YES After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, it remains to prove termination of the 48-rule system { 0 0 0 -> 0 0 1 0 1 , 0 2 0 -> 0 0 2 1 1 , 0 3 2 -> 2 1 3 0 , 0 4 2 -> 4 1 1 1 0 2 , 3 0 4 -> 0 1 3 4 1 , 3 2 0 -> 0 2 1 3 , 3 2 0 -> 3 0 2 1 , 3 2 0 -> 0 1 2 1 3 , 3 2 0 -> 3 0 1 2 1 4 , 3 2 4 -> 1 2 1 3 3 4 , 3 2 4 -> 4 1 2 1 1 3 , 3 2 5 -> 1 3 5 2 , 3 2 5 -> 3 1 4 5 2 , 3 2 5 -> 1 1 3 3 5 2 , 3 2 5 -> 1 3 4 5 4 2 , 3 5 0 -> 3 1 0 5 1 1 , 5 0 2 -> 1 1 0 2 5 , 5 0 4 -> 0 5 4 1 1 , 5 2 4 -> 5 2 1 1 3 4 , 5 3 2 -> 1 1 3 5 1 2 , 5 5 0 -> 5 1 1 5 0 , 0 0 2 4 -> 0 4 0 2 1 1 , 0 3 1 2 -> 1 1 3 0 2 , 0 3 2 4 -> 2 1 3 0 4 4 , 0 4 3 2 -> 2 3 4 0 1 , 3 0 2 4 -> 3 0 4 2 1 1 , 3 0 5 4 -> 3 4 0 5 1 3 , 3 1 0 0 -> 0 1 1 3 0 1 , 3 2 4 0 -> 3 1 0 4 2 , 3 2 4 5 -> 3 1 4 2 1 5 , 3 2 5 4 -> 3 4 3 5 2 , 3 5 3 2 -> 3 3 0 2 5 , 4 0 4 2 -> 4 4 2 1 3 0 , 4 3 2 0 -> 0 2 1 3 4 , 5 4 1 0 -> 5 1 1 4 0 1 , 5 5 0 0 -> 1 1 0 5 5 0 , 5 5 2 2 -> 5 5 1 1 2 2 , 0 0 1 2 4 -> 0 0 2 1 1 4 , 0 5 3 1 2 -> 5 2 1 3 1 0 , 0 5 5 1 0 -> 5 0 0 5 1 1 , 3 0 1 4 5 -> 3 4 0 5 1 1 , 3 0 3 1 2 -> 0 2 1 1 3 3 , 3 2 2 0 4 -> 3 2 2 0 1 4 , 3 5 1 4 0 -> 1 3 3 4 5 0 , 3 5 3 0 4 -> 3 0 1 5 3 4 , 5 1 0 2 4 -> 2 1 5 4 0 3 , 5 1 3 2 0 -> 2 3 5 0 1 1 , 5 4 2 0 2 -> 5 0 4 2 1 2 } The system was reversed. After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, it remains to prove termination of the 48-rule system { 0 0 0 -> 1 0 1 0 0 , 0 2 0 -> 1 1 2 0 0 , 2 3 0 -> 0 3 1 2 , 2 4 0 -> 2 0 1 1 1 4 , 4 0 3 -> 1 4 3 1 0 , 0 2 3 -> 3 1 2 0 , 0 2 3 -> 1 2 0 3 , 0 2 3 -> 3 1 2 1 0 , 0 2 3 -> 4 1 2 1 0 3 , 4 2 3 -> 4 3 3 1 2 1 , 4 2 3 -> 3 1 1 2 1 4 , 5 2 3 -> 2 5 3 1 , 5 2 3 -> 2 5 4 1 3 , 5 2 3 -> 2 5 3 3 1 1 , 5 2 3 -> 2 4 5 4 3 1 , 0 5 3 -> 1 1 5 0 1 3 , 2 0 5 -> 5 2 0 1 1 , 4 0 5 -> 1 1 4 5 0 , 4 2 5 -> 4 3 1 1 2 5 , 2 3 5 -> 2 1 5 3 1 1 , 0 5 5 -> 0 5 1 1 5 , 4 2 0 0 -> 1 1 2 0 4 0 , 2 1 3 0 -> 2 0 3 1 1 , 4 2 3 0 -> 4 4 0 3 1 2 , 2 3 4 0 -> 1 0 4 3 2 , 4 2 0 3 -> 1 1 2 4 0 3 , 4 5 0 3 -> 3 1 5 0 4 3 , 0 0 1 3 -> 1 0 3 1 1 0 , 0 4 2 3 -> 2 4 0 1 3 , 5 4 2 3 -> 5 1 2 4 1 3 , 4 5 2 3 -> 2 5 3 4 3 , 2 3 5 3 -> 5 2 0 3 3 , 2 4 0 4 -> 0 3 1 2 4 4 , 0 2 3 4 -> 4 3 1 2 0 , 0 1 4 5 -> 1 0 4 1 1 5 , 0 0 5 5 -> 0 5 5 0 1 1 , 2 2 5 5 -> 2 2 1 1 5 5 , 4 2 1 0 0 -> 4 1 1 2 0 0 , 2 1 3 5 0 -> 0 1 3 1 2 5 , 0 1 5 5 0 -> 1 1 5 0 0 5 , 5 4 1 0 3 -> 1 1 5 0 4 3 , 2 1 3 0 3 -> 3 3 1 1 2 0 , 4 0 2 2 3 -> 4 1 0 2 2 3 , 0 4 1 5 3 -> 0 5 4 3 3 1 , 4 0 3 5 3 -> 4 3 5 1 0 3 , 4 2 0 1 5 -> 3 0 4 5 1 2 , 0 2 3 1 5 -> 1 1 0 5 3 2 , 2 0 2 4 5 -> 2 1 2 4 0 5 } Applying the dependency pairs transformation. After renaming modulo { (0,true)->0, (0,false)->1, (1,false)->2, (2,false)->3, (2,true)->4, (3,false)->5, (4,false)->6, (4,true)->7, (5,true)->8, (5,false)->9 }, it remains to prove termination of the 188-rule system { 0 1 1 -> 0 2 1 1 , 0 1 1 -> 0 1 , 0 1 1 -> 0 , 0 3 1 -> 4 1 1 , 0 3 1 -> 0 1 , 0 3 1 -> 0 , 4 5 1 -> 0 5 2 3 , 4 5 1 -> 4 , 4 6 1 -> 4 1 2 2 2 6 , 4 6 1 -> 0 2 2 2 6 , 4 6 1 -> 7 , 7 1 5 -> 7 5 2 1 , 7 1 5 -> 0 , 0 3 5 -> 4 1 , 0 3 5 -> 0 , 0 3 5 -> 4 1 5 , 0 3 5 -> 0 5 , 0 3 5 -> 4 2 1 , 0 3 5 -> 7 2 3 2 1 5 , 0 3 5 -> 4 2 1 5 , 7 3 5 -> 7 5 5 2 3 2 , 7 3 5 -> 4 2 , 7 3 5 -> 4 2 6 , 7 3 5 -> 7 , 8 3 5 -> 4 9 5 2 , 8 3 5 -> 8 5 2 , 8 3 5 -> 4 9 6 2 5 , 8 3 5 -> 8 6 2 5 , 8 3 5 -> 7 2 5 , 8 3 5 -> 4 9 5 5 2 2 , 8 3 5 -> 8 5 5 2 2 , 8 3 5 -> 4 6 9 6 5 2 , 8 3 5 -> 7 9 6 5 2 , 8 3 5 -> 8 6 5 2 , 8 3 5 -> 7 5 2 , 0 9 5 -> 8 1 2 5 , 0 9 5 -> 0 2 5 , 4 1 9 -> 8 3 1 2 2 , 4 1 9 -> 4 1 2 2 , 4 1 9 -> 0 2 2 , 7 1 9 -> 7 9 1 , 7 1 9 -> 8 1 , 7 1 9 -> 0 , 7 3 9 -> 7 5 2 2 3 9 , 7 3 9 -> 4 9 , 7 3 9 -> 8 , 4 5 9 -> 4 2 9 5 2 2 , 4 5 9 -> 8 5 2 2 , 0 9 9 -> 0 9 2 2 9 , 0 9 9 -> 8 2 2 9 , 0 9 9 -> 8 , 7 3 1 1 -> 4 1 6 1 , 7 3 1 1 -> 0 6 1 , 7 3 1 1 -> 7 1 , 7 3 1 1 -> 0 , 4 2 5 1 -> 4 1 5 2 2 , 4 2 5 1 -> 0 5 2 2 , 7 3 5 1 -> 7 6 1 5 2 3 , 7 3 5 1 -> 7 1 5 2 3 , 7 3 5 1 -> 0 5 2 3 , 7 3 5 1 -> 4 , 4 5 6 1 -> 0 6 5 3 , 4 5 6 1 -> 7 5 3 , 4 5 6 1 -> 4 , 7 3 1 5 -> 4 6 1 5 , 7 3 1 5 -> 7 1 5 , 7 3 1 5 -> 0 5 , 7 9 1 5 -> 8 1 6 5 , 7 9 1 5 -> 0 6 5 , 7 9 1 5 -> 7 5 , 0 1 2 5 -> 0 5 2 2 1 , 0 1 2 5 -> 0 , 0 6 3 5 -> 4 6 1 2 5 , 0 6 3 5 -> 7 1 2 5 , 0 6 3 5 -> 0 2 5 , 8 6 3 5 -> 8 2 3 6 2 5 , 8 6 3 5 -> 4 6 2 5 , 8 6 3 5 -> 7 2 5 , 7 9 3 5 -> 4 9 5 6 5 , 7 9 3 5 -> 8 5 6 5 , 7 9 3 5 -> 7 5 , 4 5 9 5 -> 8 3 1 5 5 , 4 5 9 5 -> 4 1 5 5 , 4 5 9 5 -> 0 5 5 , 4 6 1 6 -> 0 5 2 3 6 6 , 4 6 1 6 -> 4 6 6 , 4 6 1 6 -> 7 6 , 4 6 1 6 -> 7 , 0 3 5 6 -> 7 5 2 3 1 , 0 3 5 6 -> 4 1 , 0 3 5 6 -> 0 , 0 2 6 9 -> 0 6 2 2 9 , 0 2 6 9 -> 7 2 2 9 , 0 2 6 9 -> 8 , 0 1 9 9 -> 0 9 9 1 2 2 , 0 1 9 9 -> 8 9 1 2 2 , 0 1 9 9 -> 8 1 2 2 , 0 1 9 9 -> 0 2 2 , 4 3 9 9 -> 4 3 2 2 9 9 , 4 3 9 9 -> 4 2 2 9 9 , 4 3 9 9 -> 8 9 , 4 3 9 9 -> 8 , 7 3 2 1 1 -> 7 2 2 3 1 1 , 7 3 2 1 1 -> 4 1 1 , 7 3 2 1 1 -> 0 1 , 7 3 2 1 1 -> 0 , 4 2 5 9 1 -> 0 2 5 2 3 9 , 4 2 5 9 1 -> 4 9 , 4 2 5 9 1 -> 8 , 0 2 9 9 1 -> 8 1 1 9 , 0 2 9 9 1 -> 0 1 9 , 0 2 9 9 1 -> 0 9 , 0 2 9 9 1 -> 8 , 8 6 2 1 5 -> 8 1 6 5 , 8 6 2 1 5 -> 0 6 5 , 8 6 2 1 5 -> 7 5 , 4 2 5 1 5 -> 4 1 , 4 2 5 1 5 -> 0 , 7 1 3 3 5 -> 7 2 1 3 3 5 , 7 1 3 3 5 -> 0 3 3 5 , 7 1 3 3 5 -> 4 3 5 , 7 1 3 3 5 -> 4 5 , 0 6 2 9 5 -> 0 9 6 5 5 2 , 0 6 2 9 5 -> 8 6 5 5 2 , 0 6 2 9 5 -> 7 5 5 2 , 7 1 5 9 5 -> 7 5 9 2 1 5 , 7 1 5 9 5 -> 8 2 1 5 , 7 1 5 9 5 -> 0 5 , 7 3 1 2 9 -> 0 6 9 2 3 , 7 3 1 2 9 -> 7 9 2 3 , 7 3 1 2 9 -> 8 2 3 , 7 3 1 2 9 -> 4 , 0 3 5 2 9 -> 0 9 5 3 , 0 3 5 2 9 -> 8 5 3 , 0 3 5 2 9 -> 4 , 4 1 3 6 9 -> 4 2 3 6 1 9 , 4 1 3 6 9 -> 4 6 1 9 , 4 1 3 6 9 -> 7 1 9 , 4 1 3 6 9 -> 0 9 , 4 1 3 6 9 -> 8 , 1 1 1 ->= 2 1 2 1 1 , 1 3 1 ->= 2 2 3 1 1 , 3 5 1 ->= 1 5 2 3 , 3 6 1 ->= 3 1 2 2 2 6 , 6 1 5 ->= 2 6 5 2 1 , 1 3 5 ->= 5 2 3 1 , 1 3 5 ->= 2 3 1 5 , 1 3 5 ->= 5 2 3 2 1 , 1 3 5 ->= 6 2 3 2 1 5 , 6 3 5 ->= 6 5 5 2 3 2 , 6 3 5 ->= 5 2 2 3 2 6 , 9 3 5 ->= 3 9 5 2 , 9 3 5 ->= 3 9 6 2 5 , 9 3 5 ->= 3 9 5 5 2 2 , 9 3 5 ->= 3 6 9 6 5 2 , 1 9 5 ->= 2 2 9 1 2 5 , 3 1 9 ->= 9 3 1 2 2 , 6 1 9 ->= 2 2 6 9 1 , 6 3 9 ->= 6 5 2 2 3 9 , 3 5 9 ->= 3 2 9 5 2 2 , 1 9 9 ->= 1 9 2 2 9 , 6 3 1 1 ->= 2 2 3 1 6 1 , 3 2 5 1 ->= 3 1 5 2 2 , 6 3 5 1 ->= 6 6 1 5 2 3 , 3 5 6 1 ->= 2 1 6 5 3 , 6 3 1 5 ->= 2 2 3 6 1 5 , 6 9 1 5 ->= 5 2 9 1 6 5 , 1 1 2 5 ->= 2 1 5 2 2 1 , 1 6 3 5 ->= 3 6 1 2 5 , 9 6 3 5 ->= 9 2 3 6 2 5 , 6 9 3 5 ->= 3 9 5 6 5 , 3 5 9 5 ->= 9 3 1 5 5 , 3 6 1 6 ->= 1 5 2 3 6 6 , 1 3 5 6 ->= 6 5 2 3 1 , 1 2 6 9 ->= 2 1 6 2 2 9 , 1 1 9 9 ->= 1 9 9 1 2 2 , 3 3 9 9 ->= 3 3 2 2 9 9 , 6 3 2 1 1 ->= 6 2 2 3 1 1 , 3 2 5 9 1 ->= 1 2 5 2 3 9 , 1 2 9 9 1 ->= 2 2 9 1 1 9 , 9 6 2 1 5 ->= 2 2 9 1 6 5 , 3 2 5 1 5 ->= 5 5 2 2 3 1 , 6 1 3 3 5 ->= 6 2 1 3 3 5 , 1 6 2 9 5 ->= 1 9 6 5 5 2 , 6 1 5 9 5 ->= 6 5 9 2 1 5 , 6 3 1 2 9 ->= 5 1 6 9 2 3 , 1 3 5 2 9 ->= 2 2 1 9 5 3 , 3 1 3 6 9 ->= 3 2 3 6 1 9 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 is interpreted by / \ | 1 0 | | 0 1 | \ / 1 is interpreted by / \ | 1 0 | | 0 1 | \ / 2 is interpreted by / \ | 1 0 | | 0 1 | \ / 3 is interpreted by / \ | 1 1 | | 0 1 | \ / 4 is interpreted by / \ | 1 1 | | 0 1 | \ / 5 is interpreted by / \ | 1 0 | | 0 1 | \ / 6 is interpreted by / \ | 1 0 | | 0 1 | \ / 7 is interpreted by / \ | 1 0 | | 0 1 | \ / 8 is interpreted by / \ | 1 1 | | 0 1 | \ / 9 is interpreted by / \ | 1 1 | | 0 1 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9 }, it remains to prove termination of the 125-rule system { 0 1 1 -> 0 2 1 1 , 0 1 1 -> 0 1 , 0 1 1 -> 0 , 0 3 1 -> 4 1 1 , 4 5 1 -> 0 5 2 3 , 4 5 1 -> 4 , 4 6 1 -> 4 1 2 2 2 6 , 7 1 5 -> 7 5 2 1 , 7 1 5 -> 0 , 0 3 5 -> 4 1 , 0 3 5 -> 4 1 5 , 0 3 5 -> 4 2 1 , 0 3 5 -> 7 2 3 2 1 5 , 0 3 5 -> 4 2 1 5 , 7 3 5 -> 7 5 5 2 3 2 , 7 3 5 -> 4 2 , 7 3 5 -> 4 2 6 , 8 3 5 -> 4 9 5 2 , 8 3 5 -> 4 9 6 2 5 , 8 3 5 -> 4 9 5 5 2 2 , 8 3 5 -> 4 6 9 6 5 2 , 0 9 5 -> 8 1 2 5 , 4 1 9 -> 8 3 1 2 2 , 7 1 9 -> 7 9 1 , 7 1 9 -> 8 1 , 7 3 9 -> 7 5 2 2 3 9 , 7 3 9 -> 4 9 , 4 5 9 -> 4 2 9 5 2 2 , 0 9 9 -> 0 9 2 2 9 , 0 9 9 -> 8 2 2 9 , 7 3 1 1 -> 4 1 6 1 , 4 2 5 1 -> 4 1 5 2 2 , 7 3 5 1 -> 7 6 1 5 2 3 , 7 3 5 1 -> 7 1 5 2 3 , 7 3 5 1 -> 0 5 2 3 , 7 3 5 1 -> 4 , 4 5 6 1 -> 0 6 5 3 , 4 5 6 1 -> 7 5 3 , 4 5 6 1 -> 4 , 7 3 1 5 -> 4 6 1 5 , 7 9 1 5 -> 8 1 6 5 , 0 1 2 5 -> 0 5 2 2 1 , 0 1 2 5 -> 0 , 0 6 3 5 -> 4 6 1 2 5 , 8 6 3 5 -> 8 2 3 6 2 5 , 7 9 3 5 -> 4 9 5 6 5 , 4 5 9 5 -> 8 3 1 5 5 , 4 6 1 6 -> 0 5 2 3 6 6 , 4 6 1 6 -> 4 6 6 , 0 3 5 6 -> 7 5 2 3 1 , 0 3 5 6 -> 4 1 , 0 2 6 9 -> 0 6 2 2 9 , 0 2 6 9 -> 7 2 2 9 , 0 2 6 9 -> 8 , 0 1 9 9 -> 0 9 9 1 2 2 , 0 1 9 9 -> 8 9 1 2 2 , 4 3 9 9 -> 4 3 2 2 9 9 , 7 3 2 1 1 -> 7 2 2 3 1 1 , 7 3 2 1 1 -> 4 1 1 , 4 2 5 9 1 -> 0 2 5 2 3 9 , 4 2 5 9 1 -> 4 9 , 0 2 9 9 1 -> 8 1 1 9 , 8 6 2 1 5 -> 8 1 6 5 , 4 2 5 1 5 -> 4 1 , 7 1 3 3 5 -> 7 2 1 3 3 5 , 7 1 3 3 5 -> 0 3 3 5 , 7 1 3 3 5 -> 4 3 5 , 0 6 2 9 5 -> 0 9 6 5 5 2 , 0 6 2 9 5 -> 8 6 5 5 2 , 7 1 5 9 5 -> 7 5 9 2 1 5 , 7 1 5 9 5 -> 8 2 1 5 , 7 3 1 2 9 -> 0 6 9 2 3 , 7 3 1 2 9 -> 7 9 2 3 , 7 3 1 2 9 -> 8 2 3 , 0 3 5 2 9 -> 0 9 5 3 , 0 3 5 2 9 -> 8 5 3 , 4 1 3 6 9 -> 4 2 3 6 1 9 , 1 1 1 ->= 2 1 2 1 1 , 1 3 1 ->= 2 2 3 1 1 , 3 5 1 ->= 1 5 2 3 , 3 6 1 ->= 3 1 2 2 2 6 , 6 1 5 ->= 2 6 5 2 1 , 1 3 5 ->= 5 2 3 1 , 1 3 5 ->= 2 3 1 5 , 1 3 5 ->= 5 2 3 2 1 , 1 3 5 ->= 6 2 3 2 1 5 , 6 3 5 ->= 6 5 5 2 3 2 , 6 3 5 ->= 5 2 2 3 2 6 , 9 3 5 ->= 3 9 5 2 , 9 3 5 ->= 3 9 6 2 5 , 9 3 5 ->= 3 9 5 5 2 2 , 9 3 5 ->= 3 6 9 6 5 2 , 1 9 5 ->= 2 2 9 1 2 5 , 3 1 9 ->= 9 3 1 2 2 , 6 1 9 ->= 2 2 6 9 1 , 6 3 9 ->= 6 5 2 2 3 9 , 3 5 9 ->= 3 2 9 5 2 2 , 1 9 9 ->= 1 9 2 2 9 , 6 3 1 1 ->= 2 2 3 1 6 1 , 3 2 5 1 ->= 3 1 5 2 2 , 6 3 5 1 ->= 6 6 1 5 2 3 , 3 5 6 1 ->= 2 1 6 5 3 , 6 3 1 5 ->= 2 2 3 6 1 5 , 6 9 1 5 ->= 5 2 9 1 6 5 , 1 1 2 5 ->= 2 1 5 2 2 1 , 1 6 3 5 ->= 3 6 1 2 5 , 9 6 3 5 ->= 9 2 3 6 2 5 , 6 9 3 5 ->= 3 9 5 6 5 , 3 5 9 5 ->= 9 3 1 5 5 , 3 6 1 6 ->= 1 5 2 3 6 6 , 1 3 5 6 ->= 6 5 2 3 1 , 1 2 6 9 ->= 2 1 6 2 2 9 , 1 1 9 9 ->= 1 9 9 