YES After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, it remains to prove termination of the 50-rule system { 0 0 1 -> 0 2 3 0 1 , 0 0 1 -> 0 4 0 5 4 1 , 0 0 1 -> 2 1 0 0 3 4 , 0 0 1 -> 4 0 5 4 0 1 , 0 1 0 -> 0 0 2 1 2 , 0 1 0 -> 1 0 0 5 4 , 0 1 0 -> 0 0 2 5 4 1 , 0 1 1 -> 1 0 3 4 1 , 0 1 1 -> 5 0 3 4 1 1 , 5 0 1 -> 0 5 4 1 , 5 0 1 -> 2 5 4 0 1 , 5 0 1 -> 5 0 2 1 2 , 5 0 1 -> 0 1 4 5 4 4 , 5 0 1 -> 0 5 4 1 4 4 , 5 0 1 -> 5 0 4 3 0 1 , 5 1 0 -> 5 0 2 2 1 , 5 1 0 -> 5 0 5 4 1 , 5 1 0 -> 0 5 0 2 2 1 , 5 1 0 -> 1 4 0 5 2 3 , 5 1 0 -> 1 5 0 4 4 2 , 5 1 0 -> 4 4 1 0 4 5 , 5 1 1 -> 1 1 5 4 , 5 1 1 -> 5 4 1 1 , 5 1 1 -> 1 5 3 4 1 , 5 1 1 -> 1 1 4 5 4 4 , 5 1 1 -> 3 5 2 3 1 1 , 5 1 1 -> 4 1 2 1 5 4 , 0 1 3 0 -> 0 2 0 2 1 3 , 0 1 5 0 -> 0 0 5 4 1 5 , 0 1 5 0 -> 0 5 4 2 1 0 , 0 3 0 1 -> 0 0 4 1 3 0 , 0 3 1 0 -> 0 0 2 3 1 , 0 3 1 1 -> 5 1 1 0 3 4 , 5 0 1 0 -> 5 0 0 4 1 3 , 5 1 2 0 -> 1 4 0 5 4 2 , 5 1 2 0 -> 5 0 4 2 2 1 , 5 1 4 0 -> 1 5 4 0 2 3 , 5 1 4 0 -> 4 5 2 1 3 0 , 5 1 5 1 -> 5 4 1 5 1 , 5 3 0 1 -> 0 1 5 2 3 , 5 3 1 0 -> 1 4 3 5 0 , 5 3 1 0 -> 1 5 0 4 3 , 5 3 1 0 -> 5 4 3 1 0 , 5 3 1 0 -> 1 3 0 4 3 5 , 5 3 1 1 -> 1 1 5 3 3 4 , 0 1 2 5 0 -> 1 5 4 0 2 0 , 0 1 4 2 0 -> 1 0 4 2 3 0 , 1 4 5 1 0 -> 5 4 2 1 1 0 , 5 0 1 4 0 -> 1 4 5 4 0 0 , 5 5 1 0 0 -> 5 5 0 4 1 0 } The system was reversed. After renaming modulo { 1->0, 0->1, 3->2, 2->3, 4->4, 5->5 }, it remains to prove termination of the 50-rule system { 0 1 1 -> 0 1 2 3 1 , 0 1 1 -> 0 4 5 1 4 1 , 0 1 1 -> 4 2 1 1 0 3 , 0 1 1 -> 0 1 4 5 1 4 , 1 0 1 -> 3 0 3 1 1 , 1 0 1 -> 4 5 1 1 0 , 1 0 1 -> 0 4 5 3 1 1 , 0 0 1 -> 0 4 2 1 0 , 0 0 1 -> 0 0 4 2 1 5 , 0 1 5 -> 0 4 5 1 , 0 1 5 -> 0 1 4 5 3 , 0 1 5 -> 3 0 3 1 5 , 0 1 5 -> 4 4 5 4 0 1 , 0 1 5 -> 4 4 0 4 5 1 , 0 1 5 -> 0 1 2 4 1 5 , 1 0 5 -> 0 3 3 1 5 , 1 0 5 -> 0 4 5 1 5 , 1 0 5 -> 0 3 3 1 5 1 , 1 0 5 -> 2 3 5 1 4 0 , 1 0 5 -> 3 4 4 1 5 0 , 1 0 5 -> 5 4 1 0 4 4 , 0 0 5 -> 4 5 0 0 , 0 0 5 -> 0 0 4 5 , 0 0 5 -> 0 4 2 5 0 , 0 0 5 -> 4 4 5 4 0 0 , 0 0 5 -> 0 0 2 3 5 2 , 0 0 5 -> 4 5 0 3 0 4 , 1 2 0 1 -> 2 0 3 1 3 1 , 1 5 0 1 -> 5 0 4 5 1 1 , 1 5 0 1 -> 1 0 3 4 5 1 , 0 1 2 1 -> 1 2 0 4 1 1 , 1 0 2 1 -> 0 2 3 1 1 , 0 0 2 1 -> 4 2 1 0 0 5 , 1 0 1 5 -> 2 0 4 1 1 5 , 1 3 0 5 -> 3 4 5 1 4 0 , 1 3 0 5 -> 0 3 3 4 1 5 , 1 4 0 5 -> 2 3 1 4 5 0 , 1 4 0 5 -> 1 2 0 3 5 4 , 0 5 0 5 -> 0 5 0 4 5 , 0 1 2 5 -> 2 3 5 0 1 , 1 0 2 5 -> 1 5 2 4 0 , 1 0 2 5 -> 2 4 1 5 0 , 1 0 2 5 -> 1 0 2 4 5 , 1 0 2 5 -> 5 2 4 1 2 0 , 0 0 2 5 -> 4 2 2 5 0 0 , 1 5 3 0 1 -> 1 3 1 4 5 0 , 1 3 4 0 1 -> 1 2 3 4 1 0 , 1 0 5 4 0 -> 1 0 0 3 4 5 , 1 4 0 1 5 -> 1 1 4 5 4 0 , 1 1 0 5 5 -> 1 0 4 1 5 5 } Applying the dependency pairs transformation. After renaming modulo { (0,true)->0, (1,false)->1, (2,false)->2, (3,false)->3, (1,true)->4, (4,false)->5, (5,false)->6, (0,false)->7 }, it remains to prove termination of the 159-rule system { 0 1 1 -> 0 1 2 3 1 , 0 1 1 -> 4 2 3 1 , 0 1 1 -> 4 , 0 1 1 -> 0 5 6 1 5 1 , 0 1 1 -> 4 5 1 , 0 1 1 -> 4 1 7 3 , 0 1 1 -> 4 7 3 , 0 1 1 -> 0 3 , 0 1 1 -> 0 1 5 6 1 5 , 0 1 1 -> 4 5 6 1 5 , 0 1 1 -> 4 5 , 4 7 1 -> 0 3 1 1 , 4 7 1 -> 4 1 , 4 7 1 -> 4 , 4 7 1 -> 4 1 7 , 4 7 1 -> 4 7 , 4 7 1 -> 0 , 4 7 1 -> 0 5 6 3 1 1 , 0 7 1 -> 0 5 2 1 7 , 0 7 1 -> 4 7 , 0 7 1 -> 0 , 0 7 1 -> 0 7 5 2 1 6 , 0 7 1 -> 