YES After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, it remains to prove termination of the 49-rule system { 0 1 0 2 -> 0 0 3 1 2 , 0 1 3 4 -> 0 4 1 0 3 , 0 1 3 4 -> 0 4 1 1 3 , 0 1 3 4 -> 0 4 1 3 1 , 0 2 1 4 -> 0 4 1 2 3 , 0 2 1 4 -> 0 4 1 3 2 , 0 2 1 4 -> 2 0 4 1 4 , 0 2 1 4 -> 5 5 0 4 1 2 , 0 2 1 5 -> 5 0 4 1 2 , 0 2 2 4 -> 0 4 2 2 5 , 0 2 2 4 -> 0 4 2 5 2 , 3 4 0 2 -> 3 0 4 5 2 , 3 4 0 2 -> 3 5 0 4 2 , 0 0 1 4 5 -> 0 4 1 0 3 5 , 0 1 0 2 4 -> 2 0 0 4 1 1 , 0 1 2 3 4 -> 2 0 4 1 0 3 , 0 1 3 3 4 -> 0 0 3 1 3 4 , 0 1 4 0 2 -> 0 4 1 5 0 2 , 0 1 4 1 5 -> 2 5 0 4 1 1 , 0 1 4 3 4 -> 0 4 0 3 1 4 , 0 1 4 3 4 -> 3 0 4 1 5 4 , 0 1 4 3 5 -> 5 4 5 0 3 1 , 0 1 5 0 2 -> 0 0 4 1 2 5 , 0 1 5 1 4 -> 4 5 0 3 1 1 , 0 2 1 4 4 -> 0 4 1 2 4 3 , 0 2 1 4 5 -> 0 4 1 2 5 2 , 0 2 1 5 4 -> 5 0 2 0 4 1 , 0 2 4 1 5 -> 5 0 4 1 5 2 , 0 2 4 3 5 -> 0 4 5 2 5 3 , 0 2 5 1 4 -> 0 0 5 4 1 2 , 3 0 1 3 2 -> 0 3 1 0 3 2 , 3 0 2 1 4 -> 4 0 4 1 3 2 , 3 0 2 1 5 -> 5 3 2 0 4 1 , 3 0 4 0 2 -> 0 3 4 0 4 2 , 3 0 4 0 2 -> 0 4 1 2 0 3 , 3 0 5 1 4 -> 3 0 4 1 1 5 , 3 0 5 1 5 -> 0 4 1 3 5 5 , 3 2 4 1 2 -> 3 1 2 2 5 4 , 3 2 4 1 5 -> 3 1 4 5 2 5 , 3 4 0 1 2 -> 0 4 2 0 3 1 , 3 4 0 1 4 -> 0 4 1 5 3 4 , 3 4 0 1 5 -> 0 4 1 5 5 3 , 3 4 0 2 4 -> 0 3 4 0 4 2 , 3 4 1 2 4 -> 0 4 1 2 4 3 , 3 4 1 3 5 -> 4 3 0 3 1 5 , 3 4 3 0 2 -> 3 3 0 4 1 2 , 3 4 5 0 2 -> 0 3 0 4 2 5 , 3 5 0 2 2 -> 0 3 2 5 2 5 , 3 5 2 1 4 -> 3 5 1 0 4 2 } Applying sparse 2-untiling [Hofbauer/Geser/Waldmann, FSCD 2019]. After renaming modulo { 0->0, 2->1, 1->2, 4->3, 3->4, 5->5 }, it remains to prove termination of the 30-rule system { 0 1 2 3 -> 0 3 2 1 4 , 0 1 2 3 -> 0 3 2 4 1 , 0 1 2 3 -> 1 0 3 2 3 , 0 1 2 3 -> 5 5 0 3 2 1 , 0 1 2 5 -> 5 0 3 2 1 , 0 1 1 3 -> 0 3 1 1 5 , 0 1 1 3 -> 0 3 1 5 1 , 4 3 0 1 -> 4 0 3 5 1 , 4 3 0 1 -> 4 5 0 3 1 , 0 1 2 3 3 -> 0 3 2 1 3 4 , 0 1 2 3 5 -> 0 3 2 1 5 1 , 0 1 2 5 3 -> 5 0 1 0 3 2 , 0 1 3 2 5 -> 5 0 3 2 5 1 , 0 1 3 4 5 -> 0 3 5 1 5 4 , 0 1 5 2 3 -> 0 0 5 3 2 1 , 4 0 1 2 3 -> 3 0 3 2 4 1 , 4 0 1 2 5 -> 5 4 1 0 3 2 , 4 0 3 0 1 -> 0 4 3 0 3 1 , 4 0 3 0 1 -> 0 3 2 1 0 4 , 4 0 5 2 3 -> 4 0 3 2 2 5 , 4 0 5 2 5 -> 0 3 2 4 5 5 , 4 1 3 2 1 -> 4 2 1 1 5 3 , 4 1 3 2 5 -> 4 2 3 5 1 5 , 4 3 0 1 3 -> 0 4 3 0 3 1 , 4 3 2 1 3 -> 0 3 2 1 3 4 , 4 3 2 4 5 -> 3 4 0 4 2 5 , 4 3 4 0 1 -> 4 4 0 3 2 1 , 4 3 5 0 1 -> 0 4 0 3 1 5 , 4 5 0 1 1 -> 0 4 1 5 1 5 , 4 5 1 2 3 -> 4 5 2 0 3 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 5->3, 3->4, 4->5 }, it remains to prove termination of the 23-rule system { 0 1 2 3 -> 3 0 4 2 1 , 0 1 1 4 -> 0 4 1 1 3 , 0 1 1 4 -> 0 4 1 3 1 , 5 4 0 1 -> 5 0 4 3 1 , 5 4 0 1 -> 5 3 0 4 1 , 0 1 2 3 4 -> 3 0 1 0 4 2 , 0 1 4 2 3 -> 3 0 4 2 3 1 , 0 1 4 5 3 -> 0 4 3 1 3 5 , 0 1 3 2 4 -> 0 0 3 4 2 1 , 5 0 1 2 3 -> 3 5 1 0 4 