1 2 2 , 3 3 9 9 ->= 3 3 2 2 9 9 , 6 3 2 1 1 ->= 6 2 2 3 1 1 , 3 2 5 9 1 ->= 1 2 5 2 3 9 , 1 2 9 9 1 ->= 2 2 9 1 1 9 , 9 6 2 1 5 ->= 2 2 9 1 6 5 , 3 2 5 1 5 ->= 5 5 2 2 3 1 , 6 1 3 3 5 ->= 6 2 1 3 3 5 , 1 6 2 9 5 ->= 1 9 6 5 5 2 , 6 1 5 9 5 ->= 6 5 9 2 1 5 , 6 3 1 2 9 ->= 5 1 6 9 2 3 , 1 3 5 2 9 ->= 2 2 1 9 5 3 , 3 1 3 6 9 ->= 3 2 3 6 1 9 } 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 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 1 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 1 | \ / 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 1 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 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 1 1 | \ / 7 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 | \ / 8 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 | \ / 9 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, 6->6, 7->7, 8->8, 9->9 }, it remains to prove termination of the 122-rule system { 0 1 1 -> 0 2 1 1 , 0 1 1 -> 0 1 , 0 1 1 -> 0 , 0 3 1 -> 4 1 1 , 4 5 1 -> 0 5 2 3 , 4 5 1 -> 4 , 4 6 1 -> 4 1 2 2 2 6 , 7 1 5 -> 7 5 2 1 , 7 1 5 -> 0 , 0 3 5 -> 4 1 , 0 3 5 -> 4 1 5 , 0 3 5 -> 4 2 1 , 0 3 5 -> 7 2 3 2 1 5 , 0 3 5 -> 4 2 1 5 , 7 3 5 -> 7 5 5 2 3 2 , 7 3 5 -> 4 2 , 7 3 5 -> 4 2 6 , 8 3 5 -> 4 9 5 2 , 8 3 5 -> 4 9 6 2 5 , 8 3 5 -> 4 9 5 5 2 2 , 8 3 5 -> 4 6 9 6 5 2 , 0 9 5 -> 8 1 2 5 , 4 1 9 -> 8 3 1 2 2 , 7 1 9 -> 7 9 1 , 7 1 9 -> 8 1 , 7 3 9 -> 7 5 2 2 3 9 , 7 3 9 -> 4 9 , 4 5 9 -> 4 2 9 5 2 2 , 0 9 9 -> 0 9 2 2 9 , 0 9 9 -> 8 2 2 9 , 7 3 1 1 -> 4 1 6 1 , 4 2 5 1 -> 4 1 5 2 2 , 7 3 5 1 -> 7 6 1 5 2 3 , 7 3 5 1 -> 7 1 5 2 3 , 7 3 5 1 -> 0 5 2 3 , 7 3 5 1 -> 4 , 4 5 6 1 -> 0 6 5 3 , 4 5 6 1 -> 7 5 3 , 4 5 6 1 -> 4 , 7 3 1 5 -> 4 6 1 5 , 7 9 1 5 -> 8 1 6 5 , 0 1 2 5 -> 0 5 2 2 1 , 0 1 2 5 -> 0 , 0 6 3 5 -> 4 6 1 2 5 , 8 6 3 5 -> 8 2 3 6 2 5 , 7 9 3 5 -> 4 9 5 6 5 , 4 5 9 5 -> 8 3 1 5 5 , 4 6 1 6 -> 0 5 2 3 6 6 , 4 6 1 6 -> 4 6 6 , 0 3 5 6 -> 7 5 2 3 1 , 0 3 5 6 -> 4 1 , 0 2 6 9 -> 0 6 2 2 9 , 0 2 6 9 -> 7 2 2 9 , 0 2 6 9 -> 8 , 0 1 9 9 -> 0 9 9 1 2 2 , 0 1 9 9 -> 8 9 1 2 2 , 4 3 9 9 -> 4 3 2 2 9 9 , 7 3 2 1 1 -> 7 2 2 3 1 1 , 7 3 2 1 1 -> 4 1 1 , 4 2 5 9 1 -> 0 2 5 2 3 9 , 4 2 5 9 1 -> 4 9 , 0 2 9 9 1 -> 8 1 1 9 , 8 6 2 1 5 -> 8 1 6 5 , 4 2 5 1 5 -> 4 1 , 7 1 3 3 5 -> 7 2 1 3 3 5 , 7 1 3 3 5 -> 0 3 3 5 , 7 1 3 3 5 -> 4 3 5 , 0 6 2 9 5 -> 0 9 6 5 5 2 , 0 6 2 9 5 -> 8 6 5 5 2 , 7 1 5 9 5 -> 7 5 9 2 1 5 , 7 1 5 9 5 -> 8 2 1 5 , 0 3 5 2 9 -> 0 9 5 3 , 0 3 5 2 9 -> 8 5 3 , 4 1 3 6 9 -> 4 2 3 6 1 9 , 1 1 1 ->= 2 1 2 1 1 , 1 3 1 ->= 2 2 3 1 1 , 3 5 1 ->= 1 5 2 3 , 3 6 1 ->= 3 1 2 2 2 6 , 6 1 5 ->= 2 6 5 2 1 , 1 3 5 ->= 5 2 3 1 , 1 3 5 ->= 2 3 1 5 , 1 3 5 ->= 5 2 3 2 1 , 1 3 5 ->= 6 2 3 2 1 5 , 6 3 5 ->= 6 5 5 2 3 2 , 6 3 5 ->= 5 2 2 3 2 6 , 9 3 5 ->= 3 9 5 2 , 9 3 5 ->= 3 9 6 2 5 , 9 3 5 ->= 3 9 5 5 2 2 , 9 3 5 ->= 3 6 9 6 5 2 , 1 9 5 ->= 2 2 9 1 2 5 , 3 1 9 ->= 9 3 1 2 2 , 6 1 9 ->= 2 2 6 9 1 , 6 3 9 ->= 6 5 2 2 3 9 , 3 5 9 ->= 3 2 9 5 2 2 , 1 9 9 ->= 1 9 2 2 9 , 6 3 1 1 ->= 2 2 3 1 6 1 , 3 2 5 1 ->= 3 1 5 2 2 , 6 3 5 1 ->= 6 6 1 5 2 3 , 3 5 6 1 ->= 2 1 6 5 3 , 6 3 1 5 ->= 2 2 3 6 1 5 , 6 9 1 5 ->= 5 2 9 1 6 5 , 1 1 2 5 ->= 2 1 5 2 2 1 , 1 6 3 5 ->= 3 6 1 2 5 , 9 6 3 5 ->= 9 2 3 6 2 5 , 6 9 3 5 ->= 3 9 5 6 5 , 3 5 9 5 ->= 9 3 1 5 5 , 3 6 1 6 ->= 1 5 2 3 6 6 , 1 3 5 6 ->= 6 5 2 3 1 , 1 2 6 9 ->= 2 1 6 2 2 9 , 1 1 9 9 ->= 1 9 9 1 2 2 , 3 3 9 9 ->= 3 3 2 2 9 9 , 6 3 2 1 1 ->= 6 2 2 3 1 1 , 3 2 5 9 1 ->= 1 2 5 2 3 9 , 1 2 9 9 1 ->= 2 2 9 1 1 9 , 9 6 2 1 5 ->= 2 2 9 1 6 5 , 3 2 5 1 5 ->= 5 5 2 2 3 1 , 6 1 3 3 5 ->= 6 2 1 3 3 5 , 1 6 2 9 5 ->= 1 9 6 5 5 2 , 6 1 5 9 5 ->= 6 5 9 2 1 5 , 6 3 1 2 9 ->= 5 1 6 9 2 3 , 1 3 5 2 9 ->= 2 2 1 9 5 3 , 3 1 3 6 9 ->= 3 2 3 6 1 9 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: 0 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 1 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / 7 is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9 }, it remains to prove termination of the 117-rule system { 0 1 1 -> 0 2 1 1 , 0 1 1 -> 0 1 , 0 1 1 -> 0 , 0 3 1 -> 4 1 1 , 4 5 1 -> 0 5 2 3 , 4 5 1 -> 4 , 4 6 1 -> 4 1 2 2 2 6 , 7 1 5 -> 7 5 2 1 , 7 1 5 -> 0 , 0 3 5 -> 4 1 , 0 3 5 -> 4 1 5 , 0 3 5 -> 4 2 1 , 0 3 5 -> 7 2 3 2 1 5 , 0 3 5 -> 4 2 1 5 , 7 3 5 -> 7 5 5 2 3 2 , 7 3 5 -> 4 2 , 7 3 5 -> 4 2 6 , 8 3 5 -> 4 9 5 2 , 8 3 5 -> 4 9 6 2 5 , 8 3 5 -> 4 9 5 5 2 2 , 8 3 5 -> 4 6 9 6 5 2 , 0 9 5 -> 8 1 2 5 , 4 1 9 -> 8 3 1 2 2 , 7 3 9 -> 7 5 2 2 3 9 , 7 3 9 -> 4 9 , 4 5 9 -> 4 2 9 5 2 2 , 0 9 9 -> 0 9 2 2 9 , 0 9 9 -> 8 2 2 9 , 7 3 1 1 -> 4 1 6 1 , 4 2 5 1 -> 4 1 5 2 2 , 7 3 5 1 -> 7 6 1 5 2 3 , 7 3 5 1 -> 7 1 5 2 3 , 7 3 5 1 -> 0 5 2 3 , 7 3 5 1 -> 4 , 4 5 6 1 -> 0 6 5 3 , 4 5 6 1 -> 7 5 3 , 4 5 6 1 -> 4 , 7 3 1 5 -> 4 6 1 5 , 7 9 1 5 -> 8 1 6 5 , 0 1 2 5 -> 0 5 2 2 1 , 0 1 2 5 -> 0 , 0 6 3 5 -> 4 6 1 2 5 , 8 6 3 5 -> 8 2 3 6 2 5 , 7 9 3 5 -> 4 9 5 6 5 , 4 5 9 5 -> 8 3 1 5 5 , 4 6 1 6 -> 0 5 2 3 6 6 , 4 6 1 6 -> 4 6 6 , 0 3 5 6 -> 7 5 2 3 1 , 0 3 5 6 -> 4 1 , 0 2 6 9 -> 0 6 2 2 9 , 0 2 6 9 -> 7 2 2 9 , 0 2 6 9 -> 8 , 0 1 9 9 -> 0 9 9 1 2 2 , 0 1 9 9 -> 8 9 1 2 2 , 4 3 9 9 -> 4 3 2 2 9 9 , 7 3 2 1 1 -> 7 2 2 3 1 1 , 7 3 2 1 1 -> 4 1 1 , 4 2 5 9 1 -> 0 2 5 2 3 9 , 4 2 5 9 1 -> 4 9 , 0 2 9 9 1 -> 8 1 1 9 , 8 6 2 1 5 -> 8 1 6 5 , 4 2 5 1 5 -> 4 1 , 0 6 2 9 5 -> 0 9 6 5 5 2 , 0 6 2 9 5 -> 8 6 5 5 2 , 7 1 5 9 5 -> 7 5 9 2 1 5 , 7 1 5 9 5 -> 8 2 1 5 , 0 3 5 2 9 -> 0 9 5 3 , 0 3 5 2 9 -> 8 5 3 , 4 1 3 6 9 -> 4 2 3 6 1 9 , 1 1 1 ->= 2 1 2 1 1 , 1 3 1 ->= 2 2 3 1 1 , 3 5 1 ->= 1 5 2 3 , 3 6 1 ->= 3 1 2 2 2 6 , 6 1 5 ->= 2 6 5 2 1 , 1 3 5 ->= 5 2 3 1 , 1 3 5 ->= 2 3 1 5 , 1 3 5 ->= 5 2 3 2 1 , 1 3 5 ->= 6 2 3 2 1 5 , 6 3 5 ->= 6 5 5 2 3 2 , 6 3 5 ->= 5 2 2 3 2 6 , 9 3 5 ->= 3 9 5 2 , 9 3 5 ->= 3 9 6 2 5 , 9 3 5 ->= 3 9 5 5 2 2 , 9 3 5 ->= 3 6 9 6 5 2 , 1 9 5 ->= 2 2 9 1 2 5 , 3 1 9 ->= 9 3 1 2 2 , 6 1 9 ->= 2 2 6 9 1 , 6 3 9 ->= 6 5 2 2 3 9 , 3 5 9 ->= 3 2 9 5 2 2 , 1 9 9 ->= 1 9 2 2 9 , 6 3 1 1 ->= 2 2 3 1 6 1 , 3 2 5 1 ->= 3 1 5 2 2 , 6 3 5 1 ->= 6 6 1 5 2 3 , 3 5 6 1 ->= 2 1 6 5 3 , 6 3 1 5 ->= 2 2 3 6 1 5 , 6 9 1 5 ->= 5 2 9 1 6 5 , 1 1 2 5 ->= 2 1 5 2 2 1 , 1 6 3 5 ->= 3 6 1 2 5 , 9 6 3 5 ->= 9 2 3 6 2 5 , 6 9 3 5 ->= 3 9 5 6 5 , 3 5 9 5 ->= 9 3 1 5 5 , 3 6 1 6 ->= 1 5 2 3 6 6 , 1 3 5 6 ->= 6 5 2 3 1 , 1 2 6 9 ->= 2 1 6 2 2 9 , 1 1 9 9 ->= 1 9 9 1 2 2 , 3 3 9 9 ->= 3 3 2 2 9 9 , 6 3 2 1 1 ->= 6 2 2 3 1 1 , 3 2 5 9 1 ->= 1 2 5 2 3 9 , 1 2 9 9 1 ->= 2 2 9 1 1 9 , 9 6 2 1 5 ->= 2 2 9 1 6 5 , 3 2 5 1 5 ->= 5 5 2 2 3 1 , 6 1 3 3 5 ->= 6 2 1 3 3 5 , 1 6 2 9 5 ->= 1 9 6 5 5 2 , 6 1 5 9 5 ->= 6 5 9 2 1 5 , 6 3 1 2 9 ->= 5 1 6 9 2 3 , 1 3 5 2 9 ->= 2 2 1 9 5 3 , 3 1 3 6 9 ->= 3 2 3 6 1 9 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 1 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 1 0 | | 0 0 0 0 0 | \ / 3 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 1 1 | \ / 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 1 | | 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 1 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9 }, it remains to prove termination of the 110-rule system { 0 1 1 -> 0 2 1 1 , 0 1 1 -> 0 1 , 0 1 1 -> 0 , 0 3 1 -> 4 1 1 , 4 5 1 -> 0 5 2 3 , 4 5 1 -> 4 , 4 6 1 -> 4 1 2 2 2 6 , 0 3 5 -> 4 1 , 0 3 5 -> 4 1 5 , 0 3 5 -> 4 2 1 , 0 3 5 -> 7 2 3 2 1 5 , 0 3 5 -> 4 2 1 5 , 7 3 5 -> 7 5 5 2 3 2 , 7 3 5 -> 4 2 , 7 3 5 -> 4 2 6 , 8 3 5 -> 4 9 5 2 , 8 3 5 -> 4 9 6 2 5 , 8 3 5 -> 4 9 5 5 2 2 , 8 3 5 -> 4 6 9 6 5 2 , 0 9 5 -> 8 1 2 5 , 4 1 9 -> 8 3 1 2 2 , 7 3 9 -> 7 5 2 2 3 9 , 7 3 9 -> 4 9 , 4 5 9 -> 4 2 9 5 2 2 , 0 9 9 -> 0 9 2 2 9 , 0 9 9 -> 8 2 2 9 , 7 3 1 1 -> 4 1 6 1 , 4 2 5 1 -> 4 1 5 2 2 , 7 3 5 1 -> 7 1 5 2 3 , 4 5 6 1 -> 0 6 5 3 , 4 5 6 1 -> 7 5 3 , 4 5 6 1 -> 4 , 7 3 1 5 -> 4 6 1 5 , 7 9 1 5 -> 8 1 6 5 , 0 1 2 5 -> 0 5 2 2 1 , 0 1 2 5 -> 0 , 0 6 3 5 -> 4 6 1 2 5 , 8 6 3 5 -> 8 2 3 6 2 5 , 7 9 3 5 -> 4 9 5 6 5 , 4 5 9 5 -> 8 3 1 5 5 , 4 6 1 6 -> 0 5 2 3 6 6 , 4 6 1 6 -> 4 6 6 , 0 3 5 6 -> 7 5 2 3 1 , 0 3 5 6 -> 4 1 , 0 2 6 9 -> 0 6 2 2 9 , 0 2 6 9 -> 7 2 2 9 , 0 2 6 9 -> 8 , 0 1 9 9 -> 0 9 9 1 2 2 , 0 1 9 9 -> 8 9 1 2 2 , 4 3 9 9 -> 4 3 2 2 9 9 , 7 3 2 1 1 -> 7 2 2 3 1 1 , 7 3 2 1 1 -> 4 1 1 , 4 2 5 9 1 -> 0 2 5 2 3 9 , 4 2 5 9 1 -> 4 9 , 0 2 9 9 1 -> 8 1 1 9 , 8 6 2 1 5 -> 8 1 6 5 , 4 2 5 1 5 -> 4 1 , 0 6 2 9 5 -> 0 9 6 5 5 2 , 0 6 2 9 5 -> 8 6 5 5 2 , 0 3 5 2 9 -> 0 9 5 3 , 0 3 5 2 9 -> 8 5 3 , 4 1 3 6 9 -> 4 2 3 6 1 9 , 1 1 1 ->= 2 1 2 1 1 , 1 3 1 ->= 2 2 3 1 1 , 3 5 1 ->= 1 5 2 3 , 3 6 1 ->= 3 1 2 2 2 6 , 6 1 5 ->= 2 6 5 2 1 , 1 3 5 ->= 5 2 3 1 , 1 3 5 ->= 2 3 1 5 , 1 3 5 ->= 5 2 3 2 1 , 1 3 5 ->= 6 2 3 2 1 5 , 6 3 5 ->= 6 5 5 2 3 2 , 6 3 5 ->= 5 2 2 3 2 6 , 9 3 5 ->= 3 9 5 2 , 9 3 5 ->= 3 9 6 2 5 , 9 3 5 ->= 3 9 5 5 2 2 , 9 3 5 ->= 3 6 9 6 5 2 , 1 9 5 ->= 2 2 9 1 2 5 , 3 1 9 ->= 9 3 1 2 2 , 6 1 9 ->= 2 2 6 9 1 , 6 3 9 ->= 6 5 2 2 3 9 , 3 5 9 ->= 3 2 9 5 2 2 , 1 9 9 ->= 1 9 2 2 9 , 6 3 1 1 ->= 2 2 3 1 6 1 , 3 2 5 1 ->= 3 1 5 2 2 , 6 3 5 1 ->= 6 6 1 5 2 3 , 3 5 6 1 ->= 2 1 6 5 3 , 6 3 1 5 ->= 2 2 3 6 1 5 , 6 9 1 5 ->= 5 2 9 1 6 5 , 1 1 2 5 ->= 2 1 5 2 2 1 , 1 6 3 5 ->= 3 6 1 2 5 , 9 6 3 5 ->= 9 2 3 6 2 5 , 6 9 3 5 ->= 3 9 5 6 5 , 3 5 9 5 ->= 9 3 1 5 5 , 3 6 1 6 ->= 1 5 2 3 6 6 , 1 3 5 6 ->= 6 5 2 3 1 , 1 2 6 9 ->= 2 1 6 2 2 9 , 1 1 9 9 ->= 1 9 9 1 2 2 , 3 3 9 9 ->= 3 3 2 2 9 9 , 6 3 2 1 1 ->= 6 2 2 3 1 1 , 3 2 5 9 1 ->= 1 2 5 2 3 9 , 1 2 9 9 1 ->= 2 2 9 1 1 9 , 9 6 2 1 5 ->= 2 2 9 1 6 5 , 3 2 5 1 5 ->= 5 5 2 2 3 1 , 6 1 3 3 5 ->= 6 2 1 3 3 5 , 1 6 2 9 5 ->= 1 9 6 5 5 2 , 6 1 5 9 5 ->= 6 5 9 2 1 5 , 6 3 1 2 9 ->= 5 1 6 9 2 3 , 1 3 5 2 9 ->= 2 2 1 9 5 3 , 3 1 3 6 9 ->= 3 2 3 6 1 9 } 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 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 1 | | 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 1 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 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 1 | \ / 7 