 , 1 3 0 4 4 1 1 1 2 2 -> 1 3 4 4 1 0 1 1 2 2 , 0 4 2 4 2 4 1 5 5 5 2 -> 2 2 1 4 5 5 5 4 4 0 2 , 1 0 2 4 2 1 2 0 1 0 2 2 -> 1 0 2 4 1 2 2 0 1 0 2 2 , 0 4 3 5 3 4 2 2 2 0 2 1 0 1 5 2 -> 0 4 3 5 3 4 2 2 2 0 1 2 0 1 5 2 , 0 2 4 1 5 2 4 3 1 5 1 0 3 2 3 5 3 0 1 1 3 -> 0 2 4 1 5 2 4 1 3 5 1 0 3 2 3 5 3 0 1 1 3 , 1 0 4 2 5 3 4 0 0 4 2 4 4 5 4 5 0 0 4 4 5 -> 1 0 4 2 5 3 4 0 0 4 2 4 4 5 5 4 0 0 4 4 5 , 1 2 1 5 2 1 3 5 2 4 1 5 4 1 3 0 5 1 0 5 5 -> 1 2 1 5 2 1 3 2 5 4 1 5 4 1 3 0 5 1 0 5 5 , 3 5 0 0 2 0 5 1 4 4 0 0 5 3 4 2 1 0 2 5 5 -> 3 5 0 0 2 0 5 1 4 0 4 0 5 3 4 2 1 0 2 5 5 , 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 1 3 4 4 1 0 -> 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 3 1 4 4 1 0 , 2 0 3 3 0 4 3 1 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 -> 2 0 3 3 0 4 1 3 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 , 2 1 1 1 5 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 -> 2 1 1 5 1 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 , 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 2 3 4 0 2 0 0 4 0 2 -> 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 3 2 4 0 2 0 0 4 0 2 , 0 5 0 2 4 5 4 1 3 4 2 0 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 -> 0 5 0 2 4 5 4 1 3 4 0 2 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 , 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 0 5 5 1 3 0 0 2 -> 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 5 0 5 1 3 0 0 2 , 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 2 3 1 0 -> 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 3 2 1 0 , 2 0 5 4 3 3 2 5 3 5 5 5 1 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 -> 2 0 5 4 3 3 2 5 3 5 5 1 5 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 , 2 0 0 0 0 0 4 5 4 1 2 3 2 3 5 3 4 4 4 0 1 3 3 1 5 1 5 0 2 -> 2 0 0 0 0 0 4 5 4 1 2 3 2 3 3 5 4 4 4 0 1 3 3 1 5 1 5 0 2 , 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 4 5 5 2 3 3 3 -> 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 5 4 5 2 3 3 3 , 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 0 4 0 4 0 2 0 1 3 -> 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 4 0 0 4 0 2 0 1 3 , 5 4 4 0 4 4 4 2 1 2 3 0 3 2 1 1 2 1 3 0 1 1 4 1 1 4 0 0 5 5 -> 5 4 4 4 0 4 4 2 1 2 3 0 3 1 1 2 2 1 0 1 3 1 4 1 4 1 0 0 5 5 , 4 4 0 4 0 0 3 5 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 -> 4 4 0 4 0 0 5 3 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 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 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 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 0 0 0 0 0 0 0 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 | \ / 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 | \ / 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 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 0 1 2 1 0 3 2 -> 0 2 0 1 1 0 3 2 , 1 3 0 4 4 1 1 1 2 2 -> 1 3 4 4 1 0 1 1 2 2 , 0 4 2 4 2 4 1 5 5 5 2 -> 2 2 1 4 5 5 5 4 4 0 2 , 1 0 2 4 2 1 2 0 1 0 2 2 -> 1 0 2 4 1 2 2 0 1 0 2 2 , 0 4 3 5 3 4 2 2 2 0 2 1 0 1 5 2 -> 0 4 3 5 3 4 2 2 2 0 1 2 0 1 5 2 , 0 2 4 1 5 2 4 3 1 5 1 0 3 2 3 5 3 0 1 1 3 -> 0 2 4 1 5 2 4 1 3 5 1 0 3 2 3 5 3 0 1 1 3 , 1 2 1 5 2 1 3 5 2 4 1 5 4 1 3 0 5 1 0 5 5 -> 1 2 1 5 2 1 3 2 5 4 1 5 4 1 3 0 5 1 0 5 5 , 3 5 0 0 2 0 5 1 4 4 0 0 5 3 4 2 1 0 2 5 5 -> 3 5 0 0 2 0 5 1 4 0 4 0 5 3 4 2 1 0 2 5 5 , 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 1 3 4 4 1 0 -> 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 3 1 4 4 1 0 , 2 0 3 3 0 4 3 1 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 -> 2 0 3 3 0 4 1 3 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 , 2 1 1 1 5 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 -> 2 1 1 5 1 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 , 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 2 3 4 0 2 0 0 4 0 2 -> 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 3 2 4 0 2 0 0 4 0 2 , 0 5 0 2 4 5 4 1 3 4 2 0 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 -> 0 5 0 2 4 5 4 1 3 4 0 2 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 , 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 0 5 5 1 3 0 0 2 -> 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 5 0 5 1 3 0 0 2 , 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 2 3 1 0 -> 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 3 2 1 0 , 2 0 5 4 3 3 2 5 3 5 5 5 1 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 -> 2 0 5 4 3 3 2 5 3 5 5 1 5 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 , 2 0 0 0 0 0 4 5 4 1 2 3 2 3 5 3 4 4 4 0 1 3 3 1 5 1 5 0 2 -> 2 0 0 0 0 0 4 5 4 1 2 3 2 3 3 5 4 4 4 0 1 3 3 1 5 1 5 0 2 , 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 4 5 5 2 3 3 3 -> 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 5 4 5 2 3 3 3 , 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 0 4 0 4 0 2 0 1 3 -> 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 4 0 0 4 0 2 0 1 3 , 5 4 4 0 4 4 4 2 1 2 3 0 3 2 1 1 2 1 3 0 1 1 4 1 1 4 0 0 5 5 -> 5 4 4 4 0 4 4 2 1 2 3 0 3 1 1 2 2 1 0 1 3 1 4 1 4 1 0 0 5 5 , 4 4 0 4 0 0 3 5 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 -> 4 4 0 4 0 0 5 3 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, it remains to prove termination of the 20-rule system { 0 0 1 2 1 0 3 2 -> 0 2 0 1 1 0 3 2 , 1 3 0 4 4 1 1 1 2 2 -> 1 3 4 4 1 0 1 1 2 2 , 0 4 2 4 2 4 1 5 5 5 2 -> 2 2 1 4 5 5 5 4 4 0 2 , 1 0 2 4 2 1 2 0 1 0 2 2 -> 1 0 2 4 1 2 2 0 1 0 2 2 , 0 4 3 5 3 4 2 2 2 0 2 1 0 1 5 2 -> 0 4 3 5 3 4 2 2 2 0 1 2 0 1 5 2 , 0 2 4 1 5 2 4 3 1 5 1 0 3 2 3 5 3 0 1 1 3 -> 0 2 4 1 5 2 4 1 3 5 1 0 3 2 3 5 3 0 1 1 3 , 3 5 0 0 2 0 5 1 4 4 0 0 5 3 4 2 1 0 2 5 5 -> 3 5 0 0 2 0 5 1 4 0 4 0 5 3 4 2 1 0 2 5 5 , 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 1 3 4 4 1 0 -> 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 3 1 4 4 1 0 , 2 0 3 3 0 4 3 1 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 -> 2 0 3 3 0 4 1 3 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 , 2 1 1 1 5 