2 , 5 0 4 0 1 -> 0 5 4 0 4 1 , 5 0 4 0 1 -> 0 4 2 1 0 5 , 5 0 3 2 4 -> 5 0 4 2 2 3 , 5 0 3 2 3 -> 0 4 2 5 3 3 , 5 1 4 2 1 -> 5 2 1 1 3 4 , 5 1 4 2 3 -> 5 2 4 3 1 3 , 5 4 0 1 4 -> 0 5 4 0 4 1 , 5 4 2 1 4 -> 0 4 2 1 4 5 , 5 4 2 5 3 -> 4 5 0 5 2 3 , 5 4 5 0 1 -> 5 5 0 4 2 1 , 5 4 3 0 1 -> 0 5 0 4 1 3 , 5 3 0 1 1 -> 0 5 1 3 1 3 , 5 3 1 2 4 -> 5 3 2 0 4 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, it remains to prove termination of the 21-rule system { 0 1 2 3 -> 3 0 4 2 1 , 5 4 0 1 -> 5 0 4 3 1 , 5 4 0 1 -> 5 3 0 4 1 , 0 1 2 3 4 -> 3 0 1 0 4 2 , 0 1 4 2 3 -> 3 0 4 2 3 1 , 0 1 4 5 3 -> 0 4 3 1 3 5 , 0 1 3 2 4 -> 0 0 3 4 2 1 , 5 0 1 2 3 -> 3 5 1 0 4 2 , 5 0 4 0 1 -> 0 5 4 0 4 1 , 5 0 4 0 1 -> 0 4 2 1 0 5 , 5 0 3 2 4 -> 5 0 4 2 2 3 , 5 0 3 2 3 -> 0 4 2 5 3 3 , 5 1 4 2 1 -> 5 2 1 1 3 4 , 5 1 4 2 3 -> 5 2 4 3 1 3 , 5 4 0 1 4 -> 0 5 4 0 4 1 , 5 4 2 1 4 -> 0 4 2 1 4 5 , 5 4 2 5 3 -> 4 5 0 5 2 3 , 5 4 5 0 1 -> 5 5 0 4 2 1 , 5 4 3 0 1 -> 0 5 0 4 1 3 , 5 3 0 1 1 -> 0 5 1 3 1 3 , 5 3 1 2 4 -> 5 3 2 0 4 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 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 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 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | \ / 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 1 2 3 -> 3 0 4 2 1 , 5 4 0 1 -> 5 0 4 3 1 , 5 4 0 1 -> 5 3 0 4 1 , 0 1 4 2 3 -> 3 0 4 2 3 1 , 0 1 4 5 3 -> 0 4 3 1 3 5 , 0 1 3 2 4 -> 0 0 3 4 2 1 , 5 0 1 2 3 -> 3 5 1 0 4 2 , 5 0 4 0 1 -> 0 5 4 0 4 1 , 5 0 4 0 1 -> 0 4 2 1 0 5 , 5 0 3 2 4 -> 5 0 4 2 2 3 , 5 0 3 2 3 -> 0 4 2 5 3 3 , 5 1 4 2 1 -> 5 2 1 1 3 4 , 5 1 4 2 3 -> 5 2 4 3 1 3 , 5 4 0 1 4 -> 0 5 4 0 4 1 , 5 4 2 1 4 -> 0 4 2 1 4 5 , 5 4 2 5 3 -> 4 5 0 5 2 3 , 5 4 5 0 1 -> 5 5 0 4 2 1 , 5 4 3 0 1 -> 0 5 0 4 1 3 , 5 3 0 1 1 -> 0 5 1 3 1 3 , 5 3 1 2 4 -> 5 3 2 0 4 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 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 1 2 3 -> 3 0 4 2 1 , 5 4 0 1 -> 5 0 4 3 1 , 5 4 0 1 -> 5 3 0 4 1 , 0 1 4 2 3 -> 3 0 4 2 3 1 , 0 1 4 5 3 -> 0 4 3 1 3 5 , 5 0 1 2 3 -> 3 5 1 0 4 2 , 5 0 4 0 1 -> 0 5 4 0 4 1 , 5 0 4 0 1 -> 0 4 2 1 0 5 , 5 0 3 2 4 -> 5 0 4 2 2 3 , 5 0 3 2 3 -> 0 4 2 5 3 3 , 5 1 4 2 1 -> 5 2 1 1 3 4 , 5 1 4 2 3 -> 5 2 4 3 1 3 , 5 4 0 1 4 -> 0 5 4 0 4 1 , 5 4 2 1 4 -> 0 4 2 1 4 5 , 5 4 2 5 3 -> 4 5 0 5 2 3 , 5 4 5 0 1 -> 5 5 0 4 2 1 , 5 4 3 0 1 -> 0 5 0 4 1 3 , 5 3 0 1 1 -> 0 5 1 3 1 3 , 5 3 1 2 4 -> 5 3 2 0 4 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 1 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 1 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 1 0 0 0 0 | \ / After renaming modulo { 5->0, 0->1, 3->2, 2->3, 4->4, 1->5 }, it remains to prove termination of the 7-rule system { 0 1 2 3 4 -> 