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 | \ / 8 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 | \ / 9 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, 6->6, 7->7, 8->8, 9->9 }, it remains to prove termination of the 108-rule system { 0 1 1 -> 0 2 1 1 , 0 1 1 -> 0 1 , 0 1 1 -> 0 , 0 3 1 -> 4 1 1 , 4 5 1 -> 0 5 2 3 , 4 5 1 -> 4 , 4 6 1 -> 4 1 2 2 2 6 , 0 3 5 -> 4 1 , 0 3 5 -> 4 1 5 , 0 3 5 -> 4 2 1 , 0 3 5 -> 7 2 3 2 1 5 , 0 3 5 -> 4 2 1 5 , 7 3 5 -> 7 5 5 2 3 2 , 7 3 5 -> 4 2 , 7 3 5 -> 4 2 6 , 8 3 5 -> 4 9 5 2 , 8 3 5 -> 4 9 6 2 5 , 8 3 5 -> 4 9 5 5 2 2 , 8 3 5 -> 4 6 9 6 5 2 , 0 9 5 -> 8 1 2 5 , 4 1 9 -> 8 3 1 2 2 , 7 3 9 -> 7 5 2 2 3 9 , 7 3 9 -> 4 9 , 4 5 9 -> 4 2 9 5 2 2 , 0 9 9 -> 0 9 2 2 9 , 0 9 9 -> 8 2 2 9 , 7 3 1 1 -> 4 1 6 1 , 4 2 5 1 -> 4 1 5 2 2 , 7 3 5 1 -> 7 1 5 2 3 , 4 5 6 1 -> 0 6 5 3 , 4 5 6 1 -> 7 5 3 , 4 5 6 1 -> 4 , 7 3 1 5 -> 4 6 1 5 , 7 9 1 5 -> 8 1 6 5 , 0 1 2 5 -> 0 5 2 2 1 , 0 1 2 5 -> 0 , 0 6 3 5 -> 4 6 1 2 5 , 8 6 3 5 -> 8 2 3 6 2 5 , 7 9 3 5 -> 4 9 5 6 5 , 4 5 9 5 -> 8 3 1 5 5 , 4 6 1 6 -> 0 5 2 3 6 6 , 4 6 1 6 -> 4 6 6 , 0 3 5 6 -> 7 5 2 3 1 , 0 3 5 6 -> 4 1 , 0 2 6 9 -> 0 6 2 2 9 , 0 2 6 9 -> 7 2 2 9 , 0 2 6 9 -> 8 , 0 1 9 9 -> 0 9 9 1 2 2 , 0 1 9 9 -> 8 9 1 2 2 , 4 3 9 9 -> 4 3 2 2 9 9 , 4 2 5 9 1 -> 0 2 5 2 3 9 , 4 2 5 9 1 -> 4 9 , 0 2 9 9 1 -> 8 1 1 9 , 8 6 2 1 5 -> 8 1 6 5 , 4 2 5 1 5 -> 4 1 , 0 6 2 9 5 -> 0 9 6 5 5 2 , 0 6 2 9 5 -> 8 6 5 5 2 , 0 3 5 2 9 -> 0 9 5 3 , 0 3 5 2 9 -> 8 5 3 , 4 1 3 6 9 -> 4 2 3 6 1 9 , 1 1 1 ->= 2 1 2 1 1 , 1 3 1 ->= 2 2 3 1 1 , 3 5 1 ->= 1 5 2 3 , 3 6 1 ->= 3 1 2 2 2 6 , 6 1 5 ->= 2 6 5 2 1 , 1 3 5 ->= 5 2 3 1 , 1 3 5 ->= 2 3 1 5 , 1 3 5 ->= 5 2 3 2 1 , 1 3 5 ->= 6 2 3 2 1 5 , 6 3 5 ->= 6 5 5 2 3 2 , 6 3 5 ->= 5 2 2 3 2 6 , 9 3 5 ->= 3 9 5 2 , 9 3 5 ->= 3 9 6 2 5 , 9 3 5 ->= 3 9 5 5 2 2 , 9 3 5 ->= 3 6 9 6 5 2 , 1 9 5 ->= 2 2 9 1 2 5 , 3 1 9 ->= 9 3 1 2 2 , 6 1 9 ->= 2 2 6 9 1 , 6 3 9 ->= 6 5 2 2 3 9 , 3 5 9 ->= 3 2 9 5 2 2 , 1 9 9 ->= 1 9 2 2 9 , 6 3 1 1 ->= 2 2 3 1 6 1 , 3 2 5 1 ->= 3 1 5 2 2 , 6 3 5 1 ->= 6 6 1 5 2 3 , 3 5 6 1 ->= 2 1 6 5 3 , 6 3 1 5 ->= 2 2 3 6 1 5 , 6 9 1 5 ->= 5 2 9 1 6 5 , 1 1 2 5 ->= 2 1 5 2 2 1 , 1 6 3 5 ->= 3 6 1 2 5 , 9 6 3 5 ->= 9 2 3 6 2 5 , 6 9 3 5 ->= 3 9 5 6 5 , 3 5 9 5 ->= 9 3 1 5 5 , 3 6 1 6 ->= 1 5 2 3 6 6 , 1 3 5 6 ->= 6 5 2 3 1 , 1 2 6 9 ->= 2 1 6 2 2 9 , 1 1 9 9 ->= 1 9 9 1 2 2 , 3 3 9 9 ->= 3 3 2 2 9 9 , 6 3 2 1 1 ->= 6 2 2 3 1 1 , 3 2 5 9 1 ->= 1 2 5 2 3 9 , 1 2 9 9 1 ->= 2 2 9 1 1 9 , 9 6 2 1 5 ->= 2 2 9 1 6 5 , 3 2 5 1 5 ->= 5 5 2 2 3 1 , 6 1 3 3 5 ->= 6 2 1 3 3 5 , 1 6 2 9 5 ->= 1 9 6 5 5 2 , 6 1 5 9 5 ->= 6 5 9 2 1 5 , 6 3 1 2 9 ->= 5 1 6 9 2 3 , 1 3 5 2 9 ->= 2 2 1 9 5 3 , 3 1 3 6 9 ->= 3 2 3 6 1 9 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 1 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 1 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 | | 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 7 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9 }, it remains to prove termination of the 107-rule system { 0 1 1 -> 0 2 1 1 , 0 1 1 -> 0 1 , 0 1 1 -> 0 , 0 3 1 -> 4 1 1 , 4 5 1 -> 0 5 2 3 , 4 5 1 -> 4 , 4 6 1 -> 4 1 2 2 2 6 , 0 3 5 -> 4 1 , 0 3 5 -> 4 1 5 , 0 3 5 -> 4 2 1 , 0 3 5 -> 7 2 3 2 1 5 , 0 3 5 -> 4 2 1 5 , 7 3 5 -> 7 5 5 2 3 2 , 7 3 5 -> 4 2 , 7 3 5 -> 4 2 6 , 8 3 5 -> 4 9 5 2 , 8 3 5 -> 4 9 6 2 5 , 8 3 5 -> 4 9 5 5 2 2 , 8 3 5 -> 4 6 9 6 5 2 , 0 9 5 -> 8 1 2 5 , 4 1 9 -> 8 3 1 2 2 , 7 3 9 -> 7 5 2 2 3 9 , 7 3 9 -> 4 9 , 4 5 9 -> 4 2 9 5 2 2 , 0 9 9 -> 0 9 2 2 9 , 0 9 9 -> 8 2 2 9 , 4 2 5 1 -> 4 1 5 2 2 , 7 3 5 1 -> 7 1 5 2 3 , 4 5 6 1 -> 0 6 5 3 , 4 5 6 1 -> 7 5 3 , 4 5 6 1 -> 4 , 7 3 1 5 -> 4 6 1 5 , 7 9 1 5 -> 8 1 6 5 , 0 1 2 5 -> 0 5 2 2 1 , 0 1 2 5 -> 0 , 0 6 3 5 -> 4 6 1 2 5 , 8 6 3 5 -> 8 2 3 6 2 5 , 7 9 3 5 -> 4 9 5 6 5 , 4 5 9 5 -> 8 3 1 5 5 , 4 6 1 6 -> 0 5 2 3 6 6 , 4 6 1 6 -> 4 6 6 , 0 3 5 6 -> 7 5 2 3 1 , 0 3 5 6 -> 4 1 , 0 2 6 9 -> 0 6 2 2 9 , 0 2 6 9 -> 7 2 2 9 , 0 2 6 9 -> 8 , 0 1 9 9 -> 0 9 9 1 2 2 , 0 1 9 9 -> 8 9 1 2 2 , 4 3 9 9 -> 4 3 2 2 9 9 , 4 2 5 9 1 -> 0 2 5 2 3 9 , 4 2 5 9 1 -> 4 9 , 0 2 9 9 1 -> 8 1 1 9 , 8 6 2 1 5 -> 8 1 6 5 , 4 2 5 1 5 -> 4 1 , 0 6 2 9 5 -> 0 9 6 5 5 2 , 0 6 2 9 5 -> 8 6 5 5 2 , 0 3 5 2 9 -> 0 9 5 3 , 0 3 5 2 9 -> 8 5 3 , 4 1 3 6 9 -> 4 2 3 6 1 9 , 1 1 1 ->= 2 1 2 1 1 , 1 3 1 ->= 2 2 3 1 1 , 3 5 1 ->= 1 5 2 3 , 3 6 1 ->= 3 1 2 2 2 6 , 6 1 5 ->= 2 6 5 2 1 , 1 3 5 ->= 5 2 3 1 , 1 3 5 ->= 2 3 1 5 , 1 3 5 ->= 5 2 3 2 1 , 1 3 5 ->= 6 2 3 2 1 5 , 6 3 5 ->= 6 5 5 2 3 2 , 6 3 5 ->= 5 2 2 3 2 6 , 9 3 5 ->= 3 9 5 2 , 9 3 5 ->= 3 9 6 2 5 , 9 3 5 ->= 3 9 5 5 2 2 , 9 3 5 ->= 3 6 9 6 5 2 , 1 9 5 ->= 2 2 9 1 2 5 , 3 1 9 ->= 9 3 1 2 2 , 6 1 9 ->= 2 2 6 9 1 , 6 3 9 ->= 6 5 2 2 3 9 , 3 5 9 ->= 3 2 9 5 2 2 , 1 9 9 ->= 1 9 2 2 9 , 6 3 1 1 ->= 2 2 3 1 6 1 , 3 2 5 1 ->= 3 1 5 2 2 , 6 3 5 1 ->= 6 6 1 5 2 3 , 3 5 6 1 ->= 2 1 6 5 3 , 6 3 1 5 ->= 2 2 3 6 1 5 , 6 9 1 5 ->= 5 2 9 1 6 5 , 1 1 2 5 ->= 2 1 5 2 2 1 , 1 6 3 5 ->= 3 6 1 2 5 , 9 6 3 5 ->= 9 2 3 6 2 5 , 6 9 3 5 ->= 3 9 5 6 5 , 3 5 9 5 ->= 9 3 1 5 5 , 3 6 1 6 ->= 1 5 2 3 6 6 , 1 3 5 6 ->= 6 5 2 3 1 , 1 2 6 9 ->= 2 1 6 2 2 9 , 1 1 9 9 ->= 1 9 9 1 2 2 , 3 3 9 9 ->= 3 3 2 2 9 9 , 6 3 2 1 1 ->= 6 2 2 3 1 1 , 3 2 5 9 1 ->= 1 2 5 2 3 9 , 1 2 9 9 1 ->= 2 2 9 1 1 9 , 9 6 2 1 5 ->= 2 2 9 1 6 5 , 3 2 5 1 5 ->= 5 5 2 2 3 1 , 6 1 3 3 5 ->= 6 2 1 3 3 5 , 1 6 2 9 5 ->= 1 9 6 5 5 2 , 6 1 5 9 5 ->= 6 5 9 2 1 5 , 6 3 1 2 9 ->= 5 1 6 9 2 3 , 1 3 5 2 9 ->= 2 2 1 9 5 3 , 3 1 3 6 9 ->= 3 2 3 6 1 9 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 1 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 1 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 1 | | 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 1 | \ / 7 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9 }, it remains to prove termination of the 106-rule system { 0 1 1 -> 0 2 1 1 , 0 1 1 -> 0 1 , 0 1 1 -> 0 , 0 3 1 -> 4 1 1 , 4 5 1 -> 0 5 2 3 , 4 5 1 -> 4 , 4 6 1 -> 4 1 2 2 2 6 , 0 3 5 -> 4 1 , 0 3 5 -> 4 1 5 , 0 3 5 -> 4 2 1 , 0 3 5 -> 7 2 3 2 1 5 , 0 3 5 -> 4 2 1 5 , 7 3 5 -> 7 5 5 2 3 2 , 7 3 5 -> 4 2 , 7 3 5 -> 4 2 6 , 8 3 5 -> 4 9 5 2 , 8 3 5 -> 4 9 6 2 5 , 8 3 5 -> 4 9 5 5 2 2 , 8 3 5 -> 4 6 9 6 5 2 , 0 9 5 -> 8 1 2 5 , 4 1 9 -> 8 3 1 2 2 , 7 3 9 -> 7 5 2 2 3 9 , 7 3 9 -> 4 9 , 4 5 9 -> 4 2 9 5 2 2 , 0 9 9 -> 0 9 2 2 9 , 0 9 9 -> 8 2 2 9 , 4 2 5 1 -> 4 1 5 2 2 , 4 5 6 1 -> 0 6 5 3 , 4 5 6 1 -> 7 5 3 , 4 5 6 1 -> 4 , 7 3 1 5 -> 4 6 1 5 , 7 9 1 5 -> 8 1 6 5 , 0 1 2 5 -> 0 5 2 2 1 , 0 1 2 5 -> 0 , 0 6 3 5 -> 4 6 1 2 5 , 8 6 3 5 -> 8 2 3 6 2 5 , 7 9 3 5 -> 4 9 5 6 5 , 4 5 9 5 -> 8 3 1 5 5 , 4 6 1 6 -> 0 5 2 3 6 6 , 4 6 1 6 -> 4 6 6 , 0 3 5 6 -> 7 5 2 3 1 , 0 3 5 6 -> 4 1 , 0 2 6 9 -> 0 6 2 2 9 , 0 2 6 9 -> 7 2 2 9 , 0 2 6 9 -> 8 , 0 1 9 9 -> 0 9 9 1 2 2 , 0 1 9 9 -> 8 9 1 2 2 , 4 3 9 9 -> 4 3 2 2 9 9 , 4 2 5 9 1 -> 0 2 5 2 3 9 , 4 2 5 9 1 -> 4 9 , 0 2 9 9 1 -> 8 1 1 9 , 8 6 2 1 5 -> 8 1 6 5 , 4 2 5 1 5 -> 4 1 , 0 6 2 9 5 -> 0 9 6 5 5 2 , 0 6 2 9 5 -> 8 6 5 5 2 , 0 3 5 2 9 -> 0 9 5 3 , 0 3 5 2 9 -> 8 5 3 , 4 1 3 6 9 -> 4 2 3 6 1 9 , 1 1 1 ->= 2 1 2 1 1 , 1 3 1 ->= 2 2 3 1 1 , 3 5 1 ->= 1 5 2 3 , 3 6 1 ->= 3 1 2 2 2 6 , 6 1 5 ->= 2 6 5 2 1 , 1 3 5 ->= 5 2 3 1 , 1 3 5 ->= 2 3 1 5 , 1 3 5 ->= 5 2 3 2 1 , 1 3 5 ->= 6 2 3 2 1 5 , 6 3 5 ->= 6 5 5 2 3 2 , 6 3 5 ->= 5 2 2 3 2 6 , 9 3 5 ->= 3 9 5 2 , 9 3 5 ->= 3 9 6 2 5 , 9 3 5 ->= 3 9 5 5 2 2 , 9 3 5 ->= 3 6 9 6 5 2 , 1 9 5 ->= 2 2 9 1 2 5 , 3 1 9 ->= 9 3 1 2 2 , 6 1 9 ->= 2 2 6 9 1 , 6 3 9 ->= 6 5 2 2 3 9 , 3 5 9 ->= 3 2 9 5 2 2 , 1 9 9 ->= 1 9 2 2 9 , 6 3 1 1 ->= 2 2 3 1 6 1 , 3 2 5 1 ->= 3 1 5 2 2 , 6 3 5 1 ->= 6 6 1 5 2 3 , 3 5 6 1 ->= 2 1 6 5 3 , 6 3 1 5 ->= 2 2 3 6 1 5 , 6 9 1 5 ->= 5 2 9 1 6 5 , 1 1 2 5 ->= 2 1 5 2 2 1 , 1 6 3 5 ->= 3 6 1 2 5 , 9 6 3 5 ->= 9 2 3 6 2 5 , 6 9 3 5 ->= 3 9 5 6 5 , 3 5 9 5 ->= 9 3 1 5 5 , 3 6 1 6 ->= 1 5 2 3 6 6 , 1 3 5 6 ->= 6 5 2 3 1 , 1 2 6 9 ->= 2 1 6 2 2 9 , 1 1 9 9 ->= 1 9 9 1 2 2 , 3 3 9 9 ->= 3 3 2 2 9 9 , 6 3 2 1 1 ->= 6 2 2 3 1 1 , 3 2 5 9 1 ->= 1 2 5 2 3 9 , 1 2 9 9 1 ->= 2 2 9 1 1 9 , 9 6 2 1 5 ->= 2 2 9 1 6 5 , 3 2 5 1 5 ->= 5 5 2 2 3 1 , 6 1 3 3 5 ->= 6 2 1 3 3 5 , 1 6 2 9 5 ->= 1 9 6 5 5 2 , 6 1 5 9 5 ->= 6 5 9 2 1 5 , 6 3 1 2 9 ->= 5 1 6 9 2 3 , 1 3 5 2 9 ->= 2 2 1 9 5 3 , 3 1 3 6 9 ->= 3 2 3 6 1 9 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 1 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 1 | | 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 | | 0 1 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | | 0 1 0 0 0 | \ / 7 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9 }, it remains to prove termination of the 104-rule system { 0 1 1 -> 0 2 1 1 , 0 1 1 -> 0 1 , 0 1 1 -> 0 , 0 3 1 -> 4 1 1 , 4 5 1 -> 0 5 2 3 , 4 5 1 -> 4 , 4 6 1 -> 4 1 2 2 2 6 , 0 3 5 -> 4 1 , 0 3 5 -> 4 1 5 , 0 3 5 -> 4 2 1 , 0 3 5 -> 7 2 3 2 1 5 , 0 3 5 -> 4 2 1 5 , 7 3 5 -> 7 5 5 2 3 2 , 7 3 5 -> 4 2 , 7 3 5 -> 4 2 6 , 8 3 5 -> 4 9 5 2 , 8 3 5 -> 4 9 6 2 5 , 8 3 5 -> 4 9 5 5 2 2 , 8 3 5 -> 4 6 9 6 5 2 , 0 9 5 -> 8 1 2 5 , 4 1 9 -> 8 3 1 2 2 , 7 3 9 -> 7 5 2 2 3 9 , 7 3 9 -> 4 9 , 4 5 9 -> 4 2 9 5 2 2 , 0 9 9 -> 0 9 2 2 9 , 0 9 9 -> 8 2 2 9 , 4 2 5 1 -> 4 1 5 2 2 , 4 5 6 1 -> 0 6 5 3 , 4 5 6 1 -> 7 5 3 , 4 5 6 1 -> 4 , 7 3 1 5 -> 4 6 1 5 , 0 1 2 5 -> 0 5 2 2 1 , 0 1 2 5 -> 0 , 0 6 3 5 -> 4 6 1 2 5 , 8 6 3 5 -> 8 2 3 6 2 5 , 4 5 9 5 -> 8 3 1 5 5 , 4 6 1 6 -> 0 5 2 3 6 6 , 4 6 1 6 -> 4 6 6 , 0 3 5 6 -> 7 5 2 3 1 , 0 3 5 6 -> 4 1 , 0 2 6 9 -> 0 6 2 2 9 , 0 2 6 9 -> 7 2 2 9 , 0 2 6 9 -> 8 , 0 1 9 9 -> 0 9 9 1 2 2 , 0 1 9 9 -> 8 9 1 2 2 , 4 3 9 9 -> 4 3 2 2 9 9 , 4 2 5 9 1 -> 0 2 5 2 3 9 , 4 2 5 9 1 -> 4 9 , 0 2 9 9 1 -> 8 1 1 9 , 8 6 2 1 5 -> 8 1 6 5 , 4 2 5 1 5 -> 4 1 , 0 6 2 9 5 -> 0 9 6 5 5 2 , 0 6 2 9 5 -> 8 6 5 5 2 , 0 3 5 2 9 -> 0 9 5 3 , 0 3 5 2 9 -> 8 5 3 , 4 1 3 6 9 -> 4 2 3 6 1 9 , 1 1 1 ->= 2 1 2 1 1 , 1 3 1 ->= 2 2 3 1 1 , 3 5 1 ->= 1 5 2 3 , 3 6 1 ->= 3 1 2 2 2 6 , 6 1 