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 -> 2 1 1 5 1 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 , 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 2 3 4 0 2 0 0 4 0 2 -> 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 3 2 4 0 2 0 0 4 0 2 , 0 5 0 2 4 5 4 1 3 4 2 0 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 -> 0 5 0 2 4 5 4 1 3 4 0 2 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 , 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 0 5 5 1 3 0 0 2 -> 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 5 0 5 1 3 0 0 2 , 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 2 3 1 0 -> 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 3 2 1 0 , 2 0 5 4 3 3 2 5 3 5 5 5 1 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 -> 2 0 5 4 3 3 2 5 3 5 5 1 5 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 , 2 0 0 0 0 0 4 5 4 1 2 3 2 3 5 3 4 4 4 0 1 3 3 1 5 1 5 0 2 -> 2 0 0 0 0 0 4 5 4 1 2 3 2 3 3 5 4 4 4 0 1 3 3 1 5 1 5 0 2 , 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 4 5 5 2 3 3 3 -> 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 5 4 5 2 3 3 3 , 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 0 4 0 4 0 2 0 1 3 -> 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 4 0 0 4 0 2 0 1 3 , 5 4 4 0 4 4 4 2 1 2 3 0 3 2 1 1 2 1 3 0 1 1 4 1 1 4 0 0 5 5 -> 5 4 4 4 0 4 4 2 1 2 3 0 3 1 1 2 2 1 0 1 3 1 4 1 4 1 0 0 5 5 , 4 4 0 4 0 0 3 5 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 -> 4 4 0 4 0 0 5 3 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 | \ / 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 1 0 3 2 -> 0 2 0 1 1 0 3 2 , 1 3 0 4 4 1 1 1 2 2 -> 1 3 4 4 1 0 1 1 2 2 , 0 4 2 4 2 4 1 5 5 5 2 -> 2 2 1 4 5 5 5 4 4 0 2 , 1 0 2 4 2 1 2 0 1 0 2 2 -> 1 0 2 4 1 2 2 0 1 0 2 2 , 0 4 3 5 3 4 2 2 2 0 2 1 0 1 5 2 -> 0 4 3 5 3 4 2 2 2 0 1 2 0 1 5 2 , 0 2 4 1 5 2 4 3 1 5 1 0 3 2 3 5 3 0 1 1 3 -> 0 2 4 1 5 2 4 1 3 5 1 0 3 2 3 5 3 0 1 1 3 , 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 1 3 4 4 1 0 -> 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 3 1 4 4 1 0 , 2 0 3 3 0 4 3 1 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 -> 2 0 3 3 0 4 1 3 5 3 0 1 1 5 0 4 4 3 1 2 1 2 5 2 4 , 2 1 1 1 5 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 -> 2 1 1 5 1 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 , 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 2 3 4 0 2 0 0 4 0 2 -> 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 3 2 4 0 2 0 0 4 0 2 , 0 5 0 2 4 5 4 1 3 4 2 0 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 -> 0 5 0 2 4 5 4 1 3 4 0 2 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 , 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 0 5 5 1 3 0 0 2 -> 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 5 0 5 1 3 0 0 2 , 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 2 3 1 0 -> 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 3 2 1 0 , 2 0 5 4 3 3 2 5 3 5 5 5 1 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 -> 2 0 5 4 3 3 2 5 3 5 5 1 5 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 , 2 0 0 0 0 0 4 5 4 1 2 3 2 3 5 3 4 4 4 0 1 3 3 1 5 1 5 0 2 -> 2 0 0 0 0 0 4 5 4 1 2 3 2 3 3 5 4 4 4 0 1 3 3 1 5 1 5 0 2 , 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 4 5 5 2 3 3 3 -> 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 5 4 5 2 3 3 3 , 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 0 4 0 4 0 2 0 1 3 -> 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 4 0 0 4 0 2 0 1 3 , 5 4 4 0 4 4 4 2 1 2 3 0 3 2 1 1 2 1 3 0 1 1 4 1 1 4 0 0 5 5 -> 5 4 4 4 0 4 4 2 1 2 3 0 3 1 1 2 2 1 0 1 3 1 4 1 4 1 0 0 5 5 , 4 4 0 4 0 0 3 5 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 -> 4 4 0 4 0 0 5 3 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 } 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 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 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 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 1 0 3 2 -> 0 2 0 1 1 0 3 2 , 1 3 0 4 4 1 1 1 2 2 -> 1 3 4 4 1 0 1 1 2 2 , 0 4 2 4 2 4 1 5 5 5 2 -> 2 2 1 4 5 5 5 4 4 0 2 , 1 0 2 4 2 1 2 0 1 0 2 2 -> 1 0 2 4 1 2 2 0 1 0 2 2 , 0 4 3 5 3 4 2 2 2 0 2 1 0 1 5 2 -> 0 4 3 5 3 4 2 2 2 0 1 2 0 1 5 2 , 0 2 4 1 5 2 4 3 1 5 1 0 3 2 3 5 3 0 1 1 3 -> 0 2 4 1 5 2 4 1 3 5 1 0 3 2 3 5 3 0 1 1 3 , 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 1 3 4 4 1 0 -> 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 3 1 4 4 1 0 , 2 1 1 1 5 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 -> 2 1 1 5 1 5 1 5 5 5 4 3 2 2 1 5 5 5 5 1 2 2 3 1 1 , 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 2 3 4 0 2 0 0 4 0 2 -> 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 3 2 4 0 2 0 0 4 0 2 , 0 5 0 2 4 5 4 1 3 4 2 0 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 -> 0 5 0 2 4 5 4 1 3 4 0 2 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 , 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 0 5 5 1 3 0 0 2 -> 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 5 0 5 1 3 0 0 2 , 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 2 3 1 0 -> 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 3 2 1 0 , 2 0 5 4 3 3 2 5 3 5 5 5 1 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 -> 2 0 5 4 3 3 2 5 3 5 5 1 5 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 , 2 0 0 0 0 0 4 5 4 1 2 3 2 3 5 3 4 4 4 0 1 3 3 1 5 1 5 0 2 -> 2 0 0 0 0 0 4 5 4 1 2 3 2 3 3 5 4 4 4 0 1 3 3 1 5 1 5 0 2 , 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 4 5 5 2 3 3 3 -> 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 5 4 5 2 3 3 3 , 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 0 4 0 4 0 2 0 1 3 -> 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 4 0 0 4 0 2 0 1 3 , 5 4 4 0 4 4 4 2 1 2 3 0 3 2 1 1 2 1 3 0 1 1 4 1 1 4 0 0 5 5 -> 5 4 4 4 0 4 4 2 1 2 3 0 3 1 1 2 2 1 0 1 3 1 4 1 4 1 0 0 5 5 , 4 4 0 4 0 0 3 5 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 -> 4 4 0 4 0 0 5 3 