0 1 4 3 3 2 , 0 1 2 3 2 -> 1 4 3 0 2 2 , 0 5 4 3 5 -> 0 3 5 5 2 4 , 0 5 4 3 2 -> 0 3 4 2 5 2 , 0 4 3 5 4 -> 1 4 3 5 4 0 , 0 4 3 0 2 -> 4 0 1 0 3 2 , 0 2 5 3 4 -> 0 2 3 1 4 5 } 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 1 0 0 0 1 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 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 | \ / 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 1 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 1 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, it remains to prove termination of the 6-rule system { 0 1 2 3 4 -> 0 1 4 3 3 2 , 0 5 4 3 5 -> 0 3 5 5 2 4 , 0 5 4 3 2 -> 0 3 4 2 5 2 , 0 4 3 5 4 -> 1 4 3 5 4 0 , 0 4 3 0 2 -> 4 0 1 0 3 2 , 0 2 5 3 4 -> 0 2 3 1 4 5 } 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 1 0 0 0 1 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 1 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, it remains to prove termination of the 5-rule system { 0 1 2 3 4 -> 0 1 4 3 3 2 , 0 5 4 3 5 -> 0 3 5 5 2 4 , 0 5 4 3 2 -> 0 3 4 2 5 2 , 0 4 3 5 4 -> 1 4 3 5 4 0 , 0 2 5 3 4 -> 0 2 3 1 4 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 1 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 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 4-rule system { 0 1 2 3 4 -> 0 1 4 3 3 2 , 0 5 4 3 5 -> 0 3 5 5 2 4 , 0 5 4 3 2 -> 0 3 4 2 5 2 , 0 2 5 3 4 -> 0 2 3 1 4 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 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 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 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 5->1, 4->2, 3->3, 2->4, 1->5 }, it remains to prove termination of the 3-rule system { 0 1 2 3 1 -> 0 3 1 1 4 2 , 0 1 2 3 4 -> 0 3 2 4 1 4 , 0 4 1 3 2 -> 0 4 3 5 2 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 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 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 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, it remains to prove termination of the 2-rule system { 0 1 2 3 4 -> 0 3 2 4 1 4 , 0 4 1 3 2 -> 0 4 3 5 2 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 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 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 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 4->1, 1->2, 3->3, 2->4, 5->5 }, it remains to prove termination of the 1-rule system { 0 1 2 3 4 -> 0 1 3 5 4 2 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 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 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 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { }, it remains to prove termination of the 0-rule system { } The system is trivially terminating.