YES After renaming modulo { 0->0, 1->1, 2->2 }, it remains to prove termination of the 5-rule system { 0 1 2 1 -> 1 2 1 1 0 1 2 0 1 2 , 0 1 2 1 -> 1 2 1 1 0 1 2 0 1 2 0 1 2 , 0 1 2 1 -> 1 2 1 1 0 1 2 0 1 2 0 1 2 0 1 2 , 0 1 2 1 -> 1 2 1 1 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 , 0 1 2 1 -> 1 2 1 1 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 } Applying sparse 2-tiling [Hofbauer/Geser/Waldmann, FSCD 2019]. After renaming modulo { (1,0)->0, (0,1)->1, (1,2)->2, (2,1)->3, (1,1)->4, (2,0)->5, (2,2)->6 }, it remains to prove termination of the 30-rule system { 0 1 2 3 0 -> 4 2 3 4 0 1 2 5 1 2 5 , 0 1 2 3 4 -> 4 2 3 4 0 1 2 5 1 2 3 , 0 1 2 3 2 -> 4 2 3 4 0 1 2 5 1 2 6 , 5 1 2 3 0 -> 3 2 3 4 0 1 2 5 1 2 5 , 5 1 2 3 4 -> 3 2 3 4 0 1 2 5 1 2 3 , 5 1 2 3 2 -> 3 2 3 4 0 1 2 5 1 2 6 , 0 1 2 3 0 -> 4 2 3 4 0 1 2 5 1 2 5 1 2 5 , 0 1 2 3 4 -> 4 2 3 4 0 1 2 5 1 2 5 1 2 3 , 0 1 2 3 2 -> 4 2 3 4 0 1 2 5 1 2 5 1 2 6 , 5 1 2 3 0 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 , 5 1 2 3 4 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 3 , 5 1 2 3 2 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 6 , 0 1 2 3 0 -> 4 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 , 0 1 2 3 4 -> 4 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 3 , 0 1 2 3 2 -> 4 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 6 , 5 1 2 3 0 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 , 5 1 2 3 4 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 3 , 5 1 2 3 2 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 6 , 0 1 2 3 0 -> 4 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 5 , 0 1 2 3 4 -> 4 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 3 , 0 1 2 3 2 -> 4 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 6 , 5 1 2 3 0 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 5 , 5 1 2 3 4 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 3 , 5 1 2 3 2 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 6 , 0 1 2 3 0 -> 4 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 5 1 2 5 , 0 1 2 3 4 -> 4 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 5 1 2 3 , 0 1 2 3 2 -> 4 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 5 1 2 6 , 5 1 2 3 0 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 5 1 2 5 , 5 1 2 3 4 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 5 1 2 3 , 5 1 2 3 2 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 5 1 2 6 } 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 1 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 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6 }, it remains to prove termination of the 25-rule system { 0 1 2 3 4 -> 4 2 3 4 0 1 2 5 1 2 3 , 0 1 2 3 2 -> 4 2 3 4 0 1 2 5 1 2 6 , 5 1 2 3 0 -> 3 2 3 4 0 1 2 5 1 2 5 , 5 1 2 3 4 -> 3 2 3 4 0 1 2 5 1 2 3 , 5 1 2 3 2 -> 3 2 3 4 0 1 2 5 1 2 6 , 0 1 2 3 4 -> 4 2 3 4 0 1 2 5 1 2 5 1 2 3 , 0 1 2 3 2 -> 4 2 3 4 0 1 2 5 1 2 5 1 2 6 , 5 1 2 3 0 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 , 5 1 2 3 4 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 3 , 5 1 2 3 2 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 6 , 0 1 2 3 4 -> 4 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 3 , 0 1 2 3 2 -> 4 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 6 , 5 1 2 3 0 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 , 5 1 2 3 4 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 3 , 5 1 2 3 2 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 6 , 0 1 2 3 4 -> 4 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 3 , 0 1 2 3 2 -> 4 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 6 , 5 1 2 3 0 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 5 , 5 1 2 3 4 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 3 , 5 1 2 3 2 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 6 , 0 1 2 3 4 -> 4 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 5 1 2 3 , 0 1 2 3 2 -> 4 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 5 1 2 6 , 5 1 2 3 0 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 5 1 2 5 , 5 1 2 3 4 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 5 1 2 3 , 5 1 2 3 2 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 5 1 2 6 } 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 1 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 