0 5 2 1 6 , 0 7 1 -> 4 6 , 0 1 6 -> 0 5 6 1 , 0 1 6 -> 4 , 0 1 6 -> 0 1 5 6 3 , 0 1 6 -> 4 5 6 3 , 0 1 6 -> 0 3 1 6 , 0 1 6 -> 4 6 , 0 1 6 -> 0 1 , 0 1 6 -> 0 1 2 5 1 6 , 0 1 6 -> 4 2 5 1 6 , 4 7 6 -> 0 3 3 1 6 , 4 7 6 -> 4 6 , 4 7 6 -> 0 5 6 1 6 , 4 7 6 -> 0 3 3 1 6 1 , 4 7 6 -> 4 6 1 , 4 7 6 -> 4 , 4 7 6 -> 4 5 7 , 4 7 6 -> 0 , 4 7 6 -> 4 6 7 , 4 7 6 -> 4 7 5 5 , 4 7 6 -> 0 5 5 , 0 7 6 -> 0 7 , 0 7 6 -> 0 , 0 7 6 -> 0 7 5 6 , 0 7 6 -> 0 5 6 , 0 7 6 -> 0 5 2 6 7 , 0 7 6 -> 0 7 2 3 6 2 , 0 7 6 -> 0 2 3 6 2 , 0 7 6 -> 0 3 7 5 , 0 7 6 -> 0 5 , 4 2 7 1 -> 0 3 1 3 1 , 4 2 7 1 -> 4 3 1 , 4 2 7 1 -> 4 , 4 6 7 1 -> 0 5 6 1 1 , 4 6 7 1 -> 4 1 , 4 6 7 1 -> 4 , 4 6 7 1 -> 4 7 3 5 6 1 , 4 6 7 1 -> 0 3 5 6 1 , 0 1 2 1 -> 4 2 7 5 1 1 , 0 1 2 1 -> 0 5 1 1 , 0 1 2 1 -> 4 1 , 0 1 2 1 -> 4 , 4 7 2 1 -> 0 2 3 1 1 , 4 7 2 1 -> 4 1 , 4 7 2 1 -> 4 , 0 7 2 1 -> 4 7 7 6 , 0 7 2 1 -> 0 7 6 , 0 7 2 1 -> 0 6 , 4 7 1 6 -> 0 5 1 1 6 , 4 7 1 6 -> 4 1 6 , 4 7 1 6 -> 4 6 , 4 3 7 6 -> 4 5 7 , 4 3 7 6 -> 0 , 4 3 7 6 -> 0 3 3 5 1 6 , 4 3 7 6 -> 4 6 , 4 5 7 6 -> 4 5 6 7 , 4 5 7 6 -> 0 , 4 5 7 6 -> 4 2 7 3 6 5 , 4 5 7 6 -> 0 3 6 5 , 0 6 7 6 -> 0 6 7 5 6 , 0 6 7 6 -> 0 5 6 , 0 1 2 6 -> 0 1 , 0 1 2 6 -> 4 , 4 7 2 6 -> 4 6 2 5 7 , 4 7 2 6 -> 0 , 4 7 2 6 -> 4 6 7 , 4 7 2 6 -> 4 7 2 5 6 , 4 7 2 6 -> 0 2 5 6 , 4 7 2 6 -> 4 2 7 , 0 7 2 6 -> 0 7 , 0 7 2 6 -> 0 , 4 6 3 7 1 -> 4 3 1 5 6 7 , 4 6 3 7 1 -> 4 5 6 7 , 4 6 3 7 1 -> 0 , 4 3 5 7 1 -> 4 2 3 5 1 7 , 4 3 5 7 1 -> 4 7 , 4 3 5 7 1 -> 0 , 4 7 6 5 7 -> 4 7 7 3 5 6 , 4 7 6 5 7 -> 0 7 3 5 6 , 4 7 6 5 7 -> 0 3 5 6 , 4 5 7 1 6 -> 4 1 5 6 5 7 , 4 5 7 1 6 -> 4 5 6 5 7 , 4 5 7 1 6 -> 0 , 4 1 7 6 6 -> 4 7 5 1 6 6 , 4 1 7 6 6 -> 0 5 1 6 6 , 4 1 7 6 6 -> 4 6 6 , 7 1 1 ->= 7 1 2 3 1 , 7 1 1 ->= 7 5 6 1 5 1 , 7 1 1 ->= 5 2 1 1 7 3 , 7 1 1 ->= 7 1 5 6 1 5 , 1 7 1 ->= 3 7 3 1 1 , 1 7 1 ->= 5 6 1 1 7 , 1 7 1 ->= 7 5 6 3 1 1 , 7 7 1 ->= 7 5 2 1 7 , 7 7 1 ->= 7 7 5 2 1 6 , 7 1 6 ->= 7 5 6 1 , 7 1 6 ->= 7 1 5 6 3 , 7 1 6 ->= 3 7 3 1 6 , 7 1 6 ->= 5 5 6 5 7 1 , 7 1 6 ->= 5 5 7 5 6 1 , 7 1 6 ->= 7 1 2 5 1 6 , 1 7 6 ->= 7 3 3 1 6 , 1 7 6 ->= 7 5 6 1 6 , 1 7 6 ->= 7 3 3 1 6 1 , 1 7 6 ->= 2 3 6 1 5 7 , 1 7 6 ->= 3 5 5 1 6 7 , 1 7 6 ->= 6 5 1 7 5 5 , 7 7 6 ->= 5 6 7 7 , 7 7 6 ->= 7 7 5 6 , 7 7 6 ->= 7 5 2 6 7 , 7 7 6 ->= 5 5 6 5 7 7 , 7 7 6 ->= 7 7 2 3 6 2 , 7 7 6 ->= 5 6 7 3 7 5 , 1 2 7 1 ->= 2 7 3 1 3 1 , 1 6 7 1 ->= 6 7 5 6 1 1 , 1 6 7 1 ->= 1 7 3 5 6 1 , 7 1 2 1 ->= 1 2 7 5 1 1 , 1 7 2 1 ->= 7 2 3 1 1 , 7 7 2 1 ->= 5 2 1 7 7 6 , 1 7 1 6 ->= 2 7 5 1 1 6 , 1 3 7 6 ->= 3 5 6 1 5 7 , 1 3 7 6 ->= 7 3 3 5 1 6 , 1 5 7 6 ->= 2 3 1 5 6 7 , 1 5 7 6 ->= 1 2 7 3 6 5 , 7 6 7 6 ->= 7 6 7 5 6 , 7 1 2 6 ->= 2 3 6 7 1 , 1 7 2 6 ->= 1 6 2 5 7 , 1 7 2 6 ->= 2 5 1 6 7 , 1 7 2 6 ->= 1 7 2 5 6 , 1 7 2 6 ->= 6 2 5 1 2 7 , 7 7 2 6 ->= 5 2 2 6 7 7 , 1 6 3 7 1 ->= 1 3 1 5 6 7 , 1 3 5 7 1 ->= 1 2 3 5 1 7 , 1 7 6 5 7 ->= 1 7 7 3 5 6 , 1 5 7 1 6 ->= 1 1 5 6 5 7 , 1 1 7 6 6 ->= 1 7 5 1 6 6 } 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 1 | | 0 1 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 5->4, 6->5, 4->6, 7->7 }, it remains to prove termination of the 120-rule system { 0 1 1 -> 0 1 2 3 1 , 0 1 1 -> 0 4 5 1 4 1 , 0 1 1 -> 6 1 7 3 , 0 1 1 -> 6 7 3 , 0 1 1 -> 0 3 , 0 1 1 -> 0 1 4 5 1 4 , 6 7 1 -> 0 3 1 1 , 6 7 1 -> 6 1 7 , 6 7 1 -> 6 7 , 6 7 1 -> 0 , 6 7 1 -> 0 4 5 3 1 1 , 0 7 1 -> 0 4 2 1 7 , 0 7 1 -> 0 7 4 2 1 5 , 0 1 5 -> 0 4 5 1 , 0 1 5 -> 0 1 4 5 3 , 0 1 5 -> 0 3 1 5 , 0 1 5 -> 0 1 , 0 1 5 -> 0 1 2 4 1 5 , 6 7 5 -> 0 3 3 1 5 , 6 7 5 -> 0 4 5 1 5 , 6 7 5 -> 0 3 3 1 5 1 , 6 7 5 -> 6 4 7 , 6 7 5 -> 0 , 6 7 5 -> 6 5 7 , 6 7 5 -> 6 7 4 4 , 6 7 5 -> 0 4 4 , 0 7 5 -> 0 7 , 0 7 5 -> 0 7 4 5 , 0 7 5 -> 0 4 2 5 7 , 0 7 5 -> 0 7 2 3 5 2 , 0 7 5 -> 0 3 7 4 , 6 2 7 1 -> 0 3 1 3 1 , 6 5 7 1 -> 0 4 5 1 1 , 6 5 7 1 -> 6 7 3 4 5 1 , 6 5 7 1 -> 0 3 4 5 1 , 0 1 2 1 -> 6 2 7 4 1 1 , 0 1 2 1 -> 0 4 1 1 , 6 7 2 1 -> 0 2 3 1 1 , 0 7 2 1 -> 6 7 7 5 , 0 7 2 1 -> 0 7 5 , 6 7 1 5 -> 0 4 1 1 5 , 6 3 7 5 -> 6 4 7 , 6 3 7 5 -> 0 , 6 3 7 5 -> 0 3 3 4 1 5 , 6 4 7 5 -> 6 4 5 7 , 6 4 7 5 -> 0 , 6 4 7 5 -> 6 2 7 3 5 4 , 6 4 7 5 -> 0 3 5 4 , 0 5 7 5 -> 0 5 7 4 5 , 0 1 2 5 -> 0 1 , 6 7 2 5 -> 6 5 2 4 7 , 6 7 2 5 -> 0 , 6 7 2 5 -> 6 5 7 , 6 7 2 5 -> 6 7 2 4 5 , 6 7 2 5 -> 0 2 4 5 , 6 7 2 5 -> 6 2 7 , 0 7 2 5 -> 0 7 , 6 5 3 7 1 -> 6 3 1 4 5 7 , 6 5 3 7 1 -> 6 4 5 7 , 6 5 3 7 1 -> 0 , 6 3 4 7 1 -> 6 2 3 4 1 7 , 6 3 4 7 1 -> 6 7 , 6 3 4 7 1 -> 0 , 6 7 5 4 7 -> 6 7 7 3 4 5 , 6 7 5 4 7 -> 0 7 3 4 5 , 6 4 7 1 5 -> 6 1 4 5 4 7 , 6 4 7 1 5 -> 6 4 5 4 7 , 6 4 7 1 5 -> 0 , 6 1 7 5 5 -> 6 7 4 1 5 5 , 6 1 7 5 5 -> 0 4 1 5 5 , 7 1 1 ->= 7 1 2 3 1 , 7 1 1 ->= 7 4 5 1 4 1 , 7 1 1 ->= 4 2 1 1 7 3 , 7 1 1 ->= 7 1 4 5 1 4 , 1 7 1 ->= 3 7 3 1 1 , 1 7 1 ->= 4 5 1 1 7 , 1 7 1 ->= 7 4 5 3 1 1 , 7 7 1 ->= 7 4 2 1 7 , 7 7 1 ->= 7 7 4 2 1 5 , 7 1 5 ->= 7 4 5 1 , 7 1 5 ->= 7 1 4 5 3 , 7 1 5 ->= 3 7 3 1 5 , 7 1 5 ->= 4 4 5 4 7 1 , 7 1 5 ->= 4 4 7 4 5 1 , 7 1 5 ->= 7 1 2 4 1 5 , 1 7 5 ->= 7 3 3 1 5 , 1 7 5 ->= 7 4 5 1 5 , 1 7 5 ->= 7 3 3 1 5 1 , 1 7 5 ->= 2 3 5 1 4 7 , 1 7 5 ->= 3 4 4 1 5 7 , 1 7 5 ->= 5 4 1 7 4 4 , 7 7 5 ->= 4 5 7 7 , 7 7 5 ->= 7 7 4 5 , 7 7 5 ->= 7 4 2 5 7 , 7 7 5 ->= 4 4 5 4 7 7 , 7 7 5 ->= 7 7 2 3 5 2 , 7 7 5 ->= 4 5 7 3 7 4 , 1 2 7 1 ->= 2 7 3 1 3 1 , 1 5 7 1 ->= 5 7 4 5 1 1 , 1 5 7 1 ->= 1 7 3 4 5 1 , 7 1 2 1 ->= 1 2 7 4 1 1 , 1 7 2 1 ->= 7 2 3 1 1 , 7 7 2 1 ->= 4 2 1 7 7 5 , 1 7 1 5 ->= 2 7 4 1 1 5 , 1 3 7 5 ->= 3 4 5 1 4 7 , 1 3 7 5 ->= 7 3 3 4 1 5 , 1 4 7 5 ->= 2 3 1 4 5 7 , 1 4 7 5 ->= 1 2 7 3 5 4 , 7 5 7 5 ->= 7 5 7 4 5 , 7 1 2 5 ->= 2 3 5 7 1 , 1 7 2 5 ->= 1 5 2 4 7 , 1 7 2 5 ->= 2 4 1 5 7 , 1 7 2 5 ->= 1 7 2 4 5 , 1 7 2 5 ->= 5 2 4 1 2 7 , 7 7 2 5 ->= 4 2 2 5 7 7 , 1 5 3 7 1 ->= 1 3 1 4 5 7 , 1 3 4 7 1 ->= 1 2 3 4 1 7 , 1 7 5 4 7 ->= 1 7 7 3 4 5 , 1 4 7 1 5 ->= 1 1 4 5 4 7 , 1 1 7 5 5 ->= 1 7 4 1 5 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 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 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 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 1 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 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 | \ / 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 1 | | 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 }, it remains to prove termination of the 117-rule system { 0 1 1 -> 0 1 2 3 1 , 0 1 1 -> 0 4 5 1 4 1 , 0 1 1 -> 6 1 7 3 , 0 1 1 -> 6 7 3 , 0 1 1 -> 0 3 , 0 1 1 -> 0 1 4 5 1 4 , 6 7 1 -> 0 3 1 1 , 6 7 1 -> 6 1 7 , 6 7 1 -> 6 7 , 6 7 1 -> 0 , 6 7 1 -> 0 4 5 