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 } 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 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 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 1 0 3 2 -> 0 2 0 1 1 0 3 2 , 1 3 0 4 4 1 1 1 2 2 -> 1 3 4 4 1 0 1 1 2 2 , 0 4 2 4 2 4 1 5 5 5 2 -> 2 2 1 4 5 5 5 4 4 0 2 , 1 0 2 4 2 1 2 0 1 0 2 2 -> 1 0 2 4 1 2 2 0 1 0 2 2 , 0 4 3 5 3 4 2 2 2 0 2 1 0 1 5 2 -> 0 4 3 5 3 4 2 2 2 0 1 2 0 1 5 2 , 0 2 4 1 5 2 4 3 1 5 1 0 3 2 3 5 3 0 1 1 3 -> 0 2 4 1 5 2 4 1 3 5 1 0 3 2 3 5 3 0 1 1 3 , 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 1 3 4 4 1 0 -> 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 3 1 4 4 1 0 , 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 2 3 4 0 2 0 0 4 0 2 -> 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 3 2 4 0 2 0 0 4 0 2 , 0 5 0 2 4 5 4 1 3 4 2 0 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 -> 0 5 0 2 4 5 4 1 3 4 0 2 1 1 0 5 1 3 0 5 2 3 5 4 4 1 5 , 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 0 5 5 1 3 0 0 2 -> 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 5 0 5 1 3 0 0 2 , 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 2 3 1 0 -> 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 3 2 1 0 , 2 0 5 4 3 3 2 5 3 5 5 5 1 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 -> 2 0 5 4 3 3 2 5 3 5 5 1 5 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 , 2 0 0 0 0 0 4 5 4 1 2 3 2 3 5 3 4 4 4 0 1 3 3 1 5 1 5 0 2 -> 2 0 0 0 0 0 4 5 4 1 2 3 2 3 3 5 4 4 4 0 1 3 3 1 5 1 5 0 2 , 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 4 5 5 2 3 3 3 -> 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 5 4 5 2 3 3 3 , 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 0 4 0 4 0 2 0 1 3 -> 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 4 0 0 4 0 2 0 1 3 , 5 4 4 0 4 4 4 2 1 2 3 0 3 2 1 1 2 1 3 0 1 1 4 1 1 4 0 0 5 5 -> 5 4 4 4 0 4 4 2 1 2 3 0 3 1 1 2 2 1 0 1 3 1 4 1 4 1 0 0 5 5 , 4 4 0 4 0 0 3 5 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 -> 4 4 0 4 0 0 5 3 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 } 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 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 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 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 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0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 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 1 0 3 2 -> 0 2 0 1 1 0 3 2 , 1 3 0 4 4 1 1 1 2 2 -> 1 3 4 4 1 0 1 1 2 2 , 0 4 2 4 2 4 1 5 5 5 2 -> 2 2 1 4 5 5 5 4 4 0 2 , 1 0 2 4 2 1 2 0 1 0 2 2 -> 1 0 2 4 1 2 2 0 1 0 2 2 , 0 4 3 5 3 4 2 2 2 0 2 1 0 1 5 2 -> 0 4 3 5 3 4 2 2 2 0 1 2 0 1 5 2 , 0 2 4 1 5 2 4 3 1 5 1 0 3 2 3 5 3 0 1 1 3 -> 0 2 4 1 5 2 4 1 3 5 1 0 3 2 3 5 3 0 1 1 3 , 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 1 3 4 4 1 0 -> 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 3 1 4 4 1 0 , 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 2 3 4 0 2 0 0 4 0 2 -> 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 3 2 4 0 2 0 0 4 0 2 , 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 0 5 5 1 3 0 0 2 -> 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 5 0 5 1 3 0 0 2 , 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 2 3 1 0 -> 4 1 2 3 2 3 5 2 5 2 1 0 5 5 0 3 0 3 2 4 3 1 4 3 2 1 0 , 2 0 5 4 3 3 2 5 3 5 5 5 1 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 -> 2 0 5 4 3 3 2 5 3 5 5 1 5 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 , 2 0 0 0 0 0 4 5 4 1 2 3 2 3 5 3 4 4 4 0 1 3 3 1 5 1 5 0 2 -> 2 0 0 0 0 0 4 5 4 1 2 3 2 3 3 5 4 4 4 0 1 3 3 1 5 1 5 0 2 , 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 4 5 5 2 3 3 3 -> 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 5 4 5 2 3 3 3 , 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 0 4 0 4 0 2 0 1 3 -> 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 4 0 0 4 0 2 0 1 3 , 5 4 4 0 4 4 4 2 1 2 3 0 3 2 1 1 2 1 3 0 1 1 4 1 1 4 0 0 5 5 -> 5 4 4 4 0 4 4 2 1 2 3 0 3 1 1 2 2 1 0 1 3 1 4 1 4 1 0 0 5 5 , 4 4 0 4 0 0 3 5 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 -> 4 4 0 4 0 0 5 3 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 } 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 1 0 3 2 -> 0 2 0 1 1 0 3 2 , 1 3 0 4 4 1 1 1 2 2 -> 1 3 4 4 1 0 1 1 2 2 , 0 4 2 4 2 4 1 5 5 5 2 -> 2 2 1 4 5 5 5 4 4 0 2 , 1 0 2 4 2 1 2 0 1 0 2 2 -> 1 0 2 4 1 2 2 0 1 0 2 2 , 0 4 3 5 3 4 2 2 2 0 2 1 0 1 5 2 -> 0 4 3 5 3 4 2 2 2 0 1 2 0 1 5 2 , 0 2 4 1 5 2 4 3 1 5 1 0 3 2 3 5 3 0 1 1 3 -> 0 2 4 1 5 2 4 1 3 5 1 0 3 2 3 5 3 0 1 1 3 , 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 1 3 4 4 1 0 -> 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 3 1 4 4 1 0 , 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 2 3 4 0 2 0 0 4 0 2 -> 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 3 2 4 0 2 0 0 4 0 2 , 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 0 5 5 1 3 0 0 2 -> 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 5 0 5 1 3 0 0 2 , 2 0 5 4 3 3 2 5 3 5 5 5 1 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 -> 2 0 5 4 3 3 2 5 3 5 5 1 5 4 1 4 4 0 2 5 5 1 0 4 0 4 3 3 , 2 0 0 0 0 0 4 5 4 1 2 3 2 3 5 3 4 4 4 0 1 3 3 1 5 1 5 0 2 -> 2 0 0 0 0 0 4 5 4 1 2 3 2 3 3 5 4 4 4 0 1 3 3 1 5 1 5 0 2 , 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 4 5 5 2 3 3 3 -> 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 5 4 5 2 3 3 3 , 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 0 4 0 4 0 2 0 1 3 -> 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 4 0 0 4 0 2 0 1 3 , 5 4 4 0 4 4 4 2 1 2 3 0 3 2 1 1 2 1 3 0 1 1 4 1 1 4 0 0 5 5 -> 5 4 4 4 0 4 4 2 1 2 3 0 3 1 1 2 2 1 0 1 3 1 4 1 4 1 0 0 5 5 , 4 4 0 4 0 0 3 5 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 -> 4 4 0 4 0 0 5 3 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 29: 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 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 | \ / 