5 ->= 2 6 5 2 1 , 1 3 5 ->= 5 2 3 1 , 1 3 5 ->= 2 3 1 5 , 1 3 5 ->= 5 2 3 2 1 , 1 3 5 ->= 6 2 3 2 1 5 , 6 3 5 ->= 6 5 5 2 3 2 , 6 3 5 ->= 5 2 2 3 2 6 , 9 3 5 ->= 3 9 5 2 , 9 3 5 ->= 3 9 6 2 5 , 9 3 5 ->= 3 9 5 5 2 2 , 9 3 5 ->= 3 6 9 6 5 2 , 1 9 5 ->= 2 2 9 1 2 5 , 3 1 9 ->= 9 3 1 2 2 , 6 1 9 ->= 2 2 6 9 1 , 6 3 9 ->= 6 5 2 2 3 9 , 3 5 9 ->= 3 2 9 5 2 2 , 1 9 9 ->= 1 9 2 2 9 , 6 3 1 1 ->= 2 2 3 1 6 1 , 3 2 5 1 ->= 3 1 5 2 2 , 6 3 5 1 ->= 6 6 1 5 2 3 , 3 5 6 1 ->= 2 1 6 5 3 , 6 3 1 5 ->= 2 2 3 6 1 5 , 6 9 1 5 ->= 5 2 9 1 6 5 , 1 1 2 5 ->= 2 1 5 2 2 1 , 1 6 3 5 ->= 3 6 1 2 5 , 9 6 3 5 ->= 9 2 3 6 2 5 , 6 9 3 5 ->= 3 9 5 6 5 , 3 5 9 5 ->= 9 3 1 5 5 , 3 6 1 6 ->= 1 5 2 3 6 6 , 1 3 5 6 ->= 6 5 2 3 1 , 1 2 6 9 ->= 2 1 6 2 2 9 , 1 1 9 9 ->= 1 9 9 1 2 2 , 3 3 9 9 ->= 3 3 2 2 9 9 , 6 3 2 1 1 ->= 6 2 2 3 1 1 , 3 2 5 9 1 ->= 1 2 5 2 3 9 , 1 2 9 9 1 ->= 2 2 9 1 1 9 , 9 6 2 1 5 ->= 2 2 9 1 6 5 , 3 2 5 1 5 ->= 5 5 2 2 3 1 , 6 1 3 3 5 ->= 6 2 1 3 3 5 , 1 6 2 9 5 ->= 1 9 6 5 5 2 , 6 1 5 9 5 ->= 6 5 9 2 1 5 , 6 3 1 2 9 ->= 5 1 6 9 2 3 , 1 3 5 2 9 ->= 2 2 1 9 5 3 , 3 1 3 6 9 ->= 3 2 3 6 1 9 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: 0 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 1 | \ / 2 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 1 0 | \ / 3 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 1 | \ / 4 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 1 0 | \ / 6 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 1 0 | | 0 0 0 1 | \ / 7 is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 1 0 0 | | 0 1 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9 }, it remains to prove termination of the 102-rule system { 0 1 1 -> 0 2 1 1 , 0 1 1 -> 0 1 , 0 1 1 -> 0 , 0 3 1 -> 4 1 1 , 4 5 1 -> 0 5 2 3 , 4 5 1 -> 4 , 4 6 1 -> 4 1 2 2 2 6 , 0 3 5 -> 4 1 , 0 3 5 -> 4 1 5 , 0 3 5 -> 4 2 1 , 0 3 5 -> 7 2 3 2 1 5 , 0 3 5 -> 4 2 1 5 , 7 3 5 -> 7 5 5 2 3 2 , 7 3 5 -> 4 2 , 7 3 5 -> 4 2 6 , 8 3 5 -> 4 9 5 2 , 8 3 5 -> 4 9 6 2 5 , 8 3 5 -> 4 9 5 5 2 2 , 8 3 5 -> 4 6 9 6 5 2 , 0 9 5 -> 8 1 2 5 , 4 1 9 -> 8 3 1 2 2 , 4 5 9 -> 4 2 9 5 2 2 , 0 9 9 -> 0 9 2 2 9 , 0 9 9 -> 8 2 2 9 , 4 2 5 1 -> 4 1 5 2 2 , 4 5 6 1 -> 0 6 5 3 , 4 5 6 1 -> 7 5 3 , 4 5 6 1 -> 4 , 7 3 1 5 -> 4 6 1 5 , 0 1 2 5 -> 0 5 2 2 1 , 0 1 2 5 -> 0 , 0 6 3 5 -> 4 6 1 2 5 , 8 6 3 5 -> 8 2 3 6 2 5 , 4 5 9 5 -> 8 3 1 5 5 , 4 6 1 6 -> 0 5 2 3 6 6 , 4 6 1 6 -> 4 6 6 , 0 3 5 6 -> 7 5 2 3 1 , 0 3 5 6 -> 4 1 , 0 2 6 9 -> 0 6 2 2 9 , 0 2 6 9 -> 7 2 2 9 , 0 2 6 9 -> 8 , 0 1 9 9 -> 0 9 9 1 2 2 , 0 1 9 9 -> 8 9 1 2 2 , 4 3 9 9 -> 4 3 2 2 9 9 , 4 2 5 9 1 -> 0 2 5 2 3 9 , 4 2 5 9 1 -> 4 9 , 0 2 9 9 1 -> 8 1 1 9 , 8 6 2 1 5 -> 8 1 6 5 , 4 2 5 1 5 -> 4 1 , 0 6 2 9 5 -> 0 9 6 5 5 2 , 0 6 2 9 5 -> 8 6 5 5 2 , 0 3 5 2 9 -> 0 9 5 3 , 0 3 5 2 9 -> 8 5 3 , 4 1 3 6 9 -> 4 2 3 6 1 9 , 1 1 1 ->= 2 1 2 1 1 , 1 3 1 ->= 2 2 3 1 1 , 3 5 1 ->= 1 5 2 3 , 3 6 1 ->= 3 1 2 2 2 6 , 6 1 5 ->= 2 6 5 2 1 , 1 3 5 ->= 5 2 3 1 , 1 3 5 ->= 2 3 1 5 , 1 3 5 ->= 5 2 3 2 1 , 1 3 5 ->= 6 2 3 2 1 5 , 6 3 5 ->= 6 5 5 2 3 2 , 6 3 5 ->= 5 2 2 3 2 6 , 9 3 5 ->= 3 9 5 2 , 9 3 5 ->= 3 9 6 2 5 , 9 3 5 ->= 3 9 5 5 2 2 , 9 3 5 ->= 3 6 9 6 5 2 , 1 9 5 ->= 2 2 9 1 2 5 , 3 1 9 ->= 9 3 1 2 2 , 6 1 9 ->= 2 2 6 9 1 , 6 3 9 ->= 6 5 2 2 3 9 , 3 5 9 ->= 3 2 9 5 2 2 , 1 9 9 ->= 1 9 2 2 9 , 6 3 1 1 ->= 2 2 3 1 6 1 , 3 2 5 1 ->= 3 1 5 2 2 , 6 3 5 1 ->= 6 6 1 5 2 3 , 3 5 6 1 ->= 2 1 6 5 3 , 6 3 1 5 ->= 2 2 3 6 1 5 , 6 9 1 5 ->= 5 2 9 1 6 5 , 1 1 2 5 ->= 2 1 5 2 2 1 , 1 6 3 5 ->= 3 6 1 2 5 , 9 6 3 5 ->= 9 2 3 6 2 5 , 6 9 3 5 ->= 3 9 5 6 5 , 3 5 9 5 ->= 9 3 1 5 5 , 3 6 1 6 ->= 1 5 2 3 6 6 , 1 3 5 6 ->= 6 5 2 3 1 , 1 2 6 9 ->= 2 1 6 2 2 9 , 1 1 9 9 ->= 1 9 9 1 2 2 , 3 3 9 9 ->= 3 3 2 2 9 9 , 6 3 2 1 1 ->= 6 2 2 3 1 1 , 3 2 5 9 1 ->= 1 2 5 2 3 9 , 1 2 9 9 1 ->= 2 2 9 1 1 9 , 9 6 2 1 5 ->= 2 2 9 1 6 5 , 3 2 5 1 5 ->= 5 5 2 2 3 1 , 6 1 3 3 5 ->= 6 2 1 3 3 5 , 1 6 2 9 5 ->= 1 9 6 5 5 2 , 6 1 5 9 5 ->= 6 5 9 2 1 5 , 6 3 1 2 9 ->= 5 1 6 9 2 3 , 1 3 5 2 9 ->= 2 2 1 9 5 3 , 3 1 3 6 9 ->= 3 2 3 6 1 9 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 is interpreted by / \ | 1 0 1 0 0 1 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 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 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 1 0 0 1 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 1 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 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 1 0 0 0 0 0 0 | | 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 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 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 1 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 0 0 | \ / 6 is interpreted by / \ | 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 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 | \ / 7 is interpreted by / \ | 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 | \ / 8 is interpreted by / \ | 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 | \ / 9 is interpreted by / \ | 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 1 0 0 0 0 0 0 | | 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, 8->8, 9->9 }, it remains to prove termination of the 99-rule system { 0 1 1 -> 0 2 1 1 , 0 1 1 -> 0 1 , 0 1 1 -> 0 , 0 3 1 -> 4 1 1 , 4 5 1 -> 0 5 2 3 , 4 5 1 -> 4 , 4 6 1 -> 4 1 2 2 2 6 , 0 3 5 -> 4 1 , 0 3 5 -> 4 1 5 , 0 3 5 -> 4 2 1 , 0 3 5 -> 7 2 3 2 1 5 , 0 3 5 -> 4 2 1 5 , 7 3 5 -> 7 5 5 2 3 2 , 7 3 5 -> 4 2 , 7 3 5 -> 4 2 6 , 8 3 5 -> 4 9 5 2 , 8 3 5 -> 4 9 6 2 5 , 8 3 5 -> 4 9 5 5 2 2 , 8 3 5 -> 4 6 9 6 5 2 , 0 9 5 -> 8 1 2 5 , 4 1 9 -> 8 3 1 2 2 , 4 5 9 -> 4 2 9 5 2 2 , 0 9 9 -> 0 9 2 2 9 , 0 9 9 -> 8 2 2 9 , 4 2 5 1 -> 4 1 5 2 2 , 4 5 6 1 -> 0 6 5 3 , 4 5 6 1 -> 7 5 3 , 4 5 6 1 -> 4 , 7 3 1 5 -> 4 6 1 5 , 0 1 2 5 -> 0 5 2 2 1 , 0 1 2 5 -> 0 , 0 6 3 5 -> 4 6 1 2 5 , 8 6 3 5 -> 8 2 3 6 2 5 , 4 5 9 5 -> 8 3 1 5 5 , 4 6 1 6 -> 0 5 2 3 6 6 , 4 6 1 6 -> 4 6 6 , 0 3 5 6 -> 7 5 2 3 1 , 0 3 5 6 -> 4 1 , 0 1 9 9 -> 0 9 9 1 2 2 , 0 1 9 9 -> 8 9 1 2 2 , 4 3 9 9 -> 4 3 2 2 9 9 , 4 2 5 9 1 -> 0 2 5 2 3 9 , 4 2 5 9 1 -> 4 9 , 0 2 9 9 1 -> 8 1 1 9 , 8 6 2 1 5 -> 8 1 6 5 , 4 2 5 1 5 -> 4 1 , 0 6 2 9 5 -> 0 9 6 5 5 2 , 0 6 2 9 5 -> 8 6 5 5 2 , 0 3 5 2 9 -> 0 9 5 3 , 0 3 5 2 9 -> 8 5 3 , 4 1 3 6 9 -> 4 2 3 6 1 9 , 1 1 1 ->= 2 1 2 1 1 , 1 3 1 ->= 2 2 3 1 1 , 3 5 1 ->= 1 5 2 3 , 3 6 1 ->= 3 1 2 2 2 6 , 6 1 5 ->= 2 6 5 2 1 , 1 3 5 ->= 5 2 3 1 , 1 3 5 ->= 2 3 1 5 , 1 3 5 ->= 5 2 3 2 1 , 1 3 5 ->= 6 2 3 2 1 5 , 6 3 5 ->= 6 5 5 2 3 2 , 6 3 5 ->= 5 2 2 3 2 6 , 9 3 5 ->= 3 9 5 2 , 9 3 5 ->= 3 9 6 2 5 , 9 3 5 ->= 3 9 5 5 2 2 , 9 3 5 ->= 3 6 9 6 5 2 , 1 9 5 ->= 2 2 9 1 2 5 , 3 1 9 ->= 9 3 1 2 2 , 6 1 9 ->= 2 2 6 9 1 , 6 3 9 ->= 6 5 2 2 3 9 , 3 5 9 ->= 3 2 9 5 2 2 , 1 9 9 ->= 1 9 2 2 9 , 6 3 1 1 ->= 2 2 3 1 6 1 , 3 2 5 1 ->= 3 1 5 2 2 , 6 3 5 1 ->= 6 6 1 5 2 3 , 3 5 6 1 ->= 2 1 6 5 3 , 6 3 1 5 ->= 2 2 3 6 1 5 , 6 9 1 5 ->= 5 2 9 1 6 5 , 1 1 2 5 ->= 2 1 5 2 2 1 , 1 6 3 5 ->= 3 6 1 2 5 , 9 6 3 5 ->= 9 2 3 6 2 5 , 6 9 3 5 ->= 3 9 5 6 5 , 3 5 9 5 ->= 9 3 1 5 5 , 3 6 1 6 ->= 1 5 2 3 6 6 , 1 3 5 6 ->= 6 5 2 3 1 , 1 2 6 9 ->= 2 1 6 2 2 9 , 1 1 9 9 ->= 1 9 9 1 2 2 , 3 3 9 9 ->= 3 3 2 2 9 9 , 6 3 2 1 1 ->= 6 2 2 3 1 1 , 3 2 5 9 1 ->= 1 2 5 2 3 9 , 1 2 9 9 1 ->= 2 2 9 1 1 9 , 9 6 2 1 5 ->= 2 2 9 1 6 5 , 3 2 5 1 5 ->= 5 5 2 2 3 1 , 6 1 3 3 5 ->= 6 2 1 3 3 5 , 1 6 2 9 5 ->= 1 9 6 5 5 2 , 6 1 5 9 5 ->= 6 5 9 2 1 5 , 6 3 1 2 9 ->= 5 1 6 9 2 3 , 1 3 5 2 9 ->= 2 2 1 9 5 3 , 3 1 3 6 9 ->= 3 2 3 6 1 9 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: 0 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 1 0 | \ / 2 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 1 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 1 0 0 | | 0 1 0 0 | \ / 7 is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 1 0 0 | | 0 0 1 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9 }, it remains to prove termination of the 96-rule system { 0 1 1 -> 0 2 1 1 , 0 1 1 -> 0 1 , 0 1 1 -> 0 , 0 3 1 -> 4 1 1 , 4 5 1 -> 0 5 2 3 , 4 5 1 -> 4 , 4 6 1 -> 4 1 2 2 2 6 , 0 3 5 -> 4 1 , 0 3 5 -> 4 1 5 , 0 3 5 -> 4 2 1 , 0 3 5 -> 7 2 3 2 1 5 , 0 3 5 -> 4 2 1 5 , 8 3 5 -> 4 9 5 2 , 8 3 5 -> 4 9 6 2 5 , 8 3 5 -> 4 9 5 5 2 2 , 8 3 5 -> 4 6 9 6 5 2 , 0 9 5 -> 8 1 2 5 , 4 1 9 -> 8 3 1 2 2 , 4 5 9 -> 4 2 9 5 2 2 , 0 9 9 -> 0 9 2 2 9 , 0 9 9 -> 8 2 2 9 , 4 2 5 1 -> 4 1 5 2 2 , 4 5 6 1 -> 0 6 5 3 , 4 5 6 1 -> 7 5 3 , 4 5 6 1 -> 4 , 7 3 1 5 -> 4 6 1 5 , 0 1 2 5 -> 0 5 2 2 1 , 0 1 2 5 -> 0 , 0 6 3 5 -> 4 6 1 2 5 , 8 6 3 5 -> 8 2 3 6 2 5 , 4 5 9 5 -> 8 3 1 5 5 , 4 6 1 6 -> 0 5 2 3 6 6 , 4 6 1 6 -> 4 6 6 , 0 3 5 6 -> 7 5 2 3 1 , 0 3 5 6 -> 4 1 , 0 1 9 9 -> 0 9 9 1 2 2 , 0 1 9 9 -> 8 9 1 2 2 , 4 3 9 9 -> 4 3 2 2 9 9 , 4 2 5 9 1 -> 0 2 5 2 3 9 , 4 2 5 9 1 -> 4 9 , 0 2 9 9 1 -> 8 1 1 9 , 8 6 2 1 5 -> 8 1 6 5 , 4 2 5 1 5 -> 4 1 , 0 6 2 9 5 -> 0 9 6 5 5 2 , 0 6 2 9 5 -> 8 6 5 5 2 , 0 3 5 2 9 -> 0 9 5 3 , 0 3 5 2 9 -> 8 5 3 , 4 1 3 6 9 -> 4 2 3 6 1 9 , 1 1 1 ->= 2 1 2 1 1 , 1 3 1 ->= 2 2 3 1 1 , 3 5 1 ->= 1 5 2 3 , 3 6 1 ->= 3 1 2 2 2 6 , 6 1 5 ->= 2 6 5 2 1 , 1 3 5 ->= 5 2 3 1 , 1 3 5 ->= 2 3 1 5 , 1 3 5 ->= 5 2 3 2 1 , 1 3 5 ->= 6 2 3 2 1 5 , 6 3 5 ->= 6 5 5 2 3 2 , 6 3 5 ->= 5 2 2 3 2 6 , 9 3 5 ->= 3 9 5 2 , 9 3 5 ->= 3 9 6 2 5 , 9 3 5 ->= 3 9 5 5 2 2 , 9 3 5 ->= 3 6 9 6 5 2 , 1 9 5 ->= 2 2 9 1 2 5 , 3 1 9 ->= 9 3 1 2 2 , 6 1 9 ->= 2 2 6 9 1 , 6 3 9 ->= 6 5 2 2 3 9 , 3 5 9 ->= 3 2 9 5 2 2 , 1 9 9 ->= 1 9 2 2 9 , 6 3 1 1 ->= 2 2 3 1 6 1 , 3 2 5 1 ->= 3 1 5 2 2 , 6 3 5 1 ->= 6 6 1 5 2 3 , 3 5 6 1 ->= 2 1 6 5 3 , 6 3 1 5 ->= 2 2 3 6 1 5 , 6 9 1 5 ->= 5 2 9 1 6 5 , 1 1 2 5 ->= 2 1 5 2 2 1 , 1 6 3 5 ->= 3 6 1 2 5 , 9 6 3 5 ->= 9 2 3 6 2 5 , 6 9 3 5 ->= 3 9 5 6 5 , 3 5 9 5 ->= 9 3 1 5 5 , 3 6 1 6 ->= 1 5 2 3 6 6 , 1 3 5 6 ->= 6 5 2 3 1 , 1 2 6 9 ->= 2 1 6 2 2 9 , 1 1 9 9 ->= 1 9 9 1 2 2 , 3 3 9 9 ->= 3 3 2 2 9 9 , 6 3 2 1 1 ->= 6 2 2 3 1 1 , 3 2 5 