3 1 1 , 0 7 1 -> 0 4 2 1 7 , 0 7 1 -> 0 7 4 2 1 5 , 0 1 5 -> 0 4 5 1 , 0 1 5 -> 0 1 4 5 3 , 0 1 5 -> 0 3 1 5 , 0 1 5 -> 0 1 , 0 1 5 -> 0 1 2 4 1 5 , 6 7 5 -> 0 3 3 1 5 , 6 7 5 -> 0 4 5 1 5 , 6 7 5 -> 0 3 3 1 5 1 , 6 7 5 -> 6 4 7 , 6 7 5 -> 0 , 6 7 5 -> 6 5 7 , 6 7 5 -> 6 7 4 4 , 6 7 5 -> 0 4 4 , 0 7 5 -> 0 7 , 0 7 5 -> 0 7 4 5 , 0 7 5 -> 0 4 2 5 7 , 0 7 5 -> 0 7 2 3 5 2 , 0 7 5 -> 0 3 7 4 , 6 2 7 1 -> 0 3 1 3 1 , 6 5 7 1 -> 0 4 5 1 1 , 6 5 7 1 -> 6 7 3 4 5 1 , 6 5 7 1 -> 0 3 4 5 1 , 0 1 2 1 -> 6 2 7 4 1 1 , 0 1 2 1 -> 0 4 1 1 , 6 7 2 1 -> 0 2 3 1 1 , 0 7 2 1 -> 6 7 7 5 , 0 7 2 1 -> 0 7 5 , 6 7 1 5 -> 0 4 1 1 5 , 6 3 7 5 -> 6 4 7 , 6 3 7 5 -> 0 , 6 3 7 5 -> 0 3 3 4 1 5 , 6 4 7 5 -> 6 4 5 7 , 6 4 7 5 -> 0 , 6 4 7 5 -> 6 2 7 3 5 4 , 6 4 7 5 -> 0 3 5 4 , 0 5 7 5 -> 0 5 7 4 5 , 0 1 2 5 -> 0 1 , 6 7 2 5 -> 6 5 2 4 7 , 6 7 2 5 -> 0 , 6 7 2 5 -> 6 5 7 , 6 7 2 5 -> 6 7 2 4 5 , 6 7 2 5 -> 0 2 4 5 , 6 7 2 5 -> 6 2 7 , 0 7 2 5 -> 0 7 , 6 3 4 7 1 -> 6 2 3 4 1 7 , 6 3 4 7 1 -> 6 7 , 6 3 4 7 1 -> 0 , 6 7 5 4 7 -> 6 7 7 3 4 5 , 6 7 5 4 7 -> 0 7 3 4 5 , 6 4 7 1 5 -> 6 1 4 5 4 7 , 6 4 7 1 5 -> 6 4 5 4 7 , 6 4 7 1 5 -> 0 , 6 1 7 5 5 -> 6 7 4 1 5 5 , 6 1 7 5 5 -> 0 4 1 5 5 , 7 1 1 ->= 7 1 2 3 1 , 7 1 1 ->= 7 4 5 1 4 1 , 7 1 1 ->= 4 2 1 1 7 3 , 7 1 1 ->= 7 1 4 5 1 4 , 1 7 1 ->= 3 7 3 1 1 , 1 7 1 ->= 4 5 1 1 7 , 1 7 1 ->= 7 4 5 3 1 1 , 7 7 1 ->= 7 4 2 1 7 , 7 7 1 ->= 7 7 4 2 1 5 , 7 1 5 ->= 7 4 5 1 , 7 1 5 ->= 7 1 4 5 3 , 7 1 5 ->= 3 7 3 1 5 , 7 1 5 ->= 4 4 5 4 7 1 , 7 1 5 ->= 4 4 7 4 5 1 , 7 1 5 ->= 7 1 2 4 1 5 , 1 7 5 ->= 7 3 3 1 5 , 1 7 5 ->= 7 4 5 1 5 , 1 7 5 ->= 7 3 3 1 5 1 , 1 7 5 ->= 2 3 5 1 4 7 , 1 7 5 ->= 3 4 4 1 5 7 , 1 7 5 ->= 5 4 1 7 4 4 , 7 7 5 ->= 4 5 7 7 , 7 7 5 ->= 7 7 4 5 , 7 7 5 ->= 7 4 2 5 7 , 7 7 5 ->= 4 4 5 4 7 7 , 7 7 5 ->= 7 7 2 3 5 2 , 7 7 5 ->= 4 5 7 3 7 4 , 1 2 7 1 ->= 2 7 3 1 3 1 , 1 5 7 1 ->= 5 7 4 5 1 1 , 1 5 7 1 ->= 1 7 3 4 5 1 , 7 1 2 1 ->= 1 2 7 4 1 1 , 1 7 2 1 ->= 7 2 3 1 1 , 7 7 2 1 ->= 4 2 1 7 7 5 , 1 7 1 5 ->= 2 7 4 1 1 5 , 1 3 7 5 ->= 3 4 5 1 4 7 , 1 3 7 5 ->= 7 3 3 4 1 5 , 1 4 7 5 ->= 2 3 1 4 5 7 , 1 4 7 5 ->= 1 2 7 3 5 4 , 7 5 7 5 ->= 7 5 7 4 5 , 7 1 2 5 ->= 2 3 5 7 1 , 1 7 2 5 ->= 1 5 2 4 7 , 1 7 2 5 ->= 2 4 1 5 7 , 1 7 2 5 ->= 1 7 2 4 5 , 1 7 2 5 ->= 5 2 4 1 2 7 , 7 7 2 5 ->= 4 2 2 5 7 7 , 1 5 3 7 1 ->= 1 3 1 4 5 7 , 1 3 4 7 1 ->= 1 2 3 4 1 7 , 1 7 5 4 7 ->= 1 7 7 3 4 5 , 1 4 7 1 5 ->= 1 1 4 5 4 7 , 1 1 7 5 5 ->= 1 7 4 1 5 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 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 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 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 | \ / 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 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 | \ / 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 1 | | 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 }, it remains to prove termination of the 114-rule system { 0 1 1 -> 0 1 2 3 1 , 0 1 1 -> 0 4 5 1 4 1 , 0 1 1 -> 6 1 7 3 , 0 1 1 -> 6 7 3 , 0 1 1 -> 0 3 , 0 1 1 -> 0 1 4 5 1 4 , 6 7 1 -> 0 3 1 1 , 6 7 1 -> 6 1 7 , 6 7 1 -> 6 7 , 6 7 1 -> 0 , 6 7 1 -> 0 4 5 3 1 1 , 0 7 1 -> 0 4 2 1 7 , 0 7 1 -> 0 7 4 2 1 5 , 0 1 5 -> 0 4 5 1 , 0 1 5 -> 0 1 4 5 3 , 0 1 5 -> 0 3 1 5 , 0 1 5 -> 0 1 , 0 1 5 -> 0 