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 1 0 3 2 -> 0 2 0 1 1 0 3 2 , 1 3 0 4 4 1 1 1 2 2 -> 1 3 4 4 1 0 1 1 2 2 , 0 4 2 4 2 4 1 5 5 5 2 -> 2 2 1 4 5 5 5 4 4 0 2 , 1 0 2 4 2 1 2 0 1 0 2 2 -> 1 0 2 4 1 2 2 0 1 0 2 2 , 0 4 3 5 3 4 2 2 2 0 2 1 0 1 5 2 -> 0 4 3 5 3 4 2 2 2 0 1 2 0 1 5 2 , 0 2 4 1 5 2 4 3 1 5 1 0 3 2 3 5 3 0 1 1 3 -> 0 2 4 1 5 2 4 1 3 5 1 0 3 2 3 5 3 0 1 1 3 , 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 1 3 4 4 1 0 -> 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 3 1 4 4 1 0 , 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 2 3 4 0 2 0 0 4 0 2 -> 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 3 2 4 0 2 0 0 4 0 2 , 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 0 5 5 1 3 0 0 2 -> 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 5 0 5 1 3 0 0 2 , 2 0 0 0 0 0 4 5 4 1 2 3 2 3 5 3 4 4 4 0 1 3 3 1 5 1 5 0 2 -> 2 0 0 0 0 0 4 5 4 1 2 3 2 3 3 5 4 4 4 0 1 3 3 1 5 1 5 0 2 , 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 4 5 5 2 3 3 3 -> 2 0 3 0 5 2 1 1 5 4 0 1 2 1 5 3 1 3 0 1 1 0 5 4 5 2 3 3 3 , 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 0 4 0 4 0 2 0 1 3 -> 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 4 0 0 4 0 2 0 1 3 , 5 4 4 0 4 4 4 2 1 2 3 0 3 2 1 1 2 1 3 0 1 1 4 1 1 4 0 0 5 5 -> 5 4 4 4 0 4 4 2 1 2 3 0 3 1 1 2 2 1 0 1 3 1 4 1 4 1 0 0 5 5 , 4 4 0 4 0 0 3 5 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 -> 4 4 0 4 0 0 5 3 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 } 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 3 2 -> 0 2 0 1 1 0 3 2 , 1 3 0 4 4 1 1 1 2 2 -> 1 3 4 4 1 0 1 1 2 2 , 0 4 2 4 2 4 1 5 5 5 2 -> 2 2 1 4 5 5 5 4 4 0 2 , 1 0 2 4 2 1 2 0 1 0 2 2 -> 1 0 2 4 1 2 2 0 1 0 2 2 , 0 4 3 5 3 4 2 2 2 0 2 1 0 1 5 2 -> 0 4 3 5 3 4 2 2 2 0 1 2 0 1 5 2 , 0 2 4 1 5 2 4 3 1 5 1 0 3 2 3 5 3 0 1 1 3 -> 0 2 4 1 5 2 4 1 3 5 1 0 3 2 3 5 3 0 1 1 3 , 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 1 3 4 4 1 0 -> 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 3 1 4 4 1 0 , 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 2 3 4 0 2 0 0 4 0 2 -> 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 3 2 4 0 2 0 0 4 0 2 , 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 0 5 5 1 3 0 0 2 -> 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 5 0 5 1 3 0 0 2 , 2 0 0 0 0 0 4 5 4 1 2 3 2 3 5 3 4 4 4 0 1 3 3 1 5 1 5 0 2 -> 2 0 0 0 0 0 4 5 4 1 2 3 2 3 3 5 4 4 4 0 1 3 3 1 5 1 5 0 2 , 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 0 4 0 4 0 2 0 1 3 -> 2 2 4 3 2 2 0 5 5 5 5 0 4 0 4 3 5 5 5 0 4 0 0 4 0 2 0 1 3 , 5 4 4 0 4 4 4 2 1 2 3 0 3 2 1 1 2 1 3 0 1 1 4 1 1 4 0 0 5 5 -> 5 4 4 4 0 4 4 2 1 2 3 0 3 1 1 2 2 1 0 1 3 1 4 1 4 1 0 0 5 5 , 4 4 0 4 0 0 3 5 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 -> 4 4 0 4 0 0 5 3 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 } 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 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3 3 5 1 1 5 0 0 0 3 2 3 3 1 4 4 1 0 , 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 2 3 4 0 2 0 0 4 0 2 -> 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 3 2 4 0 2 0 0 4 0 2 , 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 0 5 5 1 3 0 0 2 -> 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 5 0 5 1 3 0 0 2 , 2 0 0 0 0 0 4 5 4 1 2 3 2 3 5 3 4 4 4 0 1 3 3 1 5 1 5 0 2 -> 2 0 0 0 0 0 4 5 4 1 2 3 2 3 3 5 4 4 4 0 1 3 3 1 5 1 5 0 2 , 5 4 4 0 4 4 4 2 1 2 3 0 3 2 1 1 2 1 3 0 1 1 4 1 1 4 0 0 5 5 -> 5 4 4 4 0 4 4 2 1 2 3 0 3 1 1 2 2 1 0 1 3 1 4 1 4 1 0 0 5 5 , 4 4 0 4 0 0 3 5 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 -> 4 4 0 4 0 0 5 3 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 } 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 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5 1 5 0 2 -> 2 0 0 0 0 0 4 5 4 1 2 3 2 3 3 5 4 4 4 0 1 3 3 1 5 1 5 0 2 , 4 4 0 4 0 0 3 5 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 -> 4 4 0 4 0 0 5 3 5 0 0 0 0 5 0 5 4 3 1 1 1 3 1 1 2 1 0 1 2 5 } 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 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 10-rule system { 0 0 1 2 1 0 3 2 -> 0 2 0 1 1 0 3 2 , 1 3 0 4 4 1 1 1 2 2 -> 1 3 4 4 1 0 1 1 2 2 , 0 4 2 4 2 4 1 5 5 5 2 -> 2 2 1 4 5 5 5 4 4 0 2 , 1 0 2 4 2 1 2 0 1 0 2 2 -> 1 0 2 4 1 2 2 0 1 0 2 2 , 0 4 3 5 3 4 2 2 2 0 2 1 0 1 5 2 -> 0 4 3 5 3 4 2 2 2 0 1 2 0 1 5 2 , 0 2 4 1 5 2 4 3 1 5 1 0 3 2 3 5 3 0 1 1 3 -> 0 2 4 1 5 2 4 1 3 5 1 0 3 2 3 5 3 0 1 1 3 , 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 1 3 4 4 1 0 -> 4 1 5 3 3 3 5 1 1 5 0 0 0 3 2 3 3 1 4 4 1 0 , 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 2 3 4 0 2 0 0 4 0 2 -> 2 1 2 1 1 5 1 3 2 0 2 2 1 4 3 3 2 4 0 2 0 0 4 0 2 , 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 0 5 5 1 3 0 0 2 -> 5 4 3 1 0 2 2 2 5 4 3 4 4 4 0 2 1 2 5 5 0 5 1 3 0 0 2 , 2 0 0 0 0 0 4 5 4 1 2 3 2 3 5 3 4 4 4 0 1 3 3 1 5 1 5 0 2 -> 2 0 0 0 0 0 4 5 4 1 2 3 2 3 3 5 4 4 4 0 1 3 3 1 5 1 5 0 2 } 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 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 | \ / 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 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 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 1->0, 3->1, 0->2, 4->3, 2->4, 5->5 }, it remains to prove termination of the 9-rule system { 0 1 2 3 3 0 0 0 4 4 -> 0 1 3 3 0 2 0 0 4 4 , 2 3 4 3 4 3 0 5 5 5 4 -> 4 4 0 3 5 5 5 3 3 2 4 , 0 2 4 3 4 0 4 2 0 2 4 4 -> 0 2 4 3 0 4 4 2 0 2 4 4 , 2 3 1 5 1 3 4 4 4 2 4 0 2 0 5 4 -> 2 3 1 5 1 3 4 4 4 2 0 4 2 0 5 4 , 2 4 3 0 5 4 3 1 0 5 0 2 1 4 1 5 1 2 0 0 1 -> 2 4 3 0 5 4 3 0 1 5 0 2 1 4 1 5 1 2 0 0 1 , 3 0 5 1 1 1 5 0 0 5 2 2 2 1 4 1 0 1 3 3 0 2 -> 3 0 5 1 1 1 5 0 0 5 2 2 2 1 4 1 1 0 3 3 0 2 , 4 0 4 0 0 5 0 1 4 2 4 4 0 3 1 4 1 3 2 4 2 2 3 2 4 -> 4 0 4 0 0 5 0 1 4 2 4 4 0 3 1 1 4 3 2 4 2 2 3 2 4 , 5 3 1 0 2 4 4 4 5 3 1 3 3 3 2 4 0 4 5 2 5 5 0 1 2 2 4 -> 5 3 1 0 2 4 4 4 5 3 1 3 3 3 2 4 0 4 5 5 2 5 0 1 2 2 4 , 4 2 2 2 2 2 3 5 3 0 4 1 4 1 5 1 3 3 3 2 0 1 1 0 5 0 5 2 4 -> 4 2 2 2 2 2 3 5 3 0 4 1 4 1 1 5 3 3 3 2 0 1 1 0 5 0 5 2 4 } The system was reversed. After renaming modulo { 4->0, 0->1, 3->2, 2->3, 1->4, 5->5 }, it remains to prove termination of the 9-rule system { 0 0 1 1 1 2 2 3 4 1 -> 0 0 1 1 3 1 2 2 4 1 , 0 5 5 5 1 2 0 2 0 2 3 -> 0 3 2 2 5 5 5 2 1 0 0 , 0 0 3 1 3 0 1 0 2 0 3 1 -> 0 0 3 1 3 0 0 1 2 0 3 1 , 0 5 1 3 1 0 3 0 0 0 2 4 5 4 2 3 -> 0 5 1 3 0 1 3 0 0 0 2 4 5 4 2 3 , 4 1 1 3 4 5 4 0 4 3 1 5 1 4 2 0 5 1 2 0 3 -> 4 1 1 3 4 5 4 0 4 3 1 5 4 1 2 0 5 1 2 0 3 , 3 1 2 2 4 1 4 0 4 3 3 3 5 1 1 5 4 4 4 5 1 2 -> 3 1 2 2 1 4 4 0 4 3 3 3 5 1 1 5 4 4 4 5 1 2 , 0 3 2 3 3 0 3 2 4 0 4 2 1 0 0 3 0 4 1 5 1 1 0 1 0 -> 0 3 2 3 3 0 3 2 0 4 4 2 1 0 0 3 0 4 1 5 1 1 0 1 0 , 0 3 3 4 1 5 5 3 5 0 1 0 3 2 2 2 4 2 5 0 0 0 3 1 4 2 5 -> 0 3 3 4 1 5 3 5 5 0 1 0 3 2 2 2 4 2 5 0 0 0 3 1 4 2 5 , 0 3 5 1 5 1 4 4 1 3 2 2 2 4 5 4 0 4 0 1 2 5 2 3 3 3 3 3 0 -> 0 3 5 1 5 1 4 4 1 3 2 2 2 5 4 4 0 4 0 1 2 5 2 3 3 3 3 3 0 } Applying the dependency pairs transformation. After renaming modulo { (0,true)->0, (0,false)->1, (1,false)->2, (2,false)->3, (3,false)->4, (4,false)->5, (3,true)->6, (4,true)->7, (5,false)->8 }, it remains to prove termination of the 103-rule system { 0 1 2 2 2 3 3 4 5 2 -> 0 1 2 2 4 2 3 3 5 2 , 0 1 2 2 2 3 3 4 5 2 -> 0 2 2 4 2 3 3 5 2 , 0 1 2 2 2 3 3 4 5 2 -> 6 2 3 3 5 2 , 0 1 2 2 2 3 3 4 5 2 -> 7 2 , 0 8 8 8 2 3 1 3 1 3 4 -> 0 4 3 3 8 8 8 3 2 1 1 , 0 8 8 8 2 3 1 3 1 3 4 -> 6 3 3 8 8 8 3 2 1 1 , 0 8 8 8 2 3 1 3 1 3 4 -> 0 1 , 0 8 8 8 2 3 1 3 1 3 4 -> 0 , 0 1 4 2 4 1 2 1 3 1 4 2 -> 0 1 4 2 4 1 1 2 3 1 4 2 , 0 1 4 2 4 1 2 1 3 1 4 2 -> 0 4 2 4 1 1 2 3 1 4 2 , 0 1 4 2 4 1 2 1 3 1 4 2 -> 6 2 4 1 1 2 3 1 4 2 , 0 1 4 2 4 1 2 1 3 1 4 2 -> 6 1 1 2 3 1 4 2 , 0 1 4 2 4 1 2 1 3 1 4 2 -> 0 1 2 3 1 4 2 , 0 1 4 2 4 1 2 1 3 1 4 2 -> 0 2 3 1 4 2 , 0 1 4 2 4 1 2 1 3 1 4 2 -> 0 4 2 , 0 1 4 2 4 1 2 1 3 1 4 2 -> 6 2 , 0 8 2 4 2 1 4 1 1 1 3 5 8 5 3 4 -> 0 8 2 4 1 2 4 1 1 1 3 5 8 5 3 4 , 0 8 2 4 2 1 4 1 1 1 3 5 8 5 3 4 -> 6 1 2 4 1 1 1 3 5 8 5 3 4 , 0 8 2 4 2 1 4 1 1 1 3 5 8 5 3 4 -> 0 2 4 1 1 1 3 5 8 5 3 4 , 0 8 2 4 2 1 4 1 1 1 3 5 8 5 3 4 -> 6 1 1 1 3 5 8 5 3 4 , 0 8 2 4 2 1 4 1 1 1 3 5 8 5 3 4 -> 0 1 1 3 5 8 5 3 4 , 0 8 2 4 2 1 4 1 1 1 3 5 8 5 3 4 -> 0 1 3 5 8 5 3 4 , 0 8 2 4 2 1 4 1 1 1 3 5 8 5 3 4 -> 0 3 5 8 5 3 4 , 0 8 2 4 2 1 4 1 1 1 3 5 8 5 3 4 -> 7 8 5 3 4 , 0 8 2 4 2 1 4 1 1 1 3 5 8 5 3 4 -> 7 3 4 , 0 8 2 4 2 1 4 1 1 1 3 5 8 5 3 4 -> 6 , 7 2 2 4 5 8 5 1 5 4 2 8 2 5 3 1 8 2 3 1 4 -> 7 2 2 4 5 8 5 1 5 4 2 8 5 2 3 1 8 2 3 1 4 , 7 2 2 4 5 8 5 1 5 4 2 8 2 5 3 1 8 2 3 1 4 -> 6 5 8 5 1 5 4 2 8 5 2 3 1 8 2 3 1 4 , 7 2 2 4 5 8 5 1 5 4 2 8 2 5 3 1 8 2 3 1 4 -> 7 8 5 1 5 4 2 8 5 2 3 1 8 2 3 1 4 , 7 2 2 4 5 8 5 1 5 4 2 8 2 5 3 1 8 2 3 1 4 -> 7 1 5 4 2 8 5 2 3 1 8 2 3 1 4 , 7 2 2 4 5 8 5 1 5 4 2 8 2 5 3 1 8 2 3 1 4 -> 0 5 4 2 8 5 2 3 1 8 2 3 1 4 , 7 2 2 4 5 8 5 1 5 4 2 8 2 5 3 1 8 2 3 1 4 -> 7 4 2 8 5 2 3 1 8 2 3 1 4 , 7 2 2 4 5 8 5 1 5 4 2 8 2 5 3 1 8 2 3 1 4 -> 6 2 8 5 2 3 1 8 2 3 1 4 , 7 2 2 4 5 8 5 1 5 4 2 8 2 5 3 1 8 2 3 1 4 -> 7 2 3 1 8 2 3 1 4 , 7 2 2 4 5 8 5 1 5 4 2 8 2 5 3 1 8 2 3 1 4 -> 0 8 2 3 1 4 , 7 2 2 4 5 8 5 1 5 4 2 8 2 5 3 1 8 2 3 1 4 -> 0 4 , 7 2 2 4 5 8 5 1 5 4 2 8 2 5 3 1 8 2 3 1 4 -> 6 , 6 2 3 3 5 2 5 1 5 4 4 4 8 2 2 8 5 5 5 8 2 3 -> 6 2 3 3 2 5 5 1 5 4 4 4 8 2 2 8 5 5 5 8 2 3 , 6 2 3 3 5 2 5 1 5 4 4 4 8 2 2 8 5 5 5 8 2 3 -> 7 5 1 5 4 4 4 8 2 2 8 5 5 5 8 2 3 , 6 2 3 3 5 2 5 1 5 4 4 4 8 2 2 8 5 5 5 8 2 3 -> 7 1 5 4 4 4 8 2 2 8 5 5 5 8 2 3 , 6 2 3 3 5 2 5 1 5 4 4 4 8 2 2 8 5 5 5 8 2 3 -> 0 5 4 4 4 8 2 2 8 5 5 5 8 2 3 , 6 2 3 3 5 2 5 1 5 4 4 4 8 2 2 8 5 5 5 8 2 3 -> 7 4 4 4 8 2 2 8 5 5 5 8 2 3 , 6 2 3 3 5 2 5 1 5 4 4 4 8 2 2 8 5 5 5 8 2 3 -> 6 4 4 8 2 2 8 5 5 5 8 2 3 , 6 2 3 3 5 2 5 1 5 4 4 4 8 2 2 8 5 5 5 8 2 3 -> 6 4 8 2 2 8 5 5 5 8 2 3 , 6 2 3 3 5 2 5 1 5 4 4 4 8 2 2 8 5 5 5 8 2 3 -> 6 8 2 2 8 5 5 5 8 2 3 , 6 2 3 3 5 2 5 1 5 4 4 4 8 2 2 8 5 5 5 8 2 3 -> 7 5 5 8 2 3 , 6 2 3 3 5 2 5 1 5 4 4 4 8 2 2 8 5 5 5 8 2 3 -> 7 5 8 2 3 , 6 2 3 3 5 2 5 1 5 4 4 4 8 2 2 8 5 5 5 8 2 3 -> 7 8 2 3 , 0 4 3 4 4 1 4 3 5 1 5 3 2 1 1 4 1 5 2 8 2 2 1 2 1 -> 0 4 3 4 4 1 4 3 1 5 5 3 2 1 1 4 1 5 2 8 2 2 1 2 1 , 0 4 3 4 4 1 4 3 5 1 5 3 2 1 1 4 1 5 2 8 2 2 1 2 1 -> 6 3 4 4 1 4 3 1 5 5 3 2 1 1 4 1 5 2 8 2 2 1 2 1 , 0 4 3 4 4 1 4 3 5 1 5 3 2 1 1 4 1 5 2 8 2 2 1 2 1 -> 6 4 1 4 3 1 5 5 3 2 1 1 4 1 5 2 8 2 2 1 2 1 , 0 4 3 4 4 1 4 3 5 1 5 3 2 1 1 4 1 5 2 8 2 2 1 2 1 -> 6 1 4 3 1 5 5 3 2 1 1 4 1 5 2 8 2 2 1 2 1 , 0 4 3 4 4 1 4 3 5 1 5 3 2 1 1 4 1 5 2 8 2 2 1 2 1 -> 0 4 3 1 5 5 3 2 1 1 4 1 5 2 8 2 2 1 2 1 , 0 4 3 4 4 1 4 3 5 1 5 3 2 1 1 4 1 5 2 8 2 2 1 2 1 -> 6 3 1 5 5 3 2 1 1 4 1 5 2 8 2 2 1 2 1 , 0 4 3 4 4 1 4 3 5 1 5 3 2 1 1 4 1 5 2 8 2 2 1 2 1 -> 0 5 5 3 2 1 1 4 1 5 2 8 2 2 1 2 1 , 0 4 3 4 4 1 4 3 5 1 5 3 2 1 1 4 1 5 2 8 2 2 1 2 1 -> 7 5 3 2 1 1 4 1 5 2 8 2 2 1 2 1 , 0 4 3 4 4 1 4 3 5 1 5 3 2 1 1 4 1 5 2 8 2 2 1 2 1 -> 7 3 2 1 1 4 1 5 2 8 2 2 1 2 1 , 0 4 3 4 4 1 4 3 5 1 5 3 2 1 1 4 1 5 2 8 2 2 1 2 1 -> 0 1 4 1 5 2 8 2 2 1 2 1 , 0 4 3 4 4 1 4 3 5 1 5 3 2 1 1 4 1 5 2 8 2 2 1 2 1 -> 0 4 1 5 2 8 2 2 1 2 1 , 0 4 3 4 4 1 4 3 5 1 5 3 2 1 1 4 1 5 2 8 2 2 1 2 1 -> 6 1 5 2 8 2 2 1 2 1 , 0 4 3 4 4 1 4 3 5 1 5 3 2 1 1 4 1 5 2 8 2 2 1 2 1 -> 0 5 2 8 2 2 1 2 1 , 0 4 3 4 4 1 4 3 5 1 5 3 2 1 1 4 1 5 2 8 2 2 1 2 1 -> 7 2 8 2 2 1 2 1 , 0 4 3 4 4 1 4 3 5 1 5 3 2 1 1 4 1 5 2 8 2 2 1 2 1 -> 0 2 1 , 0 4 3 4 4 1 4 3 5 1 5 3 2 1 1 4 1 5 2 8 2 2 1 2 1 -> 0 , 0 4 4 5 2 8 8 4 8 1 2 1 4 3 3 3 5 3 8 1 1 1 4 2 5 3 8 -> 0 4 4 5 2 8 4 8 8 1 2 1 4 3 3 3 5 3 8 1 1 1 4 2 5 3 8 , 0 4 4 5 2 8 8 4 8 1 2 1 4 3 3 3 5 3 8 1 1 1 4 2 5 3 8 -> 6 4 5 2 8 4 8 8 1 2 1 4 3 3 3 5 3 8 1 1 1 4 2 5 3 8 , 0 4 4 5 2 8 8 4 8 1 2 1 4 3 3 3 5 3 8 1 1 1 4 2 5 3 8 -> 6 5 2 8 4 8 8 1 2 1 4 3 3 3 5 3 8 1 1 1 4 2 5 3 8 , 0 4 4 5 2 8 8 4 8 1 2 1 4 3 3 3 5 3 8 1 1 1 4 2 5 3 8 -> 7 2 8 4 8 8 1 2 1 4 3 3 3 5 3 8 1 1 1 4 2 5 3 8 , 0 4 4 5 2 8 8 4 8 1 2 1 4 3 3 3 5 3 8 1 1 1 4 2 5 3 8 -> 6 8 8 1 2 1 4 3 3 3 5 3 8 1 1 1 4 2 5 3 8 , 0 4 4 5 2 8 8 4 8 1 2 1 4 3 3 3 5 3 8 1 1 1 4 2 5 3 8 -> 0 2 1 4 3 3 3 5 3 8 1 1 1 4 2 5 3 8 , 0 4 4 5 2 8 8 4 8 1 