9 1 ->= 1 2 5 2 3 9 , 1 2 9 9 1 ->= 2 2 9 1 1 9 , 9 6 2 1 5 ->= 2 2 9 1 6 5 , 3 2 5 1 5 ->= 5 5 2 2 3 1 , 6 1 3 3 5 ->= 6 2 1 3 3 5 , 1 6 2 9 5 ->= 1 9 6 5 5 2 , 6 1 5 9 5 ->= 6 5 9 2 1 5 , 6 3 1 2 9 ->= 5 1 6 9 2 3 , 1 3 5 2 9 ->= 2 2 1 9 5 3 , 3 1 3 6 9 ->= 3 2 3 6 1 9 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 1 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 1 | | 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 | | 0 1 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 1 0 0 0 | | 0 1 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9 }, it remains to prove termination of the 95-rule system { 0 1 1 -> 0 2 1 1 , 0 1 1 -> 0 1 , 0 1 1 -> 0 , 0 3 1 -> 4 1 1 , 4 5 1 -> 0 5 2 3 , 4 5 1 -> 4 , 4 6 1 -> 4 1 2 2 2 6 , 0 3 5 -> 4 1 , 0 3 5 -> 4 1 5 , 0 3 5 -> 4 2 1 , 0 3 5 -> 7 2 3 2 1 5 , 0 3 5 -> 4 2 1 5 , 8 3 5 -> 4 9 5 2 , 8 3 5 -> 4 9 6 2 5 , 8 3 5 -> 4 9 5 5 2 2 , 8 3 5 -> 4 6 9 6 5 2 , 0 9 5 -> 8 1 2 5 , 4 1 9 -> 8 3 1 2 2 , 4 5 9 -> 4 2 9 5 2 2 , 0 9 9 -> 0 9 2 2 9 , 0 9 9 -> 8 2 2 9 , 4 2 5 1 -> 4 1 5 2 2 , 4 5 6 1 -> 0 6 5 3 , 4 5 6 1 -> 7 5 3 , 4 5 6 1 -> 4 , 7 3 1 5 -> 4 6 1 5 , 0 1 2 5 -> 0 5 2 2 1 , 0 1 2 5 -> 0 , 0 6 3 5 -> 4 6 1 2 5 , 4 5 9 5 -> 8 3 1 5 5 , 4 6 1 6 -> 0 5 2 3 6 6 , 4 6 1 6 -> 4 6 6 , 0 3 5 6 -> 7 5 2 3 1 , 0 3 5 6 -> 4 1 , 0 1 9 9 -> 0 9 9 1 2 2 , 0 1 9 9 -> 8 9 1 2 2 , 4 3 9 9 -> 4 3 2 2 9 9 , 4 2 5 9 1 -> 0 2 5 2 3 9 , 4 2 5 9 1 -> 4 9 , 0 2 9 9 1 -> 8 1 1 9 , 8 6 2 1 5 -> 8 1 6 5 , 4 2 5 1 5 -> 4 1 , 0 6 2 9 5 -> 0 9 6 5 5 2 , 0 6 2 9 5 -> 8 6 5 5 2 , 0 3 5 2 9 -> 0 9 5 3 , 0 3 5 2 9 -> 8 5 3 , 4 1 3 6 9 -> 4 2 3 6 1 9 , 1 1 1 ->= 2 1 2 1 1 , 1 3 1 ->= 2 2 3 1 1 , 3 5 1 ->= 1 5 2 3 , 3 6 1 ->= 3 1 2 2 2 6 , 6 1 5 ->= 2 6 5 2 1 , 1 3 5 ->= 5 2 3 1 , 1 3 5 ->= 2 3 1 5 , 1 3 5 ->= 5 2 3 2 1 , 1 3 5 ->= 6 2 3 2 1 5 , 6 3 5 ->= 6 5 5 2 3 2 , 6 3 5 ->= 5 2 2 3 2 6 , 9 3 5 ->= 3 9 5 2 , 9 3 5 ->= 3 9 6 2 5 , 9 3 5 ->= 3 9 5 5 2 2 , 9 3 5 ->= 3 6 9 6 5 2 , 1 9 5 ->= 2 2 9 1 2 5 , 3 1 9 ->= 9 3 1 2 2 , 6 1 9 ->= 2 2 6 9 1 , 6 3 9 ->= 6 5 2 2 3 9 , 3 5 9 ->= 3 2 9 5 2 2 , 1 9 9 ->= 1 9 2 2 9 , 6 3 1 1 ->= 2 2 3 1 6 1 , 3 2 5 1 ->= 3 1 5 2 2 , 6 3 5 1 ->= 6 6 1 5 2 3 , 3 5 6 1 ->= 2 1 6 5 3 , 6 3 1 5 ->= 2 2 3 6 1 5 , 6 9 1 5 ->= 5 2 9 1 6 5 , 1 1 2 5 ->= 2 1 5 2 2 1 , 1 6 3 5 ->= 3 6 1 2 5 , 9 6 3 5 ->= 9 2 3 6 2 5 , 6 9 3 5 ->= 3 9 5 6 5 , 3 5 9 5 ->= 9 3 1 5 5 , 3 6 1 6 ->= 1 5 2 3 6 6 , 1 3 5 6 ->= 6 5 2 3 1 , 1 2 6 9 ->= 2 1 6 2 2 9 , 1 1 9 9 ->= 1 9 9 1 2 2 , 3 3 9 9 ->= 3 3 2 2 9 9 , 6 3 2 1 1 ->= 6 2 2 3 1 1 , 3 2 5 9 1 ->= 1 2 5 2 3 9 , 1 2 9 9 1 ->= 2 2 9 1 1 9 , 9 6 2 1 5 ->= 2 2 9 1 6 5 , 3 2 5 1 5 ->= 5 5 2 2 3 1 , 6 1 3 3 5 ->= 6 2 1 3 3 5 , 1 6 2 9 5 ->= 1 9 6 5 5 2 , 6 1 5 9 5 ->= 6 5 9 2 1 5 , 6 3 1 2 9 ->= 5 1 6 9 2 3 , 1 3 5 2 9 ->= 2 2 1 9 5 3 , 3 1 3 6 9 ->= 3 2 3 6 1 9 } 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 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 1 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 1 | \ / 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 1 1 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 6 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 1 1 | \ / 7 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 | \ / 8 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 | \ / 9 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, 6->6, 7->7, 8->8, 9->9 }, it remains to prove termination of the 94-rule system { 0 1 1 -> 0 2 1 1 , 0 1 1 -> 0 1 , 0 1 1 -> 0 , 0 3 1 -> 4 1 1 , 4 5 1 -> 0 5 2 3 , 4 5 1 -> 4 , 4 6 1 -> 4 1 2 2 2 6 , 0 3 5 -> 4 1 , 0 3 5 -> 4 1 5 , 0 3 5 -> 4 2 1 , 0 3 5 -> 7 2 3 2 1 5 , 0 3 5 -> 4 2 1 5 , 8 3 5 -> 4 9 5 2 , 8 3 5 -> 4 9 6 2 5 , 8 3 5 -> 4 9 5 5 2 2 , 8 3 5 -> 4 6 9 6 5 2 , 0 9 5 -> 8 1 2 5 , 4 1 9 -> 8 3 1 2 2 , 4 5 9 -> 4 2 9 5 2 2 , 0 9 9 -> 0 9 2 2 9 , 0 9 9 -> 8 2 2 9 , 4 2 5 1 -> 4 1 5 2 2 , 4 5 6 1 -> 0 6 5 3 , 4 5 6 1 -> 7 5 3 , 4 5 6 1 -> 4 , 7 3 1 5 -> 4 6 1 5 , 0 1 2 5 -> 0 5 2 2 1 , 0 1 2 5 -> 0 , 0 6 3 5 -> 4 6 1 2 5 , 4 5 9 5 -> 8 3 1 5 5 , 4 6 1 6 -> 0 5 2 3 6 6 , 4 6 1 6 -> 4 6 6 , 0 3 5 6 -> 7 5 2 3 1 , 0 3 5 6 -> 4 1 , 0 1 9 9 -> 0 9 9 1 2 2 , 0 1 9 9 -> 8 9 1 2 2 , 4 3 9 9 -> 4 3 2 2 9 9 , 4 2 5 9 1 -> 0 2 5 2 3 9 , 4 2 5 9 1 -> 4 9 , 0 2 9 9 1 -> 8 1 1 9 , 8 6 2 1 5 -> 8 1 6 5 , 4 2 5 1 5 -> 4 1 , 0 6 2 9 5 -> 0 9 6 5 5 2 , 0 6 2 9 5 -> 8 6 5 5 2 , 0 3 5 2 9 -> 0 9 5 3 , 0 3 5 2 9 -> 8 5 3 , 4 1 3 6 9 -> 4 2 3 6 1 9 , 1 1 1 ->= 2 1 2 1 1 , 1 3 1 ->= 2 2 3 1 1 , 3 5 1 ->= 1 5 2 3 , 3 6 1 ->= 3 1 2 2 2 6 , 6 1 5 ->= 2 6 5 2 1 , 1 3 5 ->= 5 2 3 1 , 1 3 5 ->= 2 3 1 5 , 1 3 5 ->= 5 2 3 2 1 , 1 3 5 ->= 6 2 3 2 1 5 , 6 3 5 ->= 6 5 5 2 3 2 , 6 3 5 ->= 5 2 2 3 2 6 , 9 3 5 ->= 3 9 5 2 , 9 3 5 ->= 3 9 6 2 5 , 9 3 5 ->= 3 9 5 5 2 2 , 9 3 5 ->= 3 6 9 6 5 2 , 1 9 5 ->= 2 2 9 1 2 5 , 3 1 9 ->= 9 3 1 2 2 , 6 1 9 ->= 2 2 6 9 1 , 6 3 9 ->= 6 5 2 2 3 9 , 3 5 9 ->= 3 2 9 5 2 2 , 1 9 9 ->= 1 9 2 2 9 , 6 3 1 1 ->= 2 2 3 1 6 1 , 3 2 5 1 ->= 3 1 5 2 2 , 6 3 5 1 ->= 6 6 1 5 2 3 , 3 5 6 1 ->= 2 1 6 5 3 , 6 3 1 5 ->= 2 2 3 6 1 5 , 6 9 1 5 ->= 5 2 9 1 6 5 , 1 1 2 5 ->= 2 1 5 2 2 1 , 1 6 3 5 ->= 3 6 1 2 5 , 9 6 3 5 ->= 9 2 3 6 2 5 , 6 9 3 5 ->= 3 9 5 6 5 , 3 5 9 5 ->= 9 3 1 5 5 , 3 6 1 6 ->= 1 5 2 3 6 6 , 1 3 5 6 ->= 6 5 2 3 1 , 1 2 6 9 ->= 2 1 6 2 2 9 , 1 1 9 9 ->= 1 9 9 1 2 2 , 3 3 9 9 ->= 3 3 2 2 9 9 , 6 3 2 1 1 ->= 6 2 2 3 1 1 , 3 2 5 9 1 ->= 1 2 5 2 3 9 , 1 2 9 9 1 ->= 2 2 9 1 1 9 , 9 6 2 1 5 ->= 2 2 9 1 6 5 , 3 2 5 1 5 ->= 5 5 2 2 3 1 , 6 1 3 3 5 ->= 6 2 1 3 3 5 , 1 6 2 9 5 ->= 1 9 6 5 5 2 , 6 1 5 9 5 ->= 6 5 9 2 1 5 , 1 3 5 2 9 ->= 2 2 1 9 5 3 , 3 1 3 6 9 ->= 3 2 3 6 1 9 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: 0 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 1 0 | \ / 2 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / 4 is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 1 | \ / 7 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 6->5, 5->6, 7->7, 8->8, 9->9 }, it remains to prove termination of the 87-rule system { 0 1 1 -> 0 2 1 1 , 0 1 1 -> 0 1 , 0 1 1 -> 0 , 0 3 1 -> 4 1 1 , 4 5 1 -> 4 1 2 2 2 5 , 0 3 6 -> 4 1 , 0 3 6 -> 4 1 6 , 0 3 6 -> 4 2 1 , 0 3 6 -> 7 2 3 2 1 6 , 0 3 6 -> 4 2 1 6 , 8 3 6 -> 4 9 6 2 , 8 3 6 -> 4 9 5 2 6 , 8 3 6 -> 4 9 6 6 2 2 , 8 3 6 -> 4 5 9 5 6 2 , 0 9 6 -> 8 1 2 6 , 4 1 9 -> 8 3 1 2 2 , 0 9 9 -> 0 9 2 2 9 , 0 9 9 -> 8 2 2 9 , 4 2 6 1 -> 4 1 6 2 2 , 7 3 1 6 -> 4 5 1 6 , 0 1 2 6 -> 0 6 2 2 1 , 0 1 2 6 -> 0 , 0 5 3 6 -> 4 5 1 2 6 , 4 5 1 5 -> 0 6 2 3 5 5 , 4 5 1 5 -> 4 5 5 , 0 3 6 5 -> 7 6 2 3 1 , 0 3 6 5 -> 4 1 , 0 1 9 9 -> 0 9 9 1 2 2 , 0 1 9 9 -> 8 9 1 2 2 , 4 3 9 9 -> 4 3 2 2 9 9 , 4 2 6 9 1 -> 0 2 6 2 3 9 , 4 2 6 9 1 -> 4 9 , 0 2 9 9 1 -> 8 1 1 9 , 8 5 2 1 6 -> 8 1 5 6 , 4 2 6 1 6 -> 4 1 , 0 5 2 9 6 -> 0 9 5 6 6 2 , 0 5 2 9 6 -> 8 5 6 6 2 , 0 3 6 2 9 -> 0 9 6 3 , 0 3 6 2 9 -> 8 6 3 , 4 1 3 5 9 -> 4 2 3 5 1 9 , 1 1 1 ->= 2 1 2 1 1 , 1 3 1 ->= 2 2 3 1 1 , 3 6 1 ->= 1 6 2 3 , 3 5 1 ->= 3 1 2 2 2 5 , 5 1 6 ->= 2 5 6 2 1 , 1 3 6 ->= 6 2 3 1 , 1 3 6 ->= 2 3 1 6 , 1 3 6 ->= 6 2 3 2 1 , 1 3 6 ->= 5 2 3 2 1 6 , 5 3 6 ->= 5 6 6 2 3 2 , 5 3 6 ->= 6 2 2 3 2 5 , 9 3 6 ->= 3 9 6 2 , 9 3 6 ->= 3 9 5 2 6 , 9 3 6 ->= 3 9 6 6 2 2 , 9 3 6 ->= 3 5 9 5 6 2 , 1 9 6 ->= 2 2 9 1 2 6 , 3 1 9 ->= 9 3 1 2 2 , 5 1 9 ->= 2 2 5 9 1 , 5 3 9 ->= 5 6 2 2 3 9 , 3 6 9 ->= 3 2 9 6 2 2 , 1 9 9 ->= 1 9 2 2 9 , 5 3 1 1 ->= 2 2 3 1 5 1 , 3 2 6 1 ->= 3 1 6 2 2 , 5 3 6 1 ->= 5 5 1 6 2 3 , 3 6 5 1 ->= 2 1 5 6 3 , 5 3 1 6 ->= 2 2 3 5 1 6 , 5 9 1 6 ->= 6 2 9 1 5 6 , 1 1 2 6 ->= 2 1 6 2 2 1 , 1 5 3 6 ->= 3 5 1 2 6 , 9 5 3 6 ->= 9 2 3 5 2 6 , 5 9 3 6 ->= 3 9 6 5 6 , 3 6 9 6 ->= 9 3 1 6 6 , 3 5 1 5 ->= 1 6 2 3 5 5 , 1 3 6 5 ->= 5 6 2 3 1 , 1 2 5 9 ->= 2 1 5 2 2 9 , 1 1 9 9 ->= 1 9 9 1 2 2 , 3 3 9 9 ->= 3 3 2 2 9 9 , 5 3 2 1 1 ->= 5 2 2 3 1 1 , 3 2 6 9 1 ->= 1 2 6 2 3 9 , 1 2 9 9 1 ->= 2 2 9 1 1 9 , 9 5 2 1 6 ->= 2 2 9 1 5 6 , 3 2 6 1 6 ->= 6 6 2 2 3 1 , 5 1 3 3 6 ->= 5 2 1 3 3 6 , 1 5 2 9 6 ->= 1 9 5 6 6 2 , 5 1 6 9 6 ->= 5 6 9 2 1 6 , 1 3 6 2 9 ->= 2 2 1 9 6 3 , 3 1 3 5 9 ->= 3 2 3 5 1 9 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 1 0 | | 0 1 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 1 0 | | 0 1 0 0 0 | | 0 1 0 0 0 | \ / 4 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 | \ / 5 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 1 0 | | 0 0 0 1 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 1 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9 }, it remains to prove termination of the 86-rule system { 0 1 1 -> 0 2 1 1 , 0 1 1 -> 0 1 , 0 1 1 -> 0 , 0 3 1 -> 4 1 1 , 4 5 1 -> 4 1 2 2 2 5 , 0 3 6 -> 4 1 , 0 3 6 -> 4 1 6 , 0 3 6 -> 4 2 1 , 0 3 6 -> 7 2 3 2 1 6 , 0 3 6 -> 4 2 1 6 , 8 3 6 -> 4 9 6 2 , 8 3 6 -> 4 9 5 2 6 , 8 3 6 -> 4 9 6 6 2 2 , 8 3 6 -> 4 5 9 5 6 2 , 0 9 6 -> 8 1 2 6 , 4 1 9 -> 8 3 1 2 2 , 0 9 9 -> 0 9 2 2 9 , 0 9 9 -> 8 2 2 9 , 4 2 6 1 -> 4 1 6 2 2 , 7 3 1 6 -> 4 5 1 6 , 0 1 2 6 -> 0 6 2 2 1 , 0 1 2 6 -> 0 , 0 5 3 6 -> 4 5 1 2 6 , 4 5 1 5 -> 0 6 2 3 5 5 , 4 5 1 5 -> 4 5 5 , 0 3 6 5 -> 7 6 2 3 1 , 0 3 6 5 -> 4 1 , 0 1 9 9 -> 0 9 9 1 2 2 , 0 1 9 9 -> 8 9 1 2 2 , 4 2 6 9 1 -> 0 2 6 2 3 9 , 4 2 6 9 1 -> 4 9 , 0 2 9 9 1 -> 8 1 1 9 , 8 5 2 1 6 -> 8 1 5 6 , 4 2 6 1 6 -> 4 1 , 0 5 2 9 6 -> 0 9 5 6 6 2 , 0 5 2 9 6 -> 8 5 6 6 2 , 0 3 6 2 9 -> 0 9 6 3 , 0 3 6 2 9 -> 8 6 3 , 4 1 3 5 9 -> 4 2 3 5 1 9 , 1 1 1 ->= 2 1 2 1 1 , 1 3 1 ->= 2 2 3 1 1 , 3 6 1 ->= 1 6 2 3 , 3 5 1 ->= 3 1 2 2 2 5 , 5 1 6 ->= 2 5 6 2 1 , 1 3 6 ->= 6 2 3 1 , 1 3 6 ->= 2 3 1 6 , 1 3 6 ->= 6 2 3 2 1 , 1 3 6 ->= 5 2 3 2 1 6 , 5 3 6 ->= 5 6 6 2 3 2 , 5 3 6 ->= 6 2 2 3 2 5 , 9 3 6 ->= 3 9 6 2 , 9 3 6 ->= 3 9 5 2 6 , 9 3 6 ->= 3 9 6 6 2 2 , 9 3 6 ->= 3 5 9 5 6 2 , 1 9 6 ->= 2 2 9 1 2 6 , 3 1 9 ->= 9 3 1 2 2 , 5 1 9 ->= 2 2 5 9 1 , 5 3 9 ->= 5 6 2 2 3 9 , 3 6 9 ->= 3 2 9 6 2 2 , 1 9 9 ->= 1 9 2 2 9 , 5 3 1 1 ->= 2 2 3 1 5 1 , 3 2 6 1 ->= 3 1 6 2 2 , 5 3 6 1 ->= 5 5 1 6 2 3 , 3 6 5 1 ->= 2 1 5 