1 2 4 1 5 , 6 7 5 -> 0 3 3 1 5 , 6 7 5 -> 0 4 5 1 5 , 6 7 5 -> 0 3 3 1 5 1 , 6 7 5 -> 6 4 7 , 6 7 5 -> 0 , 6 7 5 -> 6 5 7 , 6 7 5 -> 6 7 4 4 , 6 7 5 -> 0 4 4 , 0 7 5 -> 0 7 , 0 7 5 -> 0 7 4 5 , 0 7 5 -> 0 4 2 5 7 , 0 7 5 -> 0 7 2 3 5 2 , 0 7 5 -> 0 3 7 4 , 6 2 7 1 -> 0 3 1 3 1 , 6 5 7 1 -> 0 4 5 1 1 , 6 5 7 1 -> 6 7 3 4 5 1 , 6 5 7 1 -> 0 3 4 5 1 , 0 1 2 1 -> 6 2 7 4 1 1 , 0 1 2 1 -> 0 4 1 1 , 6 7 2 1 -> 0 2 3 1 1 , 0 7 2 1 -> 6 7 7 5 , 0 7 2 1 -> 0 7 5 , 6 7 1 5 -> 0 4 1 1 5 , 6 3 7 5 -> 6 4 7 , 6 3 7 5 -> 0 , 6 3 7 5 -> 0 3 3 4 1 5 , 6 4 7 5 -> 6 4 5 7 , 6 4 7 5 -> 0 , 6 4 7 5 -> 6 2 7 3 5 4 , 6 4 7 5 -> 0 3 5 4 , 0 5 7 5 -> 0 5 7 4 5 , 0 1 2 5 -> 0 1 , 6 7 2 5 -> 6 5 2 4 7 , 6 7 2 5 -> 0 , 6 7 2 5 -> 6 5 7 , 6 7 2 5 -> 6 7 2 4 5 , 6 7 2 5 -> 0 2 4 5 , 6 7 2 5 -> 6 2 7 , 0 7 2 5 -> 0 7 , 6 7 5 4 7 -> 6 7 7 3 4 5 , 6 7 5 4 7 -> 0 7 3 4 5 , 6 4 7 1 5 -> 6 1 4 5 4 7 , 6 4 7 1 5 -> 6 4 5 4 7 , 6 4 7 1 5 -> 0 , 6 1 7 5 5 -> 6 7 4 1 5 5 , 6 1 7 5 5 -> 0 4 1 5 5 , 7 1 1 ->= 7 1 2 3 1 , 7 1 1 ->= 7 4 5 1 4 1 , 7 1 1 ->= 4 2 1 1 7 3 , 7 1 1 ->= 7 1 4 5 1 4 , 1 7 1 ->= 3 7 3 1 1 , 1 7 1 ->= 4 5 1 1 7 , 1 7 1 ->= 7 4 5 3 1 1 , 7 7 1 ->= 7 4 2 1 7 , 7 7 1 ->= 7 7 4 2 1 5 , 7 1 5 ->= 7 4 5 1 , 7 1 5 ->= 7 1 4 5 3 , 7 1 5 ->= 3 7 3 1 5 , 7 1 5 ->= 4 4 5 4 7 1 , 7 1 5 ->= 4 4 7 4 5 1 , 7 1 5 ->= 7 1 2 4 1 5 , 1 7 5 ->= 7 3 3 1 5 , 1 7 5 ->= 7 4 5 1 5 , 1 7 5 ->= 7 3 3 1 5 1 , 1 7 5 ->= 2 3 5 1 4 7 , 1 7 5 ->= 3 4 4 1 5 7 , 1 7 5 ->= 5 4 1 7 4 4 , 7 7 5 ->= 4 5 7 7 , 7 7 5 ->= 7 7 4 5 , 7 7 5 ->= 7 4 2 5 7 , 7 7 5 ->= 4 4 5 4 7 7 , 7 7 5 ->= 7 7 2 3 5 2 , 7 7 5 ->= 4 5 7 3 7 4 , 1 2 7 1 ->= 2 7 3 1 3 1 , 1 5 7 1 ->= 5 7 4 5 1 1 , 1 5 7 1 ->= 1 7 3 4 5 1 , 7 1 2 1 ->= 1 2 7 4 1 1 , 1 7 2 1 ->= 7 2 3 1 1 , 7 7 2 1 ->= 4 2 1 7 7 5 , 1 7 1 5 ->= 2 7 4 1 1 5 , 1 3 7 5 ->= 3 4 5 1 4 7 , 1 3 7 5 ->= 7 3 3 4 1 5 , 1 4 7 5 ->= 2 3 1 4 5 7 , 1 4 7 5 ->= 1 2 7 3 5 4 , 7 5 7 5 ->= 7 5 7 4 5 , 7 1 2 5 ->= 2 3 5 7 1 , 1 7 2 5 ->= 1 5 2 4 7 , 1 7 2 5 ->= 2 4 1 5 7 , 1 7 2 5 ->= 1 7 2 4 5 , 1 7 2 5 ->= 5 2 4 1 2 7 , 7 7 2 5 ->= 4 2 2 5 7 7 , 1 5 3 7 1 ->= 1 3 1 4 5 7 , 1 3 4 7 1 ->= 1 2 3 4 1 7 , 1 7 5 4 7 ->= 1 7 7 3 4 5 , 1 4 7 1 5 ->= 1 1 4 5 4 7 , 1 1 7 5 5 ->= 1 7 4 1 5 5 } 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 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 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 1 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 1 0 | | 0 0 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 }, it remains to prove termination of the 113-rule system { 0 1 1 -> 0 1 2 3 1 , 0 1 1 -> 0 4 5 1 4 1 , 0 1 1 -> 6 1 7 3 , 0 1 1 -> 6 7 3 , 0 1 1 -> 0 3 , 0 1 1 -> 0 1 4 5 1 4 , 6 7 1 -> 0 3 1 1 , 6 7 1 -> 6 1 7 , 6 7 1 -> 6 7 , 6 7 1 -> 0 , 6 7 1 -> 0 4 5 3 1 1 , 0 7 1 -> 0 4 2 1 7 , 0 7 1 -> 0 7 4 2 1 5 , 0 1 5 -> 0 4 5 1 , 0 1 5 -> 0 1 4 5 3 , 0 1 5 -> 0 3 1 5 , 0 1 5 -> 0 1 , 0 1 5 -> 0 1 2 4 1 5 , 6 7 5 -> 0 3 3 1 5 , 6 7 5 -> 0 4 5 1 5 , 6 7 5 -> 0 3 3 1 5 1 , 6 7 5 -> 6 4 7 , 6 7 5 -> 0 , 6 7 5 -> 6 5 7 , 6 7 5 -> 6 7 4 4 , 6 7 5 -> 0 4 4 , 0 7 5 -> 0 7 , 0 7 5 -> 0 7 4 5 , 0 7 5 -> 0 4 2 5 7 , 0 7 5 -> 0 7 2 3 5 2 , 0 7 5 -> 0 3 7 4 , 6 2 7 1 -> 0 3 1 3 1 , 6 5 7 1 -> 0 4 5 1 1 , 6 5 7 1 -> 6 7 3 4 5 1 , 6 5 7 1 -> 0 3 4 5 1 , 0 1 2 1 -> 