2 1 4 3 3 3 5 3 8 1 1 1 4 2 5 3 8 -> 0 4 3 3 3 5 3 8 1 1 1 4 2 5 3 8 , 0 4 4 5 2 8 8 4 8 1 2 1 4 3 3 3 5 3 8 1 1 1 4 2 5 3 8 -> 6 3 3 3 5 3 8 1 1 1 4 2 5 3 8 , 0 4 4 5 2 8 8 4 8 1 2 1 4 3 3 3 5 3 8 1 1 1 4 2 5 3 8 -> 7 3 8 1 1 1 4 2 5 3 8 , 0 4 4 5 2 8 8 4 8 1 2 1 4 3 3 3 5 3 8 1 1 1 4 2 5 3 8 -> 0 1 1 4 2 5 3 8 , 0 4 4 5 2 8 8 4 8 1 2 1 4 3 3 3 5 3 8 1 1 1 4 2 5 3 8 -> 0 1 4 2 5 3 8 , 0 4 4 5 2 8 8 4 8 1 2 1 4 3 3 3 5 3 8 1 1 1 4 2 5 3 8 -> 0 4 2 5 3 8 , 0 4 4 5 2 8 8 4 8 1 2 1 4 3 3 3 5 3 8 1 1 1 4 2 5 3 8 -> 6 2 5 3 8 , 0 4 4 5 2 8 8 4 8 1 2 1 4 3 3 3 5 3 8 1 1 1 4 2 5 3 8 -> 7 3 8 , 0 4 8 2 8 2 5 5 2 4 3 3 3 5 8 5 1 5 1 2 3 8 3 4 4 4 4 4 1 -> 0 4 8 2 8 2 5 5 2 4 3 3 3 8 5 5 1 5 1 2 3 8 3 4 4 4 4 4 1 , 0 4 8 2 8 2 5 5 2 4 3 3 3 5 8 5 1 5 1 2 3 8 3 4 4 4 4 4 1 -> 6 8 2 8 2 5 5 2 4 3 3 3 8 5 5 1 5 1 2 3 8 3 4 4 4 4 4 1 , 0 4 8 2 8 2 5 5 2 4 3 3 3 5 8 5 1 5 1 2 3 8 3 4 4 4 4 4 1 -> 7 5 2 4 3 3 3 8 5 5 1 5 1 2 3 8 3 4 4 4 4 4 1 , 0 4 8 2 8 2 5 5 2 4 3 3 3 5 8 5 1 5 1 2 3 8 3 4 4 4 4 4 1 -> 7 2 4 3 3 3 8 5 5 1 5 1 2 3 8 3 4 4 4 4 4 1 , 0 4 8 2 8 2 5 5 2 4 3 3 3 5 8 5 1 5 1 2 3 8 3 4 4 4 4 4 1 -> 6 3 3 3 8 5 5 1 5 1 2 3 8 3 4 4 4 4 4 1 , 0 4 8 2 8 2 5 5 2 4 3 3 3 5 8 5 1 5 1 2 3 8 3 4 4 4 4 4 1 -> 7 5 1 5 1 2 3 8 3 4 4 4 4 4 1 , 0 4 8 2 8 2 5 5 2 4 3 3 3 5 8 5 1 5 1 2 3 8 3 4 4 4 4 4 1 -> 7 1 5 1 2 3 8 3 4 4 4 4 4 1 , 0 4 8 2 8 2 5 5 2 4 3 3 3 5 8 5 1 5 1 2 3 8 3 4 4 4 4 4 1 -> 0 5 1 2 3 8 3 4 4 4 4 4 1 , 0 4 8 2 8 2 5 5 2 4 3 3 3 5 8 5 1 5 1 2 3 8 3 4 4 4 4 4 1 -> 7 1 2 3 8 3 4 4 4 4 4 1 , 0 4 8 2 8 2 5 5 2 4 3 3 3 5 8 5 1 5 1 2 3 8 3 4 4 4 4 4 1 -> 0 2 3 8 3 4 4 4 4 4 1 , 0 4 8 2 8 2 5 5 2 4 3 3 3 5 8 5 1 5 1 2 3 8 3 4 4 4 4 4 1 -> 6 4 4 4 4 1 , 0 4 8 2 8 2 5 5 2 4 3 3 3 5 8 5 1 5 1 2 3 8 3 4 4 4 4 4 1 -> 6 4 4 4 1 , 0 4 8 2 8 2 5 5 2 4 3 3 3 5 8 5 1 5 1 2 3 8 3 4 4 4 4 4 1 -> 6 4 4 1 , 0 4 8 2 8 2 5 5 2 4 3 3 3 5 8 5 1 5 1 2 3 8 3 4 4 4 4 4 1 -> 6 4 1 , 0 4 8 2 8 2 5 5 2 4 3 3 3 5 8 5 1 5 1 2 3 8 3 4 4 4 4 4 1 -> 6 1 , 0 4 8 2 8 2 5 5 2 4 3 3 3 5 8 5 1 5 1 2 3 8 3 4 4 4 4 4 1 -> 0 , 1 1 2 2 2 3 3 4 5 2 ->= 1 1 2 2 4 2 3 3 5 2 , 1 8 8 8 2 3 1 3 1 3 4 ->= 1 4 3 3 8 8 8 3 2 1 1 , 1 1 4 2 4 1 2 1 3 1 4 2 ->= 1 1 4 2 4 1 1 2 3 1 4 2 , 1 8 2 4 2 1 4 1 1 1 3 5 8 5 3 4 ->= 1 8 2 4 1 2 4 1 1 1 3 5 8 5 3 4 , 5 2 2 4 5 8 5 1 5 4 2 8 2 5 3 1 8 2 3 1 4 ->= 5 2 2 4 5 8 5 1 5 4 2 8 5 2 3 1 8 2 3 1 4 , 4 2 3 3 5 2 5 1 5 4 4 4 8 2 2 8 5 5 5 8 2 3 ->= 4 2 3 3 2 5 5 1 5 4 4 4 8 2 2 8 5 5 5 8 2 3 , 1 4 3 4 4 1 4 3 5 1 5 3 2 1 1 4 1 5 2 8 2 2 1 2 1 ->= 1 4 3 4 4 1 4 3 1 5 5 3 2 1 1 4 1 5 2 8 2 2 1 2 1 , 1 4 4 5 2 8 8 4 8 1 2 1 4 3 3 3 5 3 8 1 1 1 4 2 5 3 8 ->= 1 4 4 5 2 8 4 8 8 1 2 1 4 3 3 3 5 3 8 1 1 1 4 2 5 3 8 , 1 4 8 2 8 2 5 5 2 4 3 3 3 5 8 5 1 5 1 2 3 8 3 4 4 4 4 4 1 ->= 1 4 8 2 8 2 5 5 2 4 3 3 3 8 5 5 1 5 1 2 3 8 3 4 4 4 4 4 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 is interpreted by / \ | 1 1 | | 0 1 | \ / 1 is interpreted by / \ | 1 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 | \ / 6 is interpreted by / \ | 1 1 | | 0 1 | \ / 7 is interpreted by / \ | 1 1 | | 0 1 | \ / 8 is interpreted by / \ | 1 1 | | 0 1 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 8->6, 7->7, 6->8 }, it remains to prove termination of the 18-rule system { 0 1 2 2 2 3 3 4 5 2 -> 0 1 2 2 4 2 3 3 5 2 , 0 6 6 6 2 3 1 3 1 3 4 -> 0 4 3 3 6 6 6 3 2 1 1 , 0 1 4 2 4 1 2 1 3 1 4 2 -> 0 1 4 2 4 1 1 2 3 1 4 2 , 0 6 2 4 2 1 4 1 1 1 3 5 6 5 3 4 -> 0 6 2 4 1 2 4 1 1 1 3 5 6 5 3 4 , 7 2 2 4 5 6 5 1 5 4 2 6 2 5 3 1 6 2 3 1 4 -> 7 2 2 4 5 6 5 1 5 4 2 6 5 2 3 1 6 2 3 1 4 , 8 2 3 3 5 2 5 1 5 4 4 4 6 2 2 6 5 5 5 6 2 3 -> 8 2 3 3 2 5 5 1 5 4 4 4 6 2 2 6 5 5 5 6 2 3 , 0 4 3 4 4 1 4 3 5 1 5 3 2 1 1 4 1 5 2 6 2 2 1 2 1 -> 0 4 3 4 4 1 4 3 1 5 5 3 2 1 1 4 1 5 2 6 2 2 1 2 1 , 0 4 4 5 2 6 6 4 6 1 2 1 4 3 3 3 5 3 6 1 1 1 4 2 5 3 6 -> 0 4 4 5 2 6 4 6 6 1 2 1 4 3 3 3 5 3 6 1 1 1 4 2 5 3 6 , 0 4 6 2 6 2 5 5 2 4 3 3 3 5 6 5 1 5 1 2 3 6 3 4 4 4 4 4 1 -> 0 4 6 2 6 2 5 5 2 4 3 3 3 6 5 5 1 5 1 2 3 6 3 4 4 4 4 4 1 , 1 1 2 2 2 3 3 4 5 2 ->= 1 1 2 2 4 2 3 3 5 2 , 1 6 6 6 2 3 1 3 1 3 4 ->= 1 4 3 3 6 6 6 3 2 1 1 , 1 1 4 2 4 1 2 1 3 1 4 2 ->= 1 1 4 2 4 1 1 2 3 1 4 2 , 1 6 2 4 2 1 4 1 1 1 3 5 6 5 3 4 ->= 1 6 2 4 1 2 4 1 1 1 3 5 6 5 3 4 , 5 2 2 4 5 6 5 1 5 4 2 6 2 5 3 1 6 2 3 1 4 ->= 5 2 2 4 5 6 5 1 5 4 2 6 5 2 3 1 6 2 3 1 4 , 4 2 3 3 5 2 5 1 5 4 4 4 6 2 2 6 5 5 5 6 2 3 ->= 4 2 3 3 2 5 5 1 5 4 4 4 6 2 2 6 5 5 5 6 2 3 , 1 4 3 4 4 1 4 3 5 1 5 3 2 1 1 4 1 5 2 6 2 2 1 2 1 ->= 1 4 3 4 4 1 4 3 1 5 5 3 2 1 1 4 1 5 2 6 2 2 1 2 1 , 1 4 4 5 2 6 6 4 6 1 2 1 4 3 3 3 5 3 6 1 1 1 4 2 5 3 6 ->= 1 4 4 5 2 6 4 6 6 1 2 1 4 3 3 3 5 3 6 1 1 1 4 2 5 3 6 , 1 4 6 2 6 2 5 5 2 4 3 3 3 5 6 5 1 5 1 2 3 6 3 4 4 4 4 4 1 ->= 1 4 6 2 6 2 5 5 2 4 3 3 3 6 5 5 1 5 1 2 3 6 3 4 4 4 4 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 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 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 1 | | 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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, 6->1, 2->2, 3->3, 1->4, 4->5, 5->6, 7->7, 8->8 }, it remains to prove termination of the 17-rule system { 0 1 1 1 2 3 4 3 4 3 5 -> 0 5 3 3 1 1 1 3 2 4 4 , 0 4 5 2 5 4 2 4 3 4 5 2 -> 0 4 5 2 5 4 4 2 3 4 5 2 , 0 1 2 5 2 4 5 4 4 4 3 6 1 6 3 5 -> 0 1 2 5 4 2 5 4 4 4 3 6 1 6 3 5 , 7 2 2 5 6 1 6 4 6 5 2 1 2 6 3 4 1 2 3 4 5 -> 7 2 2 5 6 1 6 4 6 5 2 1 6 2 3 4 1 2 3 4 5 , 8 2 3 3 6 2 6 4 6 5 5 5 1 2 2 1 6 6 6 1 2 3 -> 8 2 3 3 2 6 6 4 6 5 5 5 1 2 2 1 6 6 6 1 2 3 , 0 5 3 5 5 4 5 3 6 4 6 3 2 4 4 5 4 6 2 1 2 2 4 2 4 -> 0 5 3 5 5 4 5 3 4 6 6 3 2 4 4 5 4 6 2 1 2 2 4 2 4 , 0 5 5 6 2 1 1 5 1 4 2 4 5 3 3 3 6 3 1 4 4 4 5 2 6 3 1 -> 0 5 5 6 2 1 5 1 1 4 2 4 5 3 3 3 6 3 1 4 4 4 5 2 6 3 1 , 0 5 1 2 1 2 6 6 2 5 3 3 3 6 1 6 4 6 4 2 3 1 3 5 5 5 5 5 4 -> 0 5 1 2 1 2 6 6 2 5 3 3 3 1 6 6 4 6 4 2 3 1 3 5 5 5 5 5 4 , 4 4 2 2 2 3 3 5 6 2 ->= 4 4 2 2 5 2 3 3 6 2 , 4 1 1 1 2 3 4 3 4 3 5 ->= 4 5 3 3 1 1 1 3 2 4 4 , 4 4 5 2 5 4 2 4 3 4 5 2 ->= 4 4 5 2 5 4 4 2 3 4 5 2 , 4 1 2 5 2 4 5 4 4 4 3 6 1 6 3 5 ->= 4 1 2 5 4 2 5 4 4 4 3 6 1 6 3 5 , 6 2 