6 3 , 5 3 1 6 ->= 2 2 3 5 1 6 , 5 9 1 6 ->= 6 2 9 1 5 6 , 1 1 2 6 ->= 2 1 6 2 2 1 , 1 5 3 6 ->= 3 5 1 2 6 , 9 5 3 6 ->= 9 2 3 5 2 6 , 5 9 3 6 ->= 3 9 6 5 6 , 3 6 9 6 ->= 9 3 1 6 6 , 3 5 1 5 ->= 1 6 2 3 5 5 , 1 3 6 5 ->= 5 6 2 3 1 , 1 2 5 9 ->= 2 1 5 2 2 9 , 1 1 9 9 ->= 1 9 9 1 2 2 , 3 3 9 9 ->= 3 3 2 2 9 9 , 5 3 2 1 1 ->= 5 2 2 3 1 1 , 3 2 6 9 1 ->= 1 2 6 2 3 9 , 1 2 9 9 1 ->= 2 2 9 1 1 9 , 9 5 2 1 6 ->= 2 2 9 1 5 6 , 3 2 6 1 6 ->= 6 6 2 2 3 1 , 5 1 3 3 6 ->= 5 2 1 3 3 6 , 1 5 2 9 6 ->= 1 9 5 6 6 2 , 5 1 6 9 6 ->= 5 6 9 2 1 6 , 1 3 6 2 9 ->= 2 2 1 9 6 3 , 3 1 3 5 9 ->= 3 2 3 5 1 9 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 2 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 | \ / 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 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9 }, it remains to prove termination of the 82-rule system { 0 1 1 -> 0 2 1 1 , 0 1 1 -> 0 1 , 0 1 1 -> 0 , 0 3 1 -> 4 1 1 , 4 5 1 -> 4 1 2 2 2 5 , 0 3 6 -> 4 1 , 0 3 6 -> 4 1 6 , 0 3 6 -> 4 2 1 , 0 3 6 -> 7 2 3 2 1 6 , 0 3 6 -> 4 2 1 6 , 8 3 6 -> 4 9 6 2 , 8 3 6 -> 4 9 5 2 6 , 8 3 6 -> 4 9 6 6 2 2 , 8 3 6 -> 4 5 9 5 6 2 , 0 9 6 -> 8 1 2 6 , 4 1 9 -> 8 3 1 2 2 , 0 9 9 -> 0 9 2 2 9 , 0 9 9 -> 8 2 2 9 , 7 3 1 6 -> 4 5 1 6 , 0 1 2 6 -> 0 6 2 2 1 , 0 1 2 6 -> 0 , 0 5 3 6 -> 4 5 1 2 6 , 4 5 1 5 -> 0 6 2 3 5 5 , 4 5 1 5 -> 4 5 5 , 0 3 6 5 -> 7 6 2 3 1 , 0 3 6 5 -> 4 1 , 0 1 9 9 -> 0 9 9 1 2 2 , 0 1 9 9 -> 8 9 1 2 2 , 0 2 9 9 1 -> 8 1 1 9 , 8 5 2 1 6 -> 8 1 5 6 , 0 5 2 9 6 -> 0 9 5 6 6 2 , 0 5 2 9 6 -> 8 5 6 6 2 , 0 3 6 2 9 -> 0 9 6 3 , 0 3 6 2 9 -> 8 6 3 , 4 1 3 5 9 -> 4 2 3 5 1 9 , 1 1 1 ->= 2 1 2 1 1 , 1 3 1 ->= 2 2 3 1 1 , 3 6 1 ->= 1 6 2 3 , 3 5 1 ->= 3 1 2 2 2 5 , 5 1 6 ->= 2 5 6 2 1 , 1 3 6 ->= 6 2 3 1 , 1 3 6 ->= 2 3 1 6 , 1 3 6 ->= 6 2 3 2 1 , 1 3 6 ->= 5 2 3 2 1 6 , 5 3 6 ->= 5 6 6 2 3 2 , 5 3 6 ->= 6 2 2 3 2 5 , 9 3 6 ->= 3 9 6 2 , 9 3 6 ->= 3 9 5 2 6 , 9 3 6 ->= 3 9 6 6 2 2 , 9 3 6 ->= 3 5 9 5 6 2 , 1 9 6 ->= 2 2 9 1 2 6 , 3 1 9 ->= 9 3 1 2 2 , 5 1 9 ->= 2 2 5 9 1 , 5 3 9 ->= 5 6 2 2 3 9 , 3 6 9 ->= 3 2 9 6 2 2 , 1 9 9 ->= 1 9 2 2 9 , 5 3 1 1 ->= 2 2 3 1 5 1 , 3 2 6 1 ->= 3 1 6 2 2 , 5 3 6 1 ->= 5 5 1 6 2 3 , 3 6 5 1 ->= 2 1 5 6 3 , 5 3 1 6 ->= 2 2 3 5 1 6 , 5 9 1 6 ->= 6 2 9 1 5 6 , 1 1 2 6 ->= 2 1 6 2 2 1 , 1 5 3 6 ->= 3 5 1 2 6 , 9 5 3 6 ->= 9 2 3 5 2 6 , 5 9 3 6 ->= 3 9 6 5 6 , 3 6 9 6 ->= 9 3 1 6 6 , 3 5 1 5 ->= 1 6 2 3 5 5 , 1 3 6 5 ->= 5 6 2 3 1 , 1 2 5 9 ->= 2 1 5 2 2 9 , 1 1 9 9 ->= 1 9 9 1 2 2 , 3 3 9 9 ->= 3 3 2 2 9 9 , 5 3 2 1 1 ->= 5 2 2 3 1 1 , 3 2 6 9 1 ->= 1 2 6 2 3 9 , 1 2 9 9 1 ->= 2 2 9 1 1 9 , 9 5 2 1 6 ->= 2 2 9 1 5 6 , 3 2 6 1 6 ->= 6 6 2 2 3 1 , 5 1 3 3 6 ->= 5 2 1 3 3 6 , 1 5 2 9 6 ->= 1 9 5 6 6 2 , 5 1 6 9 6 ->= 5 6 9 2 1 6 , 1 3 6 2 9 ->= 2 2 1 9 6 3 , 3 1 3 5 9 ->= 3 2 3 5 1 9 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 1 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 1 0 0 0 | \ / 4 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 | \ / 5 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9 }, it remains to prove termination of the 80-rule system { 0 1 1 -> 0 2 1 1 , 0 1 1 -> 0 1 , 0 1 1 -> 0 , 0 3 1 -> 4 1 1 , 4 5 1 -> 4 1 2 2 2 5 , 0 3 6 -> 4 1 , 0 3 6 -> 4 1 6 , 0 3 6 -> 4 2 1 , 0 3 6 -> 7 2 3 2 1 6 , 0 3 6 -> 4 2 1 6 , 8 3 6 -> 4 9 6 2 , 8 3 6 -> 4 9 5 2 6 , 8 3 6 -> 4 9 6 6 2 2 , 8 3 6 -> 4 5 9 5 6 2 , 0 9 6 -> 8 1 2 6 , 4 1 9 -> 8 3 1 2 2 , 0 9 9 -> 0 9 2 2 9 , 0 9 9 -> 8 2 2 9 , 7 3 1 6 -> 4 5 1 6 , 0 1 2 6 -> 0 6 2 2 1 , 0 1 2 6 -> 0 , 0 5 3 6 -> 4 5 1 2 6 , 0 3 6 5 -> 7 6 2 3 1 , 0 3 6 5 -> 4 1 , 0 1 9 9 -> 0 9 9 1 2 2 , 0 1 9 9 -> 8 9 1 2 2 , 0 2 9 9 1 -> 8 1 1 9 , 8 5 2 1 6 -> 8 1 5 6 , 0 5 2 9 6 -> 0 9 5 6 6 2 , 0 5 2 9 6 -> 8 5 6 6 2 , 0 3 6 2 9 -> 0 9 6 3 , 0 3 6 2 9 -> 8 6 3 , 4 1 3 5 9 -> 4 2 3 5 1 9 , 1 1 1 ->= 2 1 2 1 1 , 1 3 1 ->= 2 2 3 1 1 , 3 6 1 ->= 1 6 2 3 , 3 5 1 ->= 3 1 2 2 2 5 , 5 1 6 ->= 2 5 6 2 1 , 1 3 6 ->= 6 2 3 1 , 1 3 6 ->= 2 3 1 6 , 1 3 6 ->= 6 2 3 2 1 , 1 3 6 ->= 5 2 3 2 1 6 , 5 3 6 ->= 5 6 6 2 3 2 , 5 3 6 ->= 6 2 2 3 2 5 , 9 3 6 ->= 3 9 6 2 , 9 3 6 ->= 3 9 5 2 6 , 9 3 6 ->= 3 9 6 6 2 2 , 9 3 6 ->= 3 5 9 5 6 2 , 1 9 6 ->= 2 2 9 1 2 6 , 3 1 9 ->= 9 3 1 2 2 , 5 1 9 ->= 2 2 5 9 1 , 5 3 9 ->= 5 6 2 2 3 9 , 3 6 9 ->= 3 2 9 6 2 2 , 1 9 9 ->= 1 9 2 2 9 , 5 3 1 1 ->= 2 2 3 1 5 1 , 3 2 6 1 ->= 3 1 6 2 2 , 5 3 6 1 ->= 5 5 1 6 2 3 , 3 6 5 1 ->= 2 1 5 6 3 , 5 3 1 6 ->= 2 2 3 5 1 6 , 5 9 1 6 ->= 6 2 9 1 5 6 , 1 1 2 6 ->= 2 1 6 2 2 1 , 1 5 3 6 ->= 3 5 1 2 6 , 9 5 3 6 ->= 9 2 3 5 2 6 , 5 9 3 6 ->= 3 9 6 5 6 , 3 6 9 6 ->= 9 3 1 6 6 , 3 5 1 5 ->= 1 6 2 3 5 5 , 1 3 6 5 ->= 5 6 2 3 1 , 1 2 5 9 ->= 2 1 5 2 2 9 , 1 1 9 9 ->= 1 9 9 1 2 2 , 3 3 9 9 ->= 3 3 2 2 9 9 , 5 3 2 1 1 ->= 5 2 2 3 1 1 , 3 2 6 9 1 ->= 1 2 6 2 3 9 , 1 2 9 9 1 ->= 2 2 9 1 1 9 , 9 5 2 1 6 ->= 2 2 9 1 5 6 , 3 2 6 1 6 ->= 6 6 2 2 3 1 , 5 1 3 3 6 ->= 5 2 1 3 3 6 , 1 5 2 9 6 ->= 1 9 5 6 6 2 , 5 1 6 9 6 ->= 5 6 9 2 1 6 , 1 3 6 2 9 ->= 2 2 1 9 6 3 , 3 1 3 5 9 ->= 3 2 3 5 1 9 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 is interpreted by / \ | 1 1 | | 0 1 | \ / 1 is interpreted by / \ | 1 0 | | 0 1 | \ / 2 is interpreted by / \ | 1 0 | | 0 1 | \ / 3 is interpreted by / \ | 1 0 | | 0 1 | \ / 4 is interpreted by / \ | 1 0 | | 0 1 | \ / 5 is interpreted by / \ | 1 0 | | 0 1 | \ / 6 is interpreted by / \ | 1 0 | | 0 1 | \ / 7 is interpreted by / \ | 1 0 | | 0 1 | \ / 8 is interpreted by / \ | 1 0 | | 0 1 | \ / 9 is interpreted by / \ | 1 0 | | 0 1 | \ / After renaming modulo { 0->0, 1->1, 2->2, 4->3, 5->4, 8->5, 3->6, 6->7, 9->8, 7->9 }, it remains to prove termination of the 65-rule system { 0 1 1 -> 0 2 1 1 , 0 1 1 -> 0 1 , 0 1 1 -> 0 , 3 4 1 -> 3 1 2 2 2 4 , 5 6 7 -> 3 8 7 2 , 5 6 7 -> 3 8 4 2 7 , 5 6 7 -> 3 8 7 7 2 2 , 5 6 7 -> 3 4 8 4 7 2 , 3 1 8 -> 5 6 1 2 2 , 0 8 8 -> 0 8 2 2 8 , 9 6 1 7 -> 3 4 1 7 , 0 1 2 7 -> 0 7 2 2 1 , 0 1 2 7 -> 0 , 0 1 8 8 -> 0 8 8 1 2 2 , 5 4 2 1 7 -> 5 1 4 7 , 0 4 2 8 7 -> 0 8 4 7 7 2 , 0 6 7 2 8 -> 0 8 7 6 , 3 1 6 4 8 -> 3 2 6 4 1 8 , 1 1 1 ->= 2 1 2 1 1 , 1 6 1 ->= 2 2 6 1 1 , 6 7 1 ->= 1 7 2 6 , 6 4 1 ->= 6 1 2 2 2 4 , 4 1 7 ->= 2 4 7 2 1 , 1 6 7 ->= 7 2 6 1 , 1 6 7 ->= 2 6 1 7 , 1 6 7 ->= 7 2 6 2 1 , 1 6 7 ->= 4 2 6 2 1 7 , 4 6 7 ->= 4 7 7 2 6 2 , 4 6 7 ->= 7 2 2 6 2 4 , 8 6 7 ->= 6 8 7 2 , 8 6 7 ->= 6 8 4 2 7 , 8 6 7 ->= 6 8 7 7 2 2 , 8 6 7 ->= 6 4 8 4 7 2 , 1 8 7 ->= 2 2 8 1 2 7 , 6 1 8 ->= 8 6 1 2 2 , 4 1 8 ->= 2 2 4 8 1 , 4 6 8 ->= 4 7 2 2 6 8 , 6 7 8 ->= 6 2 8 7 2 2 , 1 8 8 ->= 1 8 2 2 8 , 4 6 1 1 ->= 2 2 6 1 4 1 , 6 2 7 1 ->= 6 1 7 2 2 , 4 6 7 1 ->= 4 4 1 7 2 6 , 6 7 4 1 ->= 2 1 4 7 6 , 4 6 1 7 ->= 2 2 6 4 1 7 , 4 8 1 7 ->= 7 2 8 1 4 7 , 1 1 2 7 ->= 2 1 7 2 2 1 , 1 4 6 7 ->= 6 4 1 2 7 , 8 4 6 7 ->= 8 2 6 4 2 7 , 4 8 6 7 ->= 6 8 7 4 7 , 6 7 8 7 ->= 8 6 1 7 7 , 6 4 1 4 ->= 1 7 2 6 4 4 , 1 6 7 4 ->= 4 7 2 6 1 , 1 2 4 8 ->= 2 1 4 2 2 8 , 1 1 8 8 ->= 1 8 8 1 2 2 , 6 6 8 8 ->= 6 6 2 2 8 8 , 4 6 2 1 1 ->= 4 2 2 6 1 1 , 6 2 7 8 1 ->= 1 2 7 2 6 8 , 1 2 8 8 1 ->= 2 2 8 1 1 8 , 8 4 2 1 7 ->= 2 2 8 1 4 7 , 6 2 7 1 7 ->= 7 7 2 2 6 1 , 4 1 6 6 7 ->= 4 2 1 6 6 7 , 1 4 2 8 7 ->= 1 8 4 7 7 2 , 4 1 7 8 7 ->= 4 7 8 2 1 7 , 1 6 7 2 8 ->= 2 2 1 8 7 6 , 6 1 6 4 8 ->= 6 2 6 4 1 8 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 is interpreted by / \ | 1 1 | | 0 1 | \ / 1 is interpreted by / \ | 1 0 | | 0 1 | \ / 2 is interpreted by / \ | 1 0 | | 0 1 | \ / 3 is interpreted by / \ | 1 0 | | 0 1 | \ / 4 is interpreted by / \ | 1 0 | | 0 1 | \ / 5 is interpreted by / \ | 1 0 | | 0 1 | \ / 6 is interpreted by / \ | 1 0 | | 0 1 | \ / 7 is interpreted by / \ | 1 0 | | 0 1 | \ / 8 is interpreted by / \ | 1 0 | | 0 1 | \ / 9 is interpreted by / \ | 1 1 | | 0 1 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, it remains to prove termination of the 64-rule system { 0 1 1 -> 0 2 1 1 , 0 1 1 -> 0 1 , 0 1 1 -> 0 , 3 4 1 -> 3 1 2 2 2 4 , 5 6 7 -> 3 8 7 2 , 5 6 7 -> 3 8 4 2 7 , 5 6 7 -> 3 8 7 7 2 2 , 5 6 7 -> 3 4 8 4 7 2 , 3 1 8 -> 5 6 1 2 2 , 0 8 8 -> 0 8 2 2 8 , 0 1 2 7 -> 0 7 2 2 1 , 0 1 2 7 -> 0 , 0 1 8 8 -> 0 8 8 1 2 2 , 5 4 2 1 7 -> 5 1 4 7 , 0 4 2 8 7 -> 0 8 4 7 7 2 , 0 6 7 2 8 -> 0 8 7 6 , 3 1 6 4 8 -> 3 2 6 4 1 8 , 1 1 1 ->= 2 1 2 1 1 , 1 6 1 ->= 2 2 6 1 1 , 6 7 1 ->= 1 7 2 6 , 6 4 1 ->= 6 1 2 2 2 4 , 4 1 7 ->= 2 4 7 2 1 , 1 6 7 ->= 7 2 6 1 , 1 6 7 ->= 2 6 1 7 , 1 6 7 ->= 7 2 6 2 1 , 1 6 7 ->= 4 2 6 2 1 7 , 4 6 7 ->= 4 7 7 2 6 2 , 4 6 7 ->= 7 2 2 6 2 4 , 8 6 7 ->= 6 8 7 2 , 8 6 7 ->= 6 8 4 2 7 , 8 6 7 ->= 6 8 7 7 2 2 , 8 6 7 ->= 6 4 8 4 7 2 , 1 8 7 ->= 2 2 8 1 2 7 , 6 1 8 ->= 8 6 1 2 2 , 4 1 8 ->= 2 2 4 8 1 , 4 6 8 ->= 4 7 2 2 6 8 , 6 7 8 ->= 6 2 8 7 2 2 , 1 8 8 ->= 1 8 2 2 8 , 4 6 1 1 ->= 2 2 6 1 4 1 , 6 2 7 1 ->= 6 1 7 2 2 , 4 6 7 1 ->= 4 4 1 7 2 6 , 6 7 4 1 ->= 2 1 4 7 6 , 4 6 1 7 ->= 2 2 6 4 1 7 , 4 8 1 7 ->= 7 2 8 1 4 7 , 1 1 2 7 ->= 2 1 7 2 2 1 , 1 4 6 7 ->= 6 4 1 2 7 , 8 4 6 7 ->= 8 2 6 4 2 7 , 4 8 6 7 ->= 6 8 7 4 7 , 6 7 8 7 ->= 8 6 1 7 7 , 6 4 1 4 ->= 1 7 2 6 4 4 , 1 6 7 4 ->= 4 7 2 6 1 , 1 2 4 8 ->= 2 1 4 2 2 8 , 1 1 8 8 ->= 1 8 8 1 2 2 , 6 6 8 8 ->= 6 6 2 2 8 8 , 4 6 2 1 1 ->= 4 2 2 6 1 1 , 6 2 7 8 1 ->= 1 2 7 2 6 8 , 1 2 8 8 1 ->= 2 2 8 1 1 8 , 8 4 2 1 7 ->= 2 2 8 1 4 7 , 6 2 7 1 7 ->= 7 7 2 2 6 1 , 4 1 6 6 7 ->= 4 2 1 6 6 7 , 1 4 2 8 7 ->= 1 8 4 7 7 2 , 4 1 7 8 7 ->= 4 7 8 2 1 7 , 1 6 7 2 8 ->= 2 2 1 8 7 6 , 6 1 6 4 8 ->= 6 2 6 4 1 8 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: 0 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 1 | \ / 2 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 1 0 | \ / 7 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, it remains to prove termination of the 62-rule system { 0 1 1 -> 0 2 1 1 , 0 1 1 -> 0 1 , 0 1 1 -> 0 , 3 4 1 -> 3 1 2 2 2 4 , 5 6 7 -> 3 8 7 2 , 5 6 7 -> 3 8 4 2 7 , 5 6 7 -> 3 8 7 7 2 2 , 5 6 7 -> 3 4 8 4 7 2 , 0 8 8 -> 0 8 2 2 8 , 0 1 2 7 -> 0 7 2 2 1 , 0 1 2 7 -> 0 , 0 1 8 8 -> 0 8 8 1 2 2 , 5 4 2 1 7 -> 5 1 4 7 , 0 4 2 8 7 -> 0 8 4 7 