6 2 7 4 1 1 , 0 1 2 1 -> 0 4 1 1 , 0 7 2 1 -> 6 7 7 5 , 0 7 2 1 -> 0 7 5 , 6 7 1 5 -> 0 4 1 1 5 , 6 3 7 5 -> 6 4 7 , 6 3 7 5 -> 0 , 6 3 7 5 -> 0 3 3 4 1 5 , 6 4 7 5 -> 6 4 5 7 , 6 4 7 5 -> 0 , 6 4 7 5 -> 6 2 7 3 5 4 , 6 4 7 5 -> 0 3 5 4 , 0 5 7 5 -> 0 5 7 4 5 , 0 1 2 5 -> 0 1 , 6 7 2 5 -> 6 5 2 4 7 , 6 7 2 5 -> 0 , 6 7 2 5 -> 6 5 7 , 6 7 2 5 -> 6 7 2 4 5 , 6 7 2 5 -> 0 2 4 5 , 6 7 2 5 -> 6 2 7 , 0 7 2 5 -> 0 7 , 6 7 5 4 7 -> 6 7 7 3 4 5 , 6 7 5 4 7 -> 0 7 3 4 5 , 6 4 7 1 5 -> 6 1 4 5 4 7 , 6 4 7 1 5 -> 6 4 5 4 7 , 6 4 7 1 5 -> 0 , 6 1 7 5 5 -> 6 7 4 1 5 5 , 6 1 7 5 5 -> 0 4 1 5 5 , 7 1 1 ->= 7 1 2 3 1 , 7 1 1 ->= 7 4 5 1 4 1 , 7 1 1 ->= 4 2 1 1 7 3 , 7 1 1 ->= 7 1 4 5 1 4 , 1 7 1 ->= 3 7 3 1 1 , 1 7 1 ->= 4 5 1 1 7 , 1 7 1 ->= 7 4 5 3 1 1 , 7 7 1 ->= 7 4 2 1 7 , 7 7 1 ->= 7 7 4 2 1 5 , 7 1 5 ->= 7 4 5 1 , 7 1 5 ->= 7 1 4 5 3 , 7 1 5 ->= 3 7 3 1 5 , 7 1 5 ->= 4 4 5 4 7 1 , 7 1 5 ->= 4 4 7 4 5 1 , 7 1 5 ->= 7 1 2 4 1 5 , 1 7 5 ->= 7 3 3 1 5 , 1 7 5 ->= 7 4 5 1 5 , 1 7 5 ->= 7 3 3 1 5 1 , 1 7 5 ->= 2 3 5 1 4 7 , 1 7 5 ->= 3 4 4 1 5 7 , 1 7 5 ->= 5 4 1 7 4 4 , 7 7 5 ->= 4 5 7 7 , 7 7 5 ->= 7 7 4 5 , 7 7 5 ->= 7 4 2 5 7 , 7 7 5 ->= 4 4 5 4 7 7 , 7 7 5 ->= 7 7 2 3 5 2 , 7 7 5 ->= 4 5 7 3 7 4 , 1 2 7 1 ->= 2 7 3 1 3 1 , 1 5 7 1 ->= 5 7 4 5 1 1 , 1 5 7 1 ->= 1 7 3 4 5 1 , 7 1 2 1 ->= 1 2 7 4 1 1 , 1 7 2 1 ->= 7 2 3 1 1 , 7 7 2 1 ->= 4 2 1 7 7 5 , 1 7 1 5 ->= 2 7 4 1 1 5 , 1 3 7 5 ->= 3 4 5 1 4 7 , 1 3 7 5 ->= 7 3 3 4 1 5 , 1 4 7 5 ->= 2 3 1 4 5 7 , 1 4 7 5 ->= 1 2 7 3 5 4 , 7 5 7 5 ->= 7 5 7 4 5 , 7 1 2 5 ->= 2 3 5 7 1 , 1 7 2 5 ->= 1 5 2 4 7 , 1 7 2 5 ->= 2 4 1 5 7 , 1 7 2 5 ->= 1 7 2 4 5 , 1 7 2 5 ->= 5 2 4 1 2 7 , 7 7 2 5 ->= 4 2 2 5 7 7 , 1 5 3 7 1 ->= 1 3 1 4 5 7 , 1 3 4 7 1 ->= 1 2 3 4 1 7 , 1 7 5 4 7 ->= 1 7 7 3 4 5 , 1 4 7 1 5 ->= 1 1 4 5 4 7 , 1 1 7 5 5 ->= 1 7 4 1 5 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 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 0 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 0 1 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 1 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 1 | | 0 0 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 107-rule system { 0 1 1 -> 0 1 2 3 1 , 0 1 1 -> 0 4 5 1 4 1 , 0 1 1 -> 6 1 7 3 , 0 1 1 -> 6 7 3 , 0 1 1 -> 0 3 , 0 1 1 -> 0 1 4 5 1 4 , 0 7 1 -> 0 4 2 1 7 , 0 7 1 -> 0 7 4 2 1 5 , 0 1 5 -> 0 4 5 1 , 0 1 5 -> 0 1 4 5 3 , 0 1 5 -> 0 3 1 5 , 0 1 5 -> 0 1 , 0 1 5 -> 0 1 2 4 1 5 , 6 7 5 -> 0 3 3 1 5 , 6 7 5 -> 0 4 5 1 5 , 6 7 5 -> 0 3 3 1 5 1 , 6 7 5 -> 6 4 7 , 6 7 5 -> 0 , 6 7 5 -> 6 5 7 , 6 7 5 -> 6 7 4 4 , 6 7 5 -> 0 4 4 , 0 7 5 -> 0 7 , 0 7 5 -> 0 7 4 5 , 0 7 5 -> 0 4 2 5 7 , 0 7 5 -> 0 7 2 3 5 2 , 0 7 5 -> 0 3 7 4 , 6 2 7 1 -> 0 3 1 3 1 , 6 5 7 1 -> 0 4 5 1 1 , 6 5 7 1 -> 6 7 3 4 5 1 , 6 5 7 1 -> 0 3 4 5 1 , 0 1 2 1 -> 6 2 7 4 1 1 , 0 1 2 1 -> 0 4 1 1 , 0 7 2 1 -> 6 7 7 5 , 0 7 2 1 -> 0 7 5 , 6 3 7 5 -> 6 4 7 , 6 3 7 5 -> 0 , 6 3 7 5 -> 0 3 3 4 1 5 , 6 4 7 5 -> 6 4 5 7 , 6 4 7 5 -> 0 , 6 4 7 5 -> 6 2 7 3 5 4 , 6 4 7 5 -> 0 3 5 4 , 0 5 7 5 -> 0 5 7 4 5 , 0 1 2 5 -> 0 1 , 6 7 2 5 -> 6 5 2 4 7 , 6 7 2 5 -> 0 , 6 7 2 5 -> 6 5 7 , 6 7 2 5 -> 6 7 2 4 5 , 6 7 2 5 -> 0 2 4 5 , 6 7 2 5 -> 6 2 7 , 0 7 2 5 -> 0 7 , 6 7 5 4 7 -> 6 7 7 3 4 5 , 6 7 5 4 7 -> 0 7 3 4 5 , 6 4 7 1 5 -> 