2 5 6 1 6 4 6 5 2 1 2 6 3 4 1 2 3 4 5 ->= 6 2 2 5 6 1 6 4 6 5 2 1 6 2 3 4 1 2 3 4 5 , 5 2 3 3 6 2 6 4 6 5 5 5 1 2 2 1 6 6 6 1 2 3 ->= 5 2 3 3 2 6 6 4 6 5 5 5 1 2 2 1 6 6 6 1 2 3 , 4 5 3 5 5 4 5 3 6 4 6 3 2 4 4 5 4 6 2 1 2 2 4 2 4 ->= 4 5 3 5 5 4 5 3 4 6 6 3 2 4 4 5 4 6 2 1 2 2 4 2 4 , 4 5 5 6 2 1 1 5 1 4 2 4 5 3 3 3 6 3 1 4 4 4 5 2 6 3 1 ->= 4 5 5 6 2 1 5 1 1 4 2 4 5 3 3 3 6 3 1 4 4 4 5 2 6 3 1 , 4 5 1 2 1 2 6 6 2 5 3 3 3 6 1 6 4 6 4 2 3 1 3 5 5 5 5 5 4 ->= 4 5 1 2 1 2 6 6 2 5 3 3 3 1 6 6 4 6 4 2 3 1 3 5 5 5 5 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 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 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 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 | \ / 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 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 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 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 | | 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 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 4->1, 5->2, 2->3, 3->4, 1->5, 6->6, 7->7, 8->8 }, it remains to prove termination of the 16-rule system { 0 1 2 3 2 1 3 1 4 1 2 3 -> 0 1 2 3 2 1 1 3 4 1 2 3 , 0 5 3 2 3 1 2 1 1 1 4 6 5 6 4 2 -> 0 5 3 2 1 3 2 1 1 1 4 6 5 6 4 2 , 7 3 3 2 6 5 6 1 6 2 3 5 3 6 4 1 5 3 4 1 2 -> 7 3 3 2 6 5 6 1 6 2 3 5 6 3 4 1 5 3 4 1 2 , 8 3 4 4 6 3 6 1 6 2 2 2 5 3 3 5 6 6 6 5 3 4 -> 8 3 4 4 3 6 6 1 6 2 2 2 5 3 3 5 6 6 6 5 3 4 , 0 2 4 2 2 1 2 4 6 1 6 4 3 1 1 2 1 6 3 5 3 3 1 3 1 -> 0 2 4 2 2 1 2 4 1 6 6 4 3 1 1 2 1 6 3 5 3 3 1 3 1 , 0 2 2 6 3 5 5 2 5 1 3 1 2 4 4 4 6 4 5 1 1 1 2 3 6 4 5 -> 0 2 2 6 3 5 2 5 5 1 3 1 2 4 4 4 6 4 5 1 1 1 2 3 6 4 5 , 0 2 5 3 5 3 6 6 3 2 4 4 4 6 5 6 1 6 1 3 4 5 4 2 2 2 2 2 1 -> 0 2 5 3 5 3 6 6 3 2 4 4 4 5 6 6 1 6 1 3 4 5 4 2 2 2 2 2 1 , 1 1 3 3 3 4 4 2 6 3 ->= 1 1 3 3 2 3 4 4 6 3 , 1 5 5 5 3 4 1 4 1 4 2 ->= 1 2 4 4 5 5 5 4 3 1 1 , 1 1 2 3 2 1 3 1 4 1 2 3 ->= 1 1 2 3 2 1 1 3 4 1 2 3 , 1 5 3 2 3 1 2 1 1 1 4 6 5 6 4 2 ->= 1 5 3 2 1 3 2 1 1 1 4 6 5 6 4 2 , 6 3 3 2 6 5 6 1 6 2 3 5 3 6 4 1 5 3 4 1 2 ->= 6 3 3 2 6 5 6 1 6 2 3 5 6 3 4 1 5 3 4 1 2 , 2 3 4 4 6 3 6 1 6 2 2 2 5 3 3 5 6 6 6 5 3 4 ->= 2 3 4 4 3 6 6 1 6 2 2 2 5 3 3 5 6 6 6 5 3 4 , 1 2 4 2 2 1 2 4 6 1 6 4 3 1 1 2 1 6 3 5 3 3 1 3 1 ->= 1 2 4 2 2 1 2 4 1 6 6 4 3 1 1 2 1 6 3 5 3 3 1 3 1 , 1 2 2 6 3 5 5 2 5 1 3 1 2 4 4 4 6 4 5 1 1 1 2 3 6 4 5 ->= 1 2 2 6 3 5 2 5 5 1 3 1 2 4 4 4 6 4 5 1 1 1 2 3 6 4 5 , 1 2 5 3 5 3 6 6 3 2 4 4 4 6 5 6 1 6 1 3 4 5 4 2 2 2 2 2 1 ->= 1 2 5 3 5 3 6 6 3 2 4 4 4 5 6 6 1 6 1 3 4 5 4 2 2 2 2 2 1 } 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 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 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 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 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 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 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 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, 5->1, 3->2, 2->3, 1->4, 4->5, 6->6, 7->7, 8->8 }, it remains to prove termination of the 15-rule system { 0 1 2 3 2 4 3 4 4 4 5 6 1 6 5 3 -> 0 1 2 3 4 2 3 4 4 4 5 6 1 6 5 3 , 7 2 2 3 6 1 6 4 6 3 2 1 2 6 5 4 1 2 5 4 3 -> 7 2 2 3 6 1 6 4 6 3 2 1 6 2 5 4 1 2 5 4 3 , 8 2 5 5 6 2 6 4 6 3 3 3 1 2 2 1 6 6 6 1 2 5 -> 8 2 5 5 2 6 6 4 6 3 3 3 1 2 2 1 6 6 6 1 2 5 , 0 3 5 3 3 4 3 5 6 4 6 5 2 4 4 3 4 6 2 1 2 2 4 2 4 -> 0 3 5 3 3 4 3 5 4 6 6 5 2 4 4 3 4 6 2 1 2 2 4 2 4 , 0 3 3 6 2 1 1 3 1 4 2 4 3 5 5 5 6 5 1 4 4 4 3 2 6 5 1 -> 0 3 3 6 2 1 3 1 1 4 2 4 3 5 5 5 6 5 1 4 4 4 3 2 6 5 1 , 0 3 1 2 1 2 6 6 2 3 5 5 5 6 1 6 4 6 4 2 5 1 5 3 3 3 3 3 4 -> 0 3 1 2 1 2 6 6 2 3 5 5 5 1 6 6 4 6 4 2 5 1 5 3 3 3 3 3 4 , 4 4 2 2 2 5 5 3 6 2 ->= 4 4 2 2 3 2 5 5 6 2 , 4 1 1 1 2 5 4 5 4 5 3 ->= 4 3 5 5 1 1 1 5 2 4 4 , 4 4 3 2 3 4 2 4 5 4 3 2 ->= 4 4 3 2 3 4 4 2 5 4 3 2 , 4 1 2 3 2 4 3 4 4 4 5 6 1 6 5 3 ->= 4 1 2 3 4 2 3 4 4 4 5 6 1 6 5 3 , 6 2 2 3 6 1 6 4 6 3 2 1 2 6 5 4 1 2 5 4 3 ->= 6 2 2 3 6 1 6 4 6 3 2 1 6 2 5 4 1 2 5 4 3 , 3 2 5 5 6 2 6 4 6 3 3 3 1 2 2 1 6 6 6 1 2 5 ->= 3 2 5 5 2 6 6 4 6 3 3 3 1 2 2 1 6 6 6 1 2 5 , 4 3 5 3 3 4 3 5 6 4 6 5 2 4 4 3 4 6 2 1 2 2 4 2 4 ->= 4 3 5 3 3 4 3 5 4 6 6 5 2 4 4 3 4 6 2 1 2 2 4 2 4 , 4 3 3 6 2 1 1 3 1 4 2 4 3 5 5 5 6 5 1 4 4 4 3 2 6 5 1 ->= 4 3 3 6 2 1 3 1 1 4 2 4 3 5 5 5 6 5 1 4 4 4 3 2 6 5 1 , 4 3 1 2 1 2 6 6 2 3 5 5 5 6 1 6 4 6 4 2 5 1 5 3 3 3 3 3 4 ->= 4 3 1 2 1 2 6 6 2 3 5 5 5 1 6 6 4 6 4 2 5 1 5 3 3 3 3 3 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 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 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 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 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 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 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 { 7->0, 2->1, 3->2, 6->3, 1->4, 4->5, 5->6, 8->7, 0->8 }, it remains to prove termination of the 14-rule system { 0 1 1 2 3 4 3 5 3 2 1 4 1 3 6 5 4 1 6 5 2 -> 0 1 1 2 3 4 3 5 3 2 1 4 3 1 6 5 4 1 6 5 2 , 7 1 6 6 3 1 3 5 3 2 2 2 4 1 1 4 3 3 3 4 1 6 -> 7 1 6 6 1 3 3 5 3 2 2 2 4 1 1 4 3 3 3 4 1 6 , 8 2 6 2 2 5 2 6 3 5 3 6 1 5 5 2 5 3 1 4 1 1 5 1 5 -> 8 2 6 2 2 5 2 6 5 3 3 6 1 5 5 2 5 3 1 4 1 1 5 1 5 , 8 2 2 3 1 4 4 2 4 5 1 5 2 6 6 6 3 6 4 5 5 5 2 1 3 6 4 -> 8 2 2 3 1 4 2 4 4 5 1 5 2 6 6 6 3 6 4 5 5 5 2 1 3 6 4 , 8 2 4 1 4 1 3 3 1 2 6 6 6 3 4 3 5 3 5 1 6 4 6 2 2 2 2 2 5 -> 8 2 4 1 4 1 3 3 1 2 6 6 6 4 3 3 5 3 5 1 6 4 6 2 2 2 2 2 5 , 5 5 1 1 1 6 6 2 3 1 ->= 5 5 1 1 2 1 6 6 3 1 , 5 4 4 4 1 6 5 6 5 6 2 ->= 5 2 6 6 4 4 4 6 1 5 5 , 5 5 2 1 2 5 1 5 6 5 2 1 ->= 5 5 2 1 2 5 5 1 6 5 2 1 , 5 4 1 2 1 5 2 5 5 5 6 3 4 3 6 2 ->= 5 4 1 2 5 1 2 5 5 5 6 3 4 3 6 2 , 3 1 1 2 3 4 3 5 3 2 1 4 1 3 6 5 4 1 6 5 2 ->= 3 1 1 2 3 4 3 5 3 2 1 4 3 1 6 5 4 1 6 5 2 , 2 1 6 6 3 1 3 5 3 2 2 2 4 1 1 4 3 3 3 4 1 6 ->= 2 1 6 6 1 3 3 5 3 2 2 2 4 1 1 4 3 3 3 4 1 6 , 5 2 6 2 2 5 2 6 3 5 3 6 1 5 5 2 5 3 1 4 1 1 5 1 5 ->= 5 2 6 2 2 5 2 6 5 3 3 6 1 5 5 2 5 3 1 4 1 1 5 1 5 , 5 2 2 3 1 4 4 2 4 5 