7 2 , 0 6 7 2 8 -> 0 8 7 6 , 1 1 1 ->= 2 1 2 1 1 , 1 6 1 ->= 2 2 6 1 1 , 6 7 1 ->= 1 7 2 6 , 6 4 1 ->= 6 1 2 2 2 4 , 4 1 7 ->= 2 4 7 2 1 , 1 6 7 ->= 7 2 6 1 , 1 6 7 ->= 2 6 1 7 , 1 6 7 ->= 7 2 6 2 1 , 1 6 7 ->= 4 2 6 2 1 7 , 4 6 7 ->= 4 7 7 2 6 2 , 4 6 7 ->= 7 2 2 6 2 4 , 8 6 7 ->= 6 8 7 2 , 8 6 7 ->= 6 8 4 2 7 , 8 6 7 ->= 6 8 7 7 2 2 , 8 6 7 ->= 6 4 8 4 7 2 , 1 8 7 ->= 2 2 8 1 2 7 , 6 1 8 ->= 8 6 1 2 2 , 4 1 8 ->= 2 2 4 8 1 , 4 6 8 ->= 4 7 2 2 6 8 , 6 7 8 ->= 6 2 8 7 2 2 , 1 8 8 ->= 1 8 2 2 8 , 4 6 1 1 ->= 2 2 6 1 4 1 , 6 2 7 1 ->= 6 1 7 2 2 , 4 6 7 1 ->= 4 4 1 7 2 6 , 6 7 4 1 ->= 2 1 4 7 6 , 4 6 1 7 ->= 2 2 6 4 1 7 , 4 8 1 7 ->= 7 2 8 1 4 7 , 1 1 2 7 ->= 2 1 7 2 2 1 , 1 4 6 7 ->= 6 4 1 2 7 , 8 4 6 7 ->= 8 2 6 4 2 7 , 4 8 6 7 ->= 6 8 7 4 7 , 6 7 8 7 ->= 8 6 1 7 7 , 6 4 1 4 ->= 1 7 2 6 4 4 , 1 6 7 4 ->= 4 7 2 6 1 , 1 2 4 8 ->= 2 1 4 2 2 8 , 1 1 8 8 ->= 1 8 8 1 2 2 , 6 6 8 8 ->= 6 6 2 2 8 8 , 4 6 2 1 1 ->= 4 2 2 6 1 1 , 6 2 7 8 1 ->= 1 2 7 2 6 8 , 1 2 8 8 1 ->= 2 2 8 1 1 8 , 8 4 2 1 7 ->= 2 2 8 1 4 7 , 6 2 7 1 7 ->= 7 7 2 2 6 1 , 4 1 6 6 7 ->= 4 2 1 6 6 7 , 1 4 2 8 7 ->= 1 8 4 7 7 2 , 4 1 7 8 7 ->= 4 7 8 2 1 7 , 1 6 7 2 8 ->= 2 2 1 8 7 6 , 6 1 6 4 8 ->= 6 2 6 4 1 8 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 is interpreted by / \ | 1 1 | | 0 1 | \ / 1 is interpreted by / \ | 1 0 | | 0 1 | \ / 2 is interpreted by / \ | 1 0 | | 0 1 | \ / 3 is interpreted by / \ | 1 0 | | 0 1 | \ / 4 is interpreted by / \ | 1 0 | | 0 1 | \ / 5 is interpreted by / \ | 1 1 | | 0 1 | \ / 6 is interpreted by / \ | 1 1 | | 0 1 | \ / 7 is interpreted by / \ | 1 0 | | 0 1 | \ / 8 is interpreted by / \ | 1 0 | | 0 1 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 8->5, 7->6, 5->7, 6->8 }, it remains to prove termination of the 58-rule system { 0 1 1 -> 0 2 1 1 , 0 1 1 -> 0 1 , 0 1 1 -> 0 , 3 4 1 -> 3 1 2 2 2 4 , 0 5 5 -> 0 5 2 2 5 , 0 1 2 6 -> 0 6 2 2 1 , 0 1 2 6 -> 0 , 0 1 5 5 -> 0 5 5 1 2 2 , 7 4 2 1 6 -> 7 1 4 6 , 0 4 2 5 6 -> 0 5 4 6 6 2 , 0 8 6 2 5 -> 0 5 6 8 , 1 1 1 ->= 2 1 2 1 1 , 1 8 1 ->= 2 2 8 1 1 , 8 6 1 ->= 1 6 2 8 , 8 4 1 ->= 8 1 2 2 2 4 , 4 1 6 ->= 2 4 6 2 1 , 1 8 6 ->= 6 2 8 1 , 1 8 6 ->= 2 8 1 6 , 1 8 6 ->= 6 2 8 2 1 , 1 8 6 ->= 4 2 8 2 1 6 , 4 8 6 ->= 4 6 6 2 8 2 , 4 8 6 ->= 6 2 2 8 2 4 , 5 8 6 ->= 8 5 6 2 , 5 8 6 ->= 8 5 4 2 6 , 5 8 6 ->= 8 5 6 6 2 2 , 5 8 6 ->= 8 4 5 4 6 2 , 1 5 6 ->= 2 2 5 1 2 6 , 8 1 5 ->= 5 8 1 2 2 , 4 1 5 ->= 2 2 4 5 1 , 4 8 5 ->= 4 6 2 2 8 5 , 8 6 5 ->= 8 2 5 6 2 2 , 1 5 5 ->= 1 5 2 2 5 , 4 8 1 1 ->= 2 2 8 1 4 1 , 8 2 6 1 ->= 8 1 6 2 2 , 4 8 6 1 ->= 4 4 1 6 2 8 , 8 6 4 1 ->= 2 1 4 6 8 , 4 8 1 6 ->= 2 2 8 4 1 6 , 4 5 1 6 ->= 6 2 5 1 4 6 , 1 1 2 6 ->= 2 1 6 2 2 1 , 1 4 8 6 ->= 8 4 1 2 6 , 5 4 8 6 ->= 5 2 8 4 2 6 , 4 5 8 6 ->= 8 5 6 4 6 , 8 6 5 6 ->= 5 8 1 6 6 , 8 4 1 4 ->= 1 6 2 8 4 4 , 1 8 6 4 ->= 4 6 2 8 1 , 1 2 4 5 ->= 2 1 4 2 2 5 , 1 1 5 5 ->= 1 5 5 1 2 2 , 8 8 5 5 ->= 8 8 2 2 5 5 , 4 8 2 1 1 ->= 4 2 2 8 1 1 , 8 2 6 5 1 ->= 1 2 6 2 8 5 , 1 2 5 5 1 ->= 2 2 5 1 1 5 , 5 4 2 1 6 ->= 2 2 5 1 4 6 , 8 2 6 1 6 ->= 6 6 2 2 8 1 , 4 1 8 8 6 ->= 4 2 1 8 8 6 , 1 4 2 5 6 ->= 1 5 4 6 6 2 , 4 1 6 5 6 ->= 4 6 5 2 1 6 , 1 8 6 2 5 ->= 2 2 1 5 6 8 , 8 1 8 4 5 ->= 8 2 8 4 1 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: 0 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 1 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 5->3, 6->4, 7->5, 4->6, 8->7 }, it remains to prove termination of the 57-rule system { 0 1 1 -> 0 2 1 1 , 0 1 1 -> 0 1 , 0 1 1 -> 0 , 0 3 3 -> 0 3 2 2 3 , 0 1 2 4 -> 0 4 2 2 1 , 0 1 2 4 -> 0 , 0 1 3 3 -> 0 3 3 1 2 2 , 5 6 2 1 4 -> 5 1 6 4 , 0 6 2 3 4 -> 0 3 6 4 4 2 , 0 7 4 2 3 -> 0 3 4 7 , 1 1 1 ->= 2 1 2 1 1 , 1 7 1 ->= 2 2 7 1 1 , 7 4 1 ->= 1 4 2 7 , 7 6 1 ->= 7 1 2 2 2 6 , 6 1 4 ->= 2 6 4 2 1 , 1 7 4 ->= 4 2 7 1 , 1 7 4 ->= 2 7 1 4 , 1 7 4 ->= 4 2 7 2 1 , 1 7 4 ->= 6 2 7 2 1 4 , 6 7 4 ->= 6 4 4 2 7 2 , 6 7 4 ->= 4 2 2 7 2 6 , 3 7 4 ->= 7 3 4 2 , 3 7 4 ->= 7 3 6 2 4 , 3 7 4 ->= 7 3 4 4 2 2 , 3 7 4 ->= 7 6 3 6 4 2 , 1 3 4 ->= 2 2 3 1 2 4 , 7 1 3 ->= 3 7 1 2 2 , 6 1 3 ->= 2 2 6 3 1 , 6 7 3 ->= 6 4 2 2 7 3 , 7 4 3 ->= 7 2 3 4 2 2 , 1 3 3 ->= 1 3 2 2 3 , 6 7 1 1 ->= 2 2 7 1 6 1 , 7 2 4 1 ->= 7 1 4 2 2 , 6 7 4 1 ->= 6 6 1 4 2 7 , 7 4 6 1 ->= 2 1 6 4 7 , 6 7 1 4 ->= 2 2 7 6 1 4 , 6 3 1 4 ->= 4 2 3 1 6 4 , 1 1 2 4 ->= 2 1 4 2 2 1 , 1 6 7 4 ->= 7 6 1 2 4 , 3 6 7 4 ->= 3 2 7 6 2 4 , 6 3 7 4 ->= 7 3 4 6 4 , 7 4 3 4 ->= 3 7 1 4 4 , 7 6 1 6 ->= 1 4 2 7 6 6 , 1 7 4 6 ->= 6 4 2 7 1 , 1 2 6 3 ->= 2 1 6 2 2 3 , 1 1 3 3 ->= 1 3 3 1 2 2 , 7 7 3 3 ->= 7 7 2 2 3 3 , 6 7 2 1 1 ->= 6 2 2 7 1 1 , 7 2 4 3 1 ->= 1 2 4 2 7 3 , 1 2 3 3 1 ->= 2 2 3 1 1 3 , 3 6 2 1 4 ->= 2 2 3 1 6 4 , 7 2 4 1 4 ->= 4 4 2 2 7 1 , 6 1 7 7 4 ->= 6 2 1 7 7 4 , 1 6 2 3 4 ->= 1 3 6 4 4 2 , 6 1 4 3 4 ->= 6 4 3 2 1 4 , 1 7 4 2 3 ->= 2 2 1 3 4 7 , 7 1 7 6 3 ->= 7 2 7 6 1 3 } 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 1 1 0 | | 0 1 0 0 0 | | 0 1 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 1 | | 0 1 0 0 0 | \ / 4 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 | \ / 5 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | | 0 1 0 0 0 | \ / After renaming modulo { 0->0, 3->1, 2->2, 1->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 53-rule system { 0 1 1 -> 0 1 2 2 1 , 0 3 2 4 -> 0 4 2 2 3 , 0 3 2 4 -> 0 , 5 6 2 3 4 -> 5 3 6 4 , 0 6 2 1 4 -> 0 1 6 4 4 2 , 0 7 4 2 1 -> 0 1 4 7 , 3 3 3 ->= 2 3 2 3 3 , 3 7 3 ->= 2 2 7 3 3 , 7 4 3 ->= 3 4 2 7 , 7 6 3 ->= 7 3 2 2 2 6 , 6 3 4 ->= 2 6 4 2 3 , 3 7 4 ->= 4 2 7 3 , 3 7 4 ->= 2 7 3 4 , 3 7 4 ->= 4 2 7 2 3 , 3 7 4 ->= 6 2 7 2 3 4 , 6 7 4 ->= 6 4 4 2 7 2 , 6 7 4 ->= 4 2 2 7 2 6 , 1 7 4 ->= 7 1 4 2 , 1 7 4 ->= 7 1 6 2 4 , 1 7 4 ->= 7 1 4 4 2 2 , 1 7 4 ->= 7 6 1 6 4 2 , 3 1 4 ->= 2 2 1 3 2 4 , 7 3 1 ->= 1 7 3 2 2 , 6 3 1 ->= 2 2 6 1 3 , 6 7 1 ->= 6 4 2 2 7 1 , 7 4 1 ->= 7 2 1 4 2 2 , 3 1 1 ->= 3 1 2 2 1 , 6 7 3 3 ->= 2 2 7 3 6 3 , 7 2 4 3 ->= 7 3 4 2 2 , 6 7 4 3 ->= 6 6 3 4 2 7 , 7 4 6 3 ->= 2 3 6 4 7 , 6 7 3 4 ->= 2 2 7 6 3 4 , 6 1 3 4 ->= 4 2 1 3 6 4 , 3 3 2 4 ->= 2 3 4 2 2 3 , 3 6 7 4 ->= 7 6 3 2 4 , 1 6 7 4 ->= 1 2 7 6 2 4 , 6 1 7 4 ->= 7 1 4 6 4 , 7 4 1 4 ->= 1 7 3 4 4 , 7 6 3 6 ->= 3 4 2 7 6 6 , 3 7 4 6 ->= 6 4 2 7 3 , 3 2 6 1 ->= 2 3 6 2 2 1 , 3 3 1 1 ->= 3 1 1 3 2 2 , 7 7 1 1 ->= 7 7 2 2 1 1 , 6 7 2 3 3 ->= 6 2 2 7 3 3 , 7 2 4 1 3 ->= 3 2 4 2 7 1 , 3 2 1 1 3 ->= 2 2 1 3 3 1 , 1 6 2 3 4 ->= 2 2 1 3 6 4 , 7 2 4 3 4 ->= 4 4 2 2 7 3 , 6 3 7 7 4 ->= 6 2 3 7 7 4 , 3 6 2 1 4 ->= 3 1 6 4 4 2 , 6 3 4 1 4 ->= 6 4 1 2 3 4 , 3 7 4 2 1 ->= 2 2 3 1 4 7 , 7 3 7 6 1 ->= 7 2 7 6 3 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 0 0 1 0 0 0 1 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 1 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 48-rule system { 0 1 1 -> 0 1 2 2 1 , 0 3 2 4 -> 0 4 2 2 3 , 0 3 2 4 -> 0 , 5 6 2 3 4 -> 5 3 6 4 , 0 6 2 1 4 -> 0 1 6 4 4 2 , 0 7 4 2 1 -> 0 1 4 7 , 3 3 3 ->= 2 3 2 3 3 , 3 7 3 ->= 2 2 7 3 3 , 7 6 3 ->= 7 3 2 2 2 6 , 6 3 4 ->= 2 6 4 2 3 , 3 7 4 ->= 4 2 7 3 , 3 7 4 ->= 2 7 3 4 , 3 7 4 ->= 4 2 7 2 3 , 3 7 4 ->= 6 2 7 2 3 4 , 6 7 4 ->= 6 4 4 2 7 2 , 6 7 4 ->= 4 2 2 7 2 6 , 1 7 4 ->= 7 1 4 2 , 1 7 4 ->= 7 1 6 2 4 , 1 7 4 ->= 7 1 4 4 2 2 , 1 7 4 ->= 7 6 1 6 4 2 , 3 1 4 ->= 2 2 1 3 2 4 , 7 3 1 ->= 1 7 3 2 2 , 6 3 1 ->= 2 2 6 1 3 , 6 7 1 ->= 6 4 2 2 7 1 , 3 1 1 ->= 3 1 2 2 1 , 6 7 3 3 ->= 2 2 7 3 6 3 , 7 2 4 3 ->= 7 3 4 2 2 , 6 7 3 4 ->= 2 2 7 6 3 4 , 6 1 3 4 ->= 4 2 1 3 6 4 , 3 3 2 4 ->= 2 3 4 2 2 3 , 3 6 7 4 ->= 7 6 3 2 4 , 1 6 7 4 ->= 1 2 7 6 2 4 , 6 1 7 4 ->= 7 1 4 6 4 , 7 6 3 6 ->= 3 4 2 7 6 6 , 3 7 4 6 ->= 6 4 2 7 3 , 3 2 6 1 ->= 2 3 6 2 2 1 , 3 3 1 1 ->= 3 1 1 3 2 2 , 7 7 1 1 ->= 7 7 2 2 1 1 , 6 7 2 3 3 ->= 6 2 2 7 3 3 , 7 2 4 1 3 ->= 3 2 4 2 7 1 , 3 2 1 1 3 ->= 2 2 1 3 3 1 , 1 6 2 3 4 ->= 2 2 1 3 6 4 , 7 2 4 3 4 ->= 4 4 2 2 7 3 , 6 3 7 7 4 ->= 6 2 3 7 7 4 , 3 6 2 1 4 ->= 3 1 6 4 4 2 , 6 3 4 1 4 ->= 6 4 1 2 3 4 , 3 7 4 2 1 ->= 2 2 3 1 4 7 , 7 3 7 6 1 ->= 7 2 7 6 3 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 0 | | 0 1 | \ / 3 is interpreted by / \ | 1 1 | | 0 1 | \ / 4 is interpreted by / \ | 1 0 | | 0 1 | \ / 5 is interpreted by / \ | 1 1 | | 0 1 | \ / 6 is interpreted by / \ | 1 0 | | 0 1 | \ / 7 is interpreted by / \ | 1 1 | | 0 1 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 47-rule system { 0 1 1 -> 0 1 2 2 1 , 0 3 2 4 -> 0 4 2 2 3 , 5 6 2 3 4 -> 5 3 6 4 , 0 6 2 1 4 -> 0 1 6 4 4 2 , 0 7 4 2 1 -> 0 1 4 7 , 3 3 3 ->= 2 3 2 3 3 , 3 7 3 ->= 2 2 7 3 3 , 7 6 3 ->= 7 3 2 2 2 6 , 6 3 4 ->= 2 6 4 2 3 , 3 7 4 ->= 4 2 7 3 , 3 7 4 ->= 2 7 3 4 , 3 7 4 ->= 4 2 7 2 3 , 3 7 4 ->= 6 2 7 2 3 4 , 6 7 4 ->= 6 4 4 2 7 2 , 6 7 4 ->= 4 2 2 7 2 6 , 1 7 4 ->= 7 1 4 2 , 1 7 4 ->= 7 1 6 2 4 , 1 7 4 ->= 7 1 4 4 2 2 , 1 7 4 ->= 7 6 1 6 4 2 , 3 1 4 ->= 2 2 1 3 2 4 , 7 3 1 ->= 1 7 3 2 2 , 6 3 1 ->= 2 2 6 1 3 , 6 7 1 ->= 6 4 2 2 7 1 , 3 1 1 ->= 3 1 2 2 1 , 6 7 3 3 ->= 2 2 7 3 6 3 , 7 2 4 3 ->= 7 3 4 2 2 , 6 7 3 4 ->= 2 2 7 6 3 4 , 6 1 3 4 ->= 4 2 1 3 6 4 , 3 3 2 4 ->= 2 3 4 2 2 3 , 3 6 7 4 ->= 7 6 3 2 4 , 1 6 7 4 ->= 1 2 7 6 2 4 , 6 1 7 4 ->= 7 1 4 6 4 , 7 6 3 6 ->= 3 4 2 7 6 6 , 3 7 4 6 ->= 6 4 2 7 3 , 3 2 6 1 ->= 2 3 6 2 2 1 , 3 3 1 1 ->= 3 1 1 3 2 2 , 7 7 1 1 ->= 7 7 2 2 1 1 , 6 7 2 3 3 ->= 6 2 2 7 3 3 , 7 2 4 1 3 ->= 3 2 4 2 7 1 , 3 2 1 1 3 ->= 2 2 1 3 3 1 , 1 6 2 3 4 ->= 2 2 1 3 6 4 , 7 2 4 3 4 ->= 4 4 2 2 7 3 , 6 3 7 7 4 ->= 6 2 3 7 7 4 , 3 6 2 1 4 ->= 3 1 6 4 4 2 , 6 3 4 1 4 ->= 6 4 1 2 3 4 , 3 7 4 2 1 ->= 2 2 3 1 4 7 , 7 3 7 6 1 ->= 7 2 7 6 3 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: 0 is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 1 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 1 0 0 | | 0 1 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 1 0 0 | | 0 0 1 0 | \ / 7 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 1 0 0 | | 0 1 0 0 | \ / After renaming modulo { 5->0, 6->1, 2->2, 3->3, 4->4, 7->5, 1->6 }, it remains to prove termination