6 1 4 5 4 7 , 6 4 7 1 5 -> 6 4 5 4 7 , 6 4 7 1 5 -> 0 , 6 1 7 5 5 -> 6 7 4 1 5 5 , 6 1 7 5 5 -> 0 4 1 5 5 , 7 1 1 ->= 7 1 2 3 1 , 7 1 1 ->= 7 4 5 1 4 1 , 7 1 1 ->= 4 2 1 1 7 3 , 7 1 1 ->= 7 1 4 5 1 4 , 1 7 1 ->= 3 7 3 1 1 , 1 7 1 ->= 4 5 1 1 7 , 1 7 1 ->= 7 4 5 3 1 1 , 7 7 1 ->= 7 4 2 1 7 , 7 7 1 ->= 7 7 4 2 1 5 , 7 1 5 ->= 7 4 5 1 , 7 1 5 ->= 7 1 4 5 3 , 7 1 5 ->= 3 7 3 1 5 , 7 1 5 ->= 4 4 5 4 7 1 , 7 1 5 ->= 4 4 7 4 5 1 , 7 1 5 ->= 7 1 2 4 1 5 , 1 7 5 ->= 7 3 3 1 5 , 1 7 5 ->= 7 4 5 1 5 , 1 7 5 ->= 7 3 3 1 5 1 , 1 7 5 ->= 2 3 5 1 4 7 , 1 7 5 ->= 3 4 4 1 5 7 , 1 7 5 ->= 5 4 1 7 4 4 , 7 7 5 ->= 4 5 7 7 , 7 7 5 ->= 7 7 4 5 , 7 7 5 ->= 7 4 2 5 7 , 7 7 5 ->= 4 4 5 4 7 7 , 7 7 5 ->= 7 7 2 3 5 2 , 7 7 5 ->= 4 5 7 3 7 4 , 1 2 7 1 ->= 2 7 3 1 3 1 , 1 5 7 1 ->= 5 7 4 5 1 1 , 1 5 7 1 ->= 1 7 3 4 5 1 , 7 1 2 1 ->= 1 2 7 4 1 1 , 1 7 2 1 ->= 7 2 3 1 1 , 7 7 2 1 ->= 4 2 1 7 7 5 , 1 7 1 5 ->= 2 7 4 1 1 5 , 1 3 7 5 ->= 3 4 5 1 4 7 , 1 3 7 5 ->= 7 3 3 4 1 5 , 1 4 7 5 ->= 2 3 1 4 5 7 , 1 4 7 5 ->= 1 2 7 3 5 4 , 7 5 7 5 ->= 7 5 7 4 5 , 7 1 2 5 ->= 2 3 5 7 1 , 1 7 2 5 ->= 1 5 2 4 7 , 1 7 2 5 ->= 2 4 1 5 7 , 1 7 2 5 ->= 1 7 2 4 5 , 1 7 2 5 ->= 5 2 4 1 2 7 , 7 7 2 5 ->= 4 2 2 5 7 7 , 1 5 3 7 1 ->= 1 3 1 4 5 7 , 1 3 4 7 1 ->= 1 2 3 4 1 7 , 1 7 5 4 7 ->= 1 7 7 3 4 5 , 1 4 7 1 5 ->= 1 1 4 5 4 7 , 1 1 7 5 5 ->= 1 7 4 1 5 5 } 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 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 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 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 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 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 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 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 | \ / 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 1 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 | \ / 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 106-rule system { 0 1 1 -> 0 1 2 3 1 , 0 1 1 -> 0 4 5 1 4 1 , 0 1 1 -> 6 1 7 3 , 0 1 1 -> 6 7 3 , 0 1 1 -> 0 3 , 0 1 1 -> 0 1 4 5 1 4 , 0 7 1 -> 0 4 2 1 7 , 0 7 1 -> 0 7 4 2 1 5 , 0 1 5 -> 0 4 5 1 , 0 1 5 -> 0 1 4 5 3 , 0 1 5 -> 0 3 1 5 , 0 1 5 -> 0 1 , 0 1 5 -> 0 1 2 4 1 5 , 6 7 5 -> 0 3 3 1 5 , 6 7 5 -> 0 4 5 1 5 , 6 7 5 -> 0 3 3 1 5 1 , 6 7 5 -> 6 4 7 , 6 7 5 -> 0 , 6 7 5 -> 6 5 7 , 6 7 5 -> 6 7 4 4 , 6 7 5 -> 0 4 4 , 0 7 5 -> 0 7 , 0 7 5 -> 0 7 4 5 , 0 7 5 -> 0 4 2 5 7 , 0 7 5 -> 0 7 2 3 5 2 , 0 7 5 -> 0 3 7 4 , 6 5 7 1 -> 0 4 5 1 1 , 6 5 7 1 -> 6 7 3 4 5 1 , 6 5 7 1 -> 0 3 4 5 1 , 0 1 2 1 -> 6 2 7 4 1 1 , 0 1 2 1 -> 0 4 1 1 , 0 7 2 1 -> 6 7 7 5 , 0 7 2 1 -> 0 7 5 , 6 3 7 5 -> 6 4 7 , 6 3 7 5 -> 0 , 6 3 7 5 -> 0 3 3 4 1 5 , 6 4 7 5 -> 6 4 5 7 , 6 4 7 5 -> 0 , 6 4 7 5 -> 6 2 7 3 5 4 , 6 4 7 5 -> 0 3 5 4 , 0 5 7 5 -> 0 5 7 4 5 , 0 1 2 5 -> 0 1 , 6 7 2 5 -> 6 5 2 4 7 , 6 7 2 5 -> 0 , 6 7 2 5 -> 6 5 7 , 6 7 2 5 -> 6 7 2 4 5 , 6 7 2 5 -> 0 2 4 5 , 6 7 2 5 -> 6 2 7 , 0 7 2 5 -> 0 7 , 6 7 5 4 7 -> 6 7 7 3 4 5 , 6 7 5 4 7 -> 0 7 3 4 5 , 6 4 7 1 5 -> 6 1 4 5 4 7 , 6 4 7 1 5 -> 6 4 5 4 7 , 6 4 7 1 5 -> 0 , 6 1 7 5 5 -> 6 7 4 1 5 5 , 6 1 7 5 5 -> 0 4 1 5 5 , 7 1 1 ->= 7 1 2 3 1 , 7 1 1 ->= 7 4 5 1 4 1 , 7 1 1 ->= 4 2 1 1 7 3 , 7 1 1 ->= 7 1 4 5 1 4 , 1 7 1 ->= 3 7 3 1 1 , 1 7 1 ->= 4 