1 5 2 6 6 6 3 6 4 5 5 5 2 1 3 6 4 ->= 5 2 2 3 1 4 2 4 4 5 1 5 2 6 6 6 3 6 4 5 5 5 2 1 3 6 4 , 5 2 4 1 4 1 3 3 1 2 6 6 6 3 4 3 5 3 5 1 6 4 6 2 2 2 2 2 5 ->= 5 2 4 1 4 1 3 3 1 2 6 6 6 4 3 3 5 3 5 1 6 4 6 2 2 2 2 2 5 } 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 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 8->7 }, it remains to prove termination of the 13-rule system { 0 1 1 2 3 4 3 5 3 2 1 4 1 3 6 5 4 1 6 5 2 -> 0 1 1 2 3 4 3 5 3 2 1 4 3 1 6 5 4 1 6 5 2 , 7 2 6 2 2 5 2 6 3 5 3 6 1 5 5 2 5 3 1 4 1 1 5 1 5 -> 7 2 6 2 2 5 2 6 5 3 3 6 1 5 5 2 5 3 1 4 1 1 5 1 5 , 7 2 2 3 1 4 4 2 4 5 1 5 2 6 6 6 3 6 4 5 5 5 2 1 3 6 4 -> 7 2 2 3 1 4 2 4 4 5 1 5 2 6 6 6 3 6 4 5 5 5 2 1 3 6 4 , 7 2 4 1 4 1 3 3 1 2 6 6 6 3 4 3 5 3 5 1 6 4 6 2 2 2 2 2 5 -> 7 2 4 1 4 1 3 3 1 2 6 6 6 4 3 3 5 3 5 1 6 4 6 2 2 2 2 2 5 , 5 5 1 1 1 6 6 2 3 1 ->= 5 5 1 1 2 1 6 6 3 1 , 5 4 4 4 1 6 5 6 5 6 2 ->= 5 2 6 6 4 4 4 6 1 5 5 , 5 5 2 1 2 5 1 5 6 5 2 1 ->= 5 5 2 1 2 5 5 1 6 5 2 1 , 5 4 1 2 1 5 2 5 5 5 6 3 4 3 6 2 ->= 5 4 1 2 5 1 2 5 5 5 6 3 4 3 6 2 , 3 1 1 2 3 4 3 5 3 2 1 4 1 3 6 5 4 1 6 5 2 ->= 3 1 1 2 3 4 3 5 3 2 1 4 3 1 6 5 4 1 6 5 2 , 2 1 6 6 3 1 3 5 3 2 2 2 4 1 1 4 3 3 3 4 1 6 ->= 2 1 6 6 1 3 3 5 3 2 2 2 4 1 1 4 3 3 3 4 1 6 , 5 2 6 2 2 5 2 6 3 5 3 6 1 5 5 2 5 3 1 4 1 1 5 1 5 ->= 5 2 6 2 2 5 2 6 5 3 3 6 1 5 5 2 5 3 1 4 1 1 5 1 5 , 5 2 2 3 1 4 4 2 4 5 1 5 2 6 6 6 3 6 4 5 5 5 2 1 3 6 4 ->= 5 2 2 3 1 4 2 4 4 5 1 5 2 6 6 6 3 6 4 5 5 5 2 1 3 6 4 , 5 2 4 1 4 1 3 3 1 2 6 6 6 3 4 3 5 3 5 1 6 4 6 2 2 2 2 2 5 ->= 5 2 4 1 4 1 3 3 1 2 6 6 6 4 3 3 5 3 5 1 6 4 6 2 2 2 2 2 5 } 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 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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 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 12-rule system { 0 1 1 2 3 4 3 5 3 2 1 4 1 3 6 5 4 1 6 5 2 -> 0 1 1 2 3 4 3 5 3 2 1 4 3 1 6 5 4 1 6 5 2 , 7 2 2 3 1 4 4 2 4 5 1 5 2 6 6 6 3 6 4 5 5 5 2 1 3 6 4 -> 7 2 2 3 1 4 2 4 4 5 1 5 2 6 6 6 3 6 4 5 5 5 2 1 3 6 4 , 7 2 4 1 4 1 3 3 1 2 6 6 6 3 4 3 5 3 5 1 6 4 6 2 2 2 2 2 5 -> 7 2 4 1 4 1 3 3 1 2 6 6 6 4 3 3 5 3 5 1 6 4 6 2 2 2 2 2 5 , 5 5 1 1 1 6 6 2 3 1 ->= 5 5 1 1 2 1 6 6 3 1 , 5 4 4 4 1 6 5 6 5 6 2 ->= 5 2 6 6 4 4 4 6 1 5 5 , 5 5 2 1 2 5 1 5 6 5 2 1 ->= 5 5 2 1 2 5 5 1 6 5 2 1 , 5 4 1 2 1 5 2 5 5 5 6 3 4 3 6 2 ->= 5 4 1 2 5 1 2 5 5 5 6 3 4 3 6 2 , 3 1 1 2 3 4 3 5 3 2 1 4 1 3 6 5 4 1 6 5 2 ->= 3 1 1 2 3 4 3 5 3 2 1 4 3 1 6 5 4 1 6 5 2 , 2 1 6 6 3 1 3 5 3 2 2 2 4 1 1 4 3 3 3 4 1 6 ->= 2 1 6 6 1 3 3 5 3 2 2 2 4 1 1 4 3 3 3 4 1 6 , 5 2 6 2 2 5 2 6 3 5 3 6 1 5 5 2 5 3 1 4 1 1 5 1 5 ->= 5 2 6 2 2 5 2 6 5 3 3 6 1 5 5 2 5 3 1 4 1 1 5 1 5 , 5 2 2 3 1 4 4 2 4 5 1 5 2 6 6 6 3 6 4 5 5 5 2 1 3 6 4 ->= 5 2 2 3 1 4 2 4 4 5 1 5 2 6 6 6 3 6 4 5 5 5 2 1 3 6 4 , 5 2 4 1 4 1 3 3 1 2 6 6 6 3 4 3 5 3 5 1 6 4 6 2 2 2 2 2 5 ->= 5 2 4 1 4 1 3 3 1 2 6 6 6 4 3 3 5 3 5 1 6 4 6 2 2 2 2 2 5 } 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 11-rule system { 0 1 1 2 3 4 3 5 3 2 1 4 1 3 6 5 4 1 6 5 2 -> 0 1 1 2 3 4 3 5 3 2 1 4 3 1 6 5 4 1 6 5 2 , 7 2 4 1 4 1 3 3 1 2 6 6 6 3 4 3 5 3 5 1 6 4 6 2 2 2 2 2 5 -> 7 2 4 1 4 1 3 3 1 2 6 6 6 4 3 3 5 3 5 1 6 4 6 2 2 2 2 2 5 , 5 5 1 1 1 6 6 2 3 1 ->= 5 5 1 1 2 1 6 6 3 1 , 5 4 4 4 1 6 5 6 5 6 2 ->= 5 2 6 6 4 4 4 6 1 5 5 , 5 5 2 1 2 5 1 5 6 5 2 1 ->= 5 5 2 1 2 5 5 1 6 5 2 1 , 5 4 1 2 1 5 2 5 5 5 6 3 4 3 6 2 ->= 5 4 1 2 5 1 2 5 5 5 6 3 4 3 6 2 , 3 1 1 2 3 4 3 5 3 2 1 4 1 3 6 5 4 1 6 5 2 ->= 3 1 1 2 3 4 3 5 3 2 1 4 3 1 6 5 4 1 6 5 2 , 2 1 6 6 3 1 3 5 3 2 2 2 4 1 1 4 3 3 3 4 1 6 ->= 2 1 6 6 1 3 3 5 3 2 2 2 4 1 1 4 3 3 3 4 1 6 , 5 2 6 2 2 5 2 6 3 5 3 6 1 5 5 2 5 3 1 4 1 1 5 1 5 ->= 5 2 6 2 2 5 2 6 5 3 3 6 1 5 5 2 5 3 1 4 1 1 5 1 5 , 5 2 2 3 1 4 4 2 4 5 1 5 2 6 6 6 3 6 4 5 5 5 2 1 3 6 4 ->= 5 2 2 3 1 4 2 4 4 5 1 5 2 6 6 6 3 6 4 5 5 5 2 1 3 6 4 , 5 2 4 1 4 1 3 3 1 2 6 6 6 3 4 3 5 3 5 1 6 4 6 2 2 2 2 2 5 ->= 5 2 4 1 4 1 3 3 1 2 6 6 6 4 3 3 5 3 5 1 6 4 6 2 2 2 2 2 5 } 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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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renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6 }, it remains to prove termination of the 10-rule system { 0 1 1 2 3 4 3 5 3 2 1 4 1 3 6 5 4 1 6 5 2 -> 0 1 1 2 3 4 3 5 3 2 1 4 3 1 6 5 4 1 6 5 2 , 5 5 1 1 1 6 6 2 3 1 ->= 5 5 1 1 2 1 6 6 3 1 , 5 4 4 4 1 6 5 6 5 6 2 ->= 5 2 6 6 4 4 4 6 1 5 5 , 5 5 2 1 2 5 1 5 6 5 2 1 ->= 5 5 2 1 2 5 5 1 6 5 2 1 , 5 4 1 2 1 5 2 5 5 5 6 3 4 3 6 2 ->= 5 4 1 2 5 1 2 5 5 5 6 3 4 3 6 2 , 3 1 1 2 3 4 3 5 3 2 1 4 1 3 6 5 4 1 6 5 2 ->= 3 1 1 2 3 4 3 5 3 2 1 4 3 1 6 5 4 1 6 5 2 , 2 1 6 6 3 1 3 5 3 2 2 2 4 1 1 4 3 3 3 4 1 6 ->= 2 1 6 6 1 3 3 5 3 2 2 2 4 1 1 4 3 3 3 4 1 6 , 5 2 6 2 2 5 2 6 3 5 3 6 1 5 5 2 5 3 1 4 1 1 5 1 5 ->= 5 2 6 2 2 5 2 6 5 3 3 6 1 5 5 2 5 3 1 4 1 1 5 1 5 , 5 2 2 3 1 4 4 2 4 5 1 5 2 6 6 6 3 6 4 5 5 5 2 1 3 6 4 ->= 5 2 2 3 1 4 2 4 4 5 1 5 2 6 6 6 3 6 4 5 5 5 2 1 3 6 4 , 5 2 4 1 4 1 3 3 1 2 6 6 6 3 4 3 5 3 5 1 6 4 6 2 2 2 2 2 5 ->= 5 2 4 1 4 1 3 3 1 2 6 6 6 4 3 3 5 3 5 1 6 4 6 2 2 2 2 2 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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, 1->1, 6->2, 2->3, 3->4, 4->5 }, it remains to prove termination of the 9-rule system { 0 0 1 1 1 2 2 3 4 1 ->= 0 0 1 1 3 1 2 2 4 1 , 0 5 5 5 1 2 0 2 0 2 3 ->= 0 3 2 2 5 5 5 2 1 0 0 , 0 0 3 1 3 0 1 0 2 0 3 1 ->= 0 0 3 1 3 0 0 1 2 0 3 1 , 0 5 1 3 1 0 3 0 0 0 2 4 5 4 2 3 ->= 0 5 1 3 0 1 3 0 0 0 2 4 5 4 2 3 , 4 1 1 3 4 5 4 0 4 3 1 5 1 4 2 0 5 1 2 0 3 ->= 4 1 1 3 4 5 4 0 4 3 1 5 4 1 2 0 5 1 2 0 3 , 3 1 2 2 4 1 4 0 4 3 3 3 5 1 1 5 4 4 4 5 1 2 ->= 3 1 2 2 1 4 4 0 4 3 3 3 5 1 1 5 4 4 4 5 1 2 , 0 3 2 3 3 0 3 2 4 0 4 2 1 0 0 3 0 4 1 5 1 1 0 1 0 ->= 0 3 2 3 3 0 3 2 0 4 4 2 1 0 0 3 0 4 1 5 1 1 0 1 0 , 0 3 3 4 1 5 5 3 5 0 1 0 3 2 2 2 4 2 5 0 0 0 3 1 4 2 5 ->= 0 3 3 4 1 5 3 5 5 0 1 0 3 2 2 2 4 2 5 0 0 0 3 1 4 2 5 , 0 3 5 1 5 1 4 4 1 3 2 2 2 4 5 4 0 4 0 1 2 5 2 3 3 3 3 3 0 ->= 0 3 5 1 5 1 4 4 1 3 2 2 2 5 4 4 0 4 0 1 2 5 2 3 3 3 3 3 0 } The system is trivially terminating.