of the 43-rule system { 0 1 2 3 4 -> 0 3 1 4 , 3 3 3 ->= 2 3 2 3 3 , 3 5 3 ->= 2 2 5 3 3 , 5 1 3 ->= 5 3 2 2 2 1 , 1 3 4 ->= 2 1 4 2 3 , 3 5 4 ->= 4 2 5 3 , 3 5 4 ->= 2 5 3 4 , 3 5 4 ->= 4 2 5 2 3 , 3 5 4 ->= 1 2 5 2 3 4 , 1 5 4 ->= 1 4 4 2 5 2 , 1 5 4 ->= 4 2 2 5 2 1 , 6 5 4 ->= 5 6 4 2 , 6 5 4 ->= 5 6 1 2 4 , 6 5 4 ->= 5 6 4 4 2 2 , 6 5 4 ->= 5 1 6 1 4 2 , 3 6 4 ->= 2 2 6 3 2 4 , 5 3 6 ->= 6 5 3 2 2 , 1 3 6 ->= 2 2 1 6 3 , 1 5 6 ->= 1 4 2 2 5 6 , 3 6 6 ->= 3 6 2 2 6 , 1 5 3 3 ->= 2 2 5 3 1 3 , 5 2 4 3 ->= 5 3 4 2 2 , 1 5 3 4 ->= 2 2 5 1 3 4 , 1 6 3 4 ->= 4 2 6 3 1 4 , 3 3 2 4 ->= 2 3 4 2 2 3 , 3 1 5 4 ->= 5 1 3 2 4 , 6 1 5 4 ->= 6 2 5 1 2 4 , 1 6 5 4 ->= 5 6 4 1 4 , 5 1 3 1 ->= 3 4 2 5 1 1 , 3 5 4 1 ->= 1 4 2 5 3 , 3 2 1 6 ->= 2 3 1 2 2 6 , 3 3 6 6 ->= 3 6 6 3 2 2 , 5 5 6 6 ->= 5 5 2 2 6 6 , 1 5 2 3 3 ->= 1 2 2 5 3 3 , 5 2 4 6 3 ->= 3 2 4 2 5 6 , 3 2 6 6 3 ->= 2 2 6 3 3 6 , 6 1 2 3 4 ->= 2 2 6 3 1 4 , 5 2 4 3 4 ->= 4 4 2 2 5 3 , 1 3 5 5 4 ->= 1 2 3 5 5 4 , 3 1 2 6 4 ->= 3 6 1 4 4 2 , 1 3 4 6 4 ->= 1 4 6 2 3 4 , 3 5 4 2 6 ->= 2 2 3 6 4 5 , 5 3 5 1 6 ->= 5 2 5 1 3 6 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 10: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 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 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 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 0 0 0 0 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 1 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 1 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 | \ / 6 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, 6->6 }, it remains to prove termination of the 42-rule system { 0 1 2 3 4 -> 0 3 1 4 , 3 3 3 ->= 2 3 2 3 3 , 3 5 3 ->= 2 2 5 3 3 , 5 1 3 ->= 5 3 2 2 2 1 , 1 3 4 ->= 2 1 4 2 3 , 3 5 4 ->= 4 2 5 3 , 3 5 4 ->= 2 5 3 4 , 3 5 4 ->= 4 2 5 2 3 , 3 5 4 ->= 1 2 5 2 3 4 , 1 5 4 ->= 1 4 4 2 5 2 , 1 5 4 ->= 4 2 2 5 2 1 , 6 5 4 ->= 5 6 4 2 , 6 5 4 ->= 5 6 1 2 4 , 6 5 4 ->= 5 6 4 4 2 2 , 6 5 4 ->= 5 1 6 1 4 2 , 3 6 4 ->= 2 2 6 3 2 4 , 5 3 6 ->= 6 5 3 2 2 , 1 3 6 ->= 2 2 1 6 3 , 1 5 6 ->= 1 4 2 2 5 6 , 3 6 6 ->= 3 6 2 2 6 , 1 5 3 3 ->= 2 2 5 3 1 3 , 5 2 4 3 ->= 5 3 4 2 2 , 1 5 3 4 ->= 2 2 5 1 3 4 , 1 6 3 4 ->= 4 2 6 3 1 4 , 3 3 2 4 ->= 2 3 4 2 2 3 , 3 1 5 4 ->= 5 1 3 2 4 , 6 1 5 4 ->= 6 2 5 1 2 4 , 1 6 5 4 ->= 5 6 4 1 4 , 5 1 3 1 ->= 3 4 2 5 1 1 , 3 5 4 1 ->= 1 4 2 5 3 , 3 2 1 6 ->= 2 3 1 2 2 6 , 3 3 6 6 ->= 3 6 6 3 2 2 , 5 5 6 6 ->= 5 5 2 2 6 6 , 5 2 4 6 3 ->= 3 2 4 2 5 6 , 3 2 6 6 3 ->= 2 2 6 3 3 6 , 6 1 2 3 4 ->= 2 2 6 3 1 4 , 5 2 4 3 4 ->= 4 4 2 2 5 3 , 1 3 5 5 4 ->= 1 2 3 5 5 4 , 3 1 2 6 4 ->= 3 6 1 4 4 2 , 1 3 4 6 4 ->= 1 4 6 2 3 4 , 3 5 4 2 6 ->= 2 2 3 6 4 5 , 5 3 5 1 6 ->= 5 2 5 1 3 6 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 9: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 | | 0 0 0 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 0 | | 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 1 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 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 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 1 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 1 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 | | 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 41-rule system { 0 1 2 3 4 -> 0 3 1 4 , 3 3 3 ->= 2 3 2 3 3 , 3 5 3 ->= 2 2 5 3 3 , 5 1 3 ->= 5 3 2 2 2 1 , 1 3 4 ->= 2 1 4 2 3 , 3 5 4 ->= 4 2 5 3 , 3 5 4 ->= 2 5 3 4 , 3 5 4 ->= 4 2 5 2 3 , 3 5 4 ->= 1 2 5 2 3 4 , 1 5 4 ->= 1 4 4 2 5 2 , 1 5 4 ->= 4 2 2 5 2 1 , 6 5 4 ->= 5 6 4 2 , 6 5 4 ->= 5 6 1 2 4 , 6 5 4 ->= 5 6 4 4 2 2 , 6 5 4 ->= 5 1 6 1 4 2 , 3 6 4 ->= 2 2 6 3 2 4 , 5 3 6 ->= 6 5 3 2 2 , 1 3 6 ->= 2 2 1 6 3 , 1 5 6 ->= 1 4 2 2 5 6 , 3 6 6 ->= 3 6 2 2 6 , 5 2 4 3 ->= 5 3 4 2 2 , 1 5 3 4 ->= 2 2 5 1 3 4 , 1 6 3 4 ->= 4 2 6 3 1 4 , 3 3 2 4 ->= 2 3 4 2 2 3 , 3 1 5 4 ->= 5 1 3 2 4 , 6 1 5 4 ->= 6 2 5 1 2 4 , 1 6 5 4 ->= 5 6 4 1 4 , 5 1 3 1 ->= 3 4 2 5 1 1 , 3 5 4 1 ->= 1 4 2 5 3 , 3 2 1 6 ->= 2 3 1 2 2 6 , 3 3 6 6 ->= 3 6 6 3 2 2 , 5 5 6 6 ->= 5 5 2 2 6 6 , 5 2 4 6 3 ->= 3 2 4 2 5 6 , 3 2 6 6 3 ->= 2 2 6 3 3 6 , 6 1 2 3 4 ->= 2 2 6 3 1 4 , 5 2 4 3 4 ->= 4 4 2 2 5 3 , 1 3 5 5 4 ->= 1 2 3 5 5 4 , 3 1 2 6 4 ->= 3 6 1 4 4 2 , 1 3 4 6 4 ->= 1 4 6 2 3 4 , 3 5 4 2 6 ->= 2 2 3 6 4 5 , 5 3 5 1 6 ->= 5 2 5 1 3 6 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 1 0 0 0 | \ / 2 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 | \ / 3 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 4 is interpreted by / \ | 1 0 1 1 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 6 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6 }, it remains to prove termination of the 40-rule system { 0 1 2 3 4 -> 0 3 1 4 , 3 3 3 ->= 2 3 2 3 3 , 3 5 3 ->= 2 2 5 3 3 , 5 1 3 ->= 5 3 2 2 2 1 , 1 3 4 ->= 2 1 4 2 3 , 3 5 4 ->= 4 2 5 3 , 3 5 4 ->= 2 5 3 4 , 3 5 4 ->= 4 2 5 2 3 , 3 5 4 ->= 1 2 5 2 3 4 , 1 5 4 ->= 1 4 4 2 5 2 , 1 5 4 ->= 4 2 2 5 2 1 , 6 5 4 ->= 5 6 4 2 , 6 5 4 ->= 5 6 1 2 4 , 6 5 4 ->= 5 6 4 4 2 2 , 6 5 4 ->= 5 1 6 1 4 2 , 3 6 4 ->= 2 2 6 3 2 4 , 5 3 6 ->= 6 5 3 2 2 , 1 3 6 ->= 2 2 1 6 3 , 1 5 6 ->= 1 4 2 2 5 6 , 3 6 6 ->= 3 6 2 2 6 , 5 2 4 3 ->= 5 3 4 2 2 , 1 5 3 4 ->= 2 2 5 1 3 4 , 1 6 3 4 ->= 4 2 6 3 1 4 , 3 3 2 4 ->= 2 3 4 2 2 3 , 3 1 5 4 ->= 5 1 3 2 4 , 6 1 5 4 ->= 6 2 5 1 2 4 , 1 6 5 4 ->= 5 6 4 1 4 , 5 1 3 1 ->= 3 4 2 5 1 1 , 3 5 4 1 ->= 1 4 2 5 3 , 3 3 6 6 ->= 3 6 6 3 2 2 , 5 5 6 6 ->= 5 5 2 2 6 6 , 5 2 4 6 3 ->= 3 2 4 2 5 6 , 3 2 6 6 3 ->= 2 2 6 3 3 6 , 6 1 2 3 4 ->= 2 2 6 3 1 4 , 5 2 4 3 4 ->= 4 4 2 2 5 3 , 1 3 5 5 4 ->= 1 2 3 5 5 4 , 3 1 2 6 4 ->= 3 6 1 4 4 2 , 1 3 4 6 4 ->= 1 4 6 2 3 4 , 3 5 4 2 6 ->= 2 2 3 6 4 5 , 5 3 5 1 6 ->= 5 2 5 1 3 6 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 1 0 0 0 | | 0 1 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 1 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 1 0 0 | | 0 1 0 0 0 | | 0 1 0 1 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 1 | | 0 0 0 0 1 | \ / 6 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | | 0 1 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 39-rule system { 0 1 2 3 4 -> 0 3 1 4 , 3 3 3 ->= 2 3 2 3 3 , 3 5 3 ->= 2 2 5 3 3 , 5 1 3 ->= 5 3 2 2 2 1 , 1 3 4 ->= 2 1 4 2 3 , 3 5 4 ->= 4 2 5 3 , 3 5 4 ->= 2 5 3 4 , 3 5 4 ->= 4 2 5 2 3 , 3 5 4 ->= 1 2 5 2 3 4 , 1 5 4 ->= 1 4 4 2 5 2 , 1 5 4 ->= 4 2 2 5 2 1 , 6 5 4 ->= 5 6 4 2 , 6 5 4 ->= 5 6 1 2 4 , 6 5 4 ->= 5 6 4 4 2 2 , 6 5 4 ->= 5 1 6 1 4 2 , 3 6 4 ->= 2 2 6 3 2 4 , 5 3 6 ->= 6 5 3 2 2 , 1 3 6 ->= 2 2 1 6 3 , 1 5 6 ->= 1 4 2 2 5 6 , 3 6 6 ->= 3 6 2 2 6 , 5 2 4 3 ->= 5 3 4 2 2 , 1 5 3 4 ->= 2 2 5 1 3 4 , 1 6 3 4 ->= 4 2 6 3 1 4 , 3 3 2 4 ->= 2 3 4 2 2 3 , 3 1 5 4 ->= 5 1 3 2 4 , 1 6 5 4 ->= 5 6 4 1 4 , 5 1 3 1 ->= 3 4 2 5 1 1 , 3 5 4 1 ->= 1 4 2 5 3 , 3 3 6 6 ->= 3 6 6 3 2 2 , 5 5 6 6 ->= 5 5 2 2 6 6 , 5 2 4 6 3 ->= 3 2 4 2 5 6 , 3 2 6 6 3 ->= 2 2 6 3 3 6 , 6 1 2 3 4 ->= 2 2 6 3 1 4 , 5 2 4 3 4 ->= 4 4 2 2 5 3 , 1 3 5 5 4 ->= 1 2 3 5 5 4 , 3 1 2 6 4 ->= 3 6 1 4 4 2 , 1 3 4 6 4 ->= 1 4 6 2 3 4 , 3 5 4 2 6 ->= 2 2 3 6 4 5 , 5 3 5 1 6 ->= 5 2 5 1 3 6 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 9: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 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 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 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 0 | | 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 1 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 1 0 0 1 0 0 0 | \ / 6 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 | | 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 38-rule system { 0 1 2 3 4 -> 0 3 1 4 , 3 3 3 ->= 2 3 2 3 3 , 3 5 3 ->= 2 2 5 3 3 , 5 1 3 ->= 5 3 2 2 2 1 , 1 3 4 ->= 2 1 4 2 3 , 3 5 4 ->= 4 2 5 3 , 3 5 4 ->= 2 5 3 4 , 3 5 4 ->= 4 2 5 2 3 , 3 5 4 ->= 1 2 5 2 3 4 , 1 5 4 ->= 1 4 4 2 5 2 , 1 5 4 ->= 4 2 2 5 2 1 , 6 5 4 ->= 5 6 4 2 , 6 5 4 ->= 5 6 1 2 4 , 6 5 4 ->= 5 6 4 4 2 2 , 6 5 4 ->= 5 1 6 1 4 2 , 3 6 4 ->= 2 2 6 3 2 4 , 5 3 6 ->= 6 5 3 2 2 , 1 3 6 ->= 2 2 1 6 3 , 1 5 6 ->= 1 4 2 2 5 6 , 3 6 6 ->= 3 6 2 2 6 , 5 2 4 3 ->= 5 3 4 2 2 , 1 5 3 4 ->= 2 2 5 1 3 4 , 1 6 3 4 ->= 4 2 6 3 1 4 , 3 3 2 4 ->= 2 3 4 2 2 3 , 3 1 5 4 ->= 5 1 3 2 4 , 1 6 5 4 ->= 5 6 4 1 4 , 3 5 4 1 ->= 1 4 2 5 3 , 3 3 6 6 ->= 3 6 6 3 2 2 , 5 5 6 6 ->= 5 5 2 2 6 6 , 5 2 4 6 3 ->= 3 2 4 2 5 6 , 3 2 6 6 3 ->= 2 2 6 3 3 6 , 6 1 2 3 4 ->= 2 2 6 3 1 4 , 5 2 4 3 4 ->= 4 4 2 2 5 3 , 1 3 5 5 4 ->= 1 2 3 5 5 4 , 3 1 2 6 4 ->= 3 6 1 4 4 2 , 1 3 4 6 4 ->= 1 4 6 2 3 4 , 3 5 4 2 6 ->= 2 2 3 6 4 5 , 5 3 5 1 6 ->= 5 2 5 1 3 6 } 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 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 1 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 | \ / 6 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 { 3->0, 2->1, 5->2, 1->3, 4->4, 6->5 }, it remains to prove termination of the 37-rule system { 0 0 0 ->= 1 0 1 0 0 , 0 2 0 ->= 1 1 2 0 0 , 2 3 0 ->= 2 0 1 1 1 3 , 3 0 4 ->= 1 3 4 1 0 , 0 2 4 ->= 4 1 2 0 , 0 2 4 ->= 1 2 0 4 , 0 2 4 ->= 4 1 2 1 0 , 0 2 4 ->= 3 1 2 1 0 4 , 3 2 4 ->= 3 4 4 1 2 1 , 3 2 4 ->= 4 1 1 2 1 3 , 5 2 4 ->= 2 5 4 1 , 5 2 4 ->= 2 5 3 1 4 , 5 2 4 ->= 2 5 4 4 1 1 , 5 2 4 ->= 2 3 5 3 4 1 , 0 5 4 ->= 1 1 5 0 1 4 , 2 0 5 ->= 5 2 0 1 1 , 3 0 5 ->= 1 1 3 5 0 , 3 2 5 ->= 3 4 1 1 2 5 , 0 5 5 ->= 0 5 1 1 5 , 2 1 4 0 ->= 2 0 4 1 1 , 3 2 0 4 ->= 1 1 2 3 0 4 , 3 5 0 4 ->= 4 1 5 0 3 4 , 0 0 1 4 ->= 1 0 4 1 1 0 , 0 3 2 4 ->= 2 3 0 1 4 , 3 5 2 4 ->= 2 5 4 3 4 , 0 2 4 3 ->= 3 4 1 2 0 , 0 0 5 5 ->= 0 5 5 0 1 1 , 2 2 5 5 ->= 2 2 1 1 5 5 , 2 1 4 5 0 ->= 0 1 4 1 2 5 , 0 1 5 5 0 ->= 1 1 5 0 0 5 , 5 3 1 0 4 ->= 1 1 5 0 3 4 , 2 1 4 0 4 ->= 4 4 1 1 2 0 , 3 0 2 2 4 ->= 3 1 0 2 2 4 , 0 3 1 5 4 ->= 0 5 3 4 4 1 , 3 0 4 5 4 ->= 3 4 5 1 0 4 , 0 2 4 1 5 ->= 1 1 0 5 4 2 , 2 0 2 3 5 ->= 2 1 2 3 0 5 } The system is trivially terminating.