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6 }, it remains to prove termination of the 20-rule system { 0 1 2 3 2 -> 4 2 3 4 0 1 2 5 1 2 6 , 5 1 2 3 0 -> 3 2 3 4 0 1 2 5 1 2 5 , 5 1 2 3 4 -> 3 2 3 4 0 1 2 5 1 2 3 , 5 1 2 3 2 -> 3 2 3 4 0 1 2 5 1 2 6 , 0 1 2 3 2 -> 4 2 3 4 0 1 2 5 1 2 5 1 2 6 , 5 1 2 3 0 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 , 5 1 2 3 4 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 3 , 5 1 2 3 2 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 6 , 0 1 2 3 2 -> 4 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 6 , 5 1 2 3 0 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 , 5 1 2 3 4 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 3 , 5 1 2 3 2 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 6 , 0 1 2 3 2 -> 4 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 6 , 5 1 2 3 0 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 5 , 5 1 2 3 4 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 3 , 5 1 2 3 2 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 6 , 0 1 2 3 2 -> 4 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 5 1 2 6 , 5 1 2 3 0 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 5 1 2 5 , 5 1 2 3 4 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 5 1 2 3 , 5 1 2 3 2 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 5 1 2 6 } 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 1 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 0 0 0 0 1 | \ / 5 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 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6 }, it remains to prove termination of the 15-rule system { 0 1 2 3 2 -> 4 2 3 4 0 1 2 5 1 2 6 , 5 1 2 3 4 -> 3 2 3 4 0 1 2 5 1 2 3 , 5 1 2 3 2 -> 3 2 3 4 0 1 2 5 1 2 6 , 0 1 2 3 2 -> 4 2 3 4 0 1 2 5 1 2 5 1 2 6 , 5 1 2 3 4 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 3 , 5 1 2 3 2 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 6 , 0 1 2 3 2 -> 4 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 6 , 5 1 2 3 4 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 3 , 5 1 2 3 2 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 6 , 0 1 2 3 2 -> 4 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 6 , 5 1 2 3 4 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 3 , 5 1 2 3 2 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 6 , 0 1 2 3 2 -> 4 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 5 1 2 6 , 5 1 2 3 4 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 5 1 2 3 , 5 1 2 3 2 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 5 1 2 6 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 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 1 | \ / 5 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 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After 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 2 3 2 -> 4 2 3 4 0 1 2 5 1 2 6 , 5 1 2 3 2 -> 3 2 3 4 0 1 2 5 1 2 6 , 0 1 2 3 2 -> 4 2 3 4 0 1 2 5 1 2 5 1 2 6 , 5 1 2 3 2 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 6 , 0 1 2 3 2 -> 4 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 6 , 5 1 2 3 2 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 6 , 0 1 2 3 2 -> 4 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 6 , 5 1 2 3 2 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 6 , 0 1 2 3 2 -> 4 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 5 1 2 6 , 5 1 2 3 2 -> 3 2 3 4 0 1 2 5 1 2 5 1 2 5 1 2 5 1 2 5 1 2 6 } 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 1 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 1 0 0 0 | | 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 5->0, 1->1, 2->2, 3->3, 4->4, 0->5, 6->6 }, it remains to prove termination of the 5-rule system { 0 1 2 3 2 -> 3 2 3 4 5 1 2 0 1 2 6 , 0 1 2 3 2 -> 3 2 3 4 5 1 2 0 1 2 0 1 2 6 , 0 1 2 3 2 -> 3 2 3 4 5 1 2 0 1 2 0 1 2 0 1 2 6 , 0 1 2 3 2 -> 3 2 3 4 5 1 2 0 1 2 0 1 2 0 1 2 0 1 2 6 , 0 1 2 3 2 -> 3 2 3 4 5 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 6 } 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 1 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 1 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 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { }, it remains to prove termination of the 0-rule system { } The system is trivially terminating.