5 1 1 7 , 1 7 1 ->= 7 4 5 3 1 1 , 7 7 1 ->= 7 4 2 1 7 , 7 7 1 ->= 7 7 4 2 1 5 , 7 1 5 ->= 7 4 5 1 , 7 1 5 ->= 7 1 4 5 3 , 7 1 5 ->= 3 7 3 1 5 , 7 1 5 ->= 4 4 5 4 7 1 , 7 1 5 ->= 4 4 7 4 5 1 , 7 1 5 ->= 7 1 2 4 1 5 , 1 7 5 ->= 7 3 3 1 5 , 1 7 5 ->= 7 4 5 1 5 , 1 7 5 ->= 7 3 3 1 5 1 , 1 7 5 ->= 2 3 5 1 4 7 , 1 7 5 ->= 3 4 4 1 5 7 , 1 7 5 ->= 5 4 1 7 4 4 , 7 7 5 ->= 4 5 7 7 , 7 7 5 ->= 7 7 4 5 , 7 7 5 ->= 7 4 2 5 7 , 7 7 5 ->= 4 4 5 4 7 7 , 7 7 5 ->= 7 7 2 3 5 2 , 7 7 5 ->= 4 5 7 3 7 4 , 1 2 7 1 ->= 2 7 3 1 3 1 , 1 5 7 1 ->= 5 7 4 5 1 1 , 1 5 7 1 ->= 1 7 3 4 5 1 , 7 1 2 1 ->= 1 2 7 4 1 1 , 1 7 2 1 ->= 7 2 3 1 1 , 7 7 2 1 ->= 4 2 1 7 7 5 , 1 7 1 5 ->= 2 7 4 1 1 5 , 1 3 7 5 ->= 3 4 5 1 4 7 , 1 3 7 5 ->= 7 3 3 4 1 5 , 1 4 7 5 ->= 2 3 1 4 5 7 , 1 4 7 5 ->= 1 2 7 3 5 4 , 7 5 7 5 ->= 7 5 7 4 5 , 7 1 2 5 ->= 2 3 5 7 1 , 1 7 2 5 ->= 1 5 2 4 7 , 1 7 2 5 ->= 2 4 1 5 7 , 1 7 2 5 ->= 1 7 2 4 5 , 1 7 2 5 ->= 5 2 4 1 2 7 , 7 7 2 5 ->= 4 2 2 5 7 7 , 1 5 3 7 1 ->= 1 3 1 4 5 7 , 1 3 4 7 1 ->= 1 2 3 4 1 7 , 1 7 5 4 7 ->= 1 7 7 3 4 5 , 1 4 7 1 5 ->= 1 1 4 5 4 7 , 1 1 7 5 5 ->= 1 7 4 1 5 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | \ / 2 is interpreted by / \ | 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 1 | | 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 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 | \ / 4 is interpreted by / \ | 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 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 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 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 1 0 0 0 | | 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 1 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 96-rule system { 0 1 1 -> 0 1 2 3 1 , 0 1 1 -> 0 4 5 1 4 1 , 0 1 1 -> 6 1 7 3 , 0 1 1 -> 6 7 3 , 0 1 1 -> 0 3 , 0 1 1 -> 0 1 4 5 1 4 , 0 7 1 -> 0 4 2 1 7 , 0 7 1 -> 0 7 4 2 1 5 , 0 1 5 -> 0 4 5 1 , 0 1 5 -> 0 1 4 5 3 , 0 1 5 -> 0 3 1 5 , 0 1 5 -> 0 1 , 0 1 5 -> 0 1 2 4 1 5 , 0 7 5 -> 0 7 , 0 7 5 -> 0 7 4 5 , 0 7 5 -> 0 4 2 5 7 , 0 7 5 -> 0 7 2 3 5 2 , 0 7 5 -> 0 3 7 4 , 6 5 7 1 -> 0 4 5 1 1 , 6 5 7 1 -> 6 7 3 4 5 1 , 6 5 7 1 -> 0 3 4 5 1 , 0 1 2 1 -> 6 2 7 4 1 1 , 0 1 2 1 -> 0 4 1 1 , 0 7 2 1 -> 6 7 7 5 , 0 7 2 1 -> 0 7 5 , 6 3 7 5 -> 6 4 7 , 6 3 7 5 -> 0 , 6 3 7 5 -> 0 3 3 4 1 5 , 6 4 7 5 -> 6 4 5 7 , 6 4 7 5 -> 0 , 6 4 7 5 -> 6 2 7 3 5 4 , 6 4 7 5 -> 0 3 5 4 , 0 5 7 5 -> 0 5 7 4 5 , 0 1 2 5 -> 0 1 , 6 7 2 5 -> 6 5 2 4 7 , 6 7 2 5 -> 0 , 6 7 2 5 -> 6 5 7 , 6 7 2 5 -> 6 7 2 4 5 , 6 7 2 5 -> 0 2 4 5 , 6 7 2 5 -> 6 2 7 , 0 7 2 5 -> 0 7 , 6 4 7 1 5 -> 6 1 4 5 4 7 , 6 4 7 1 5 -> 6 4 5 4 7 , 6 4 7 1 5 -> 0 , 6 1 7 5 5 -> 6 7 4 1 5 5 , 6 1 7 5 5 -> 0 4 1 5 5 , 7 1 1 ->= 7 1 2 3 1 , 7 1 1 ->= 7 4 5 1 4 1 , 7 1 1 ->= 4 2 1 1 7 3 , 7 1 1 ->= 7 1 4 5 1 4 , 1 7 1 ->= 3 7 3 1 1 , 1 7 1 ->= 4 5 1 1 7 , 1 7 1 ->= 7 4 5 3 1 1 , 7 7 1 ->= 7 4 2 1 7 , 7 7 1 ->= 7 7 4 2 1 5 , 7 1 5 ->= 7 4 5 1 , 7 1 5 ->= 7 1 4 5 3 , 7 1 5 ->= 3 7 3 1 5 , 7 1 5 ->= 4 4 5 4 7 1 , 7 1 5 ->= 4 4 7 4 5 1 , 7 1 5 ->= 7 1 2 4 1 5 , 1 7 5 ->= 7 3 3 1 5 , 1 7 5 ->= 7 4 5 1 5 , 1 7 5 ->= 7 3 3 1 5 1 , 1 7 5 ->= 2 3 5 1 4 7 , 1 7 5 ->= 3 4 4 1 5 7 , 1 7 5 ->= 5 4 1 7 4 4 , 7 7 5 ->= 4 5 7 7 , 7 7 5 ->= 7 7 4 5 , 7 7 5 ->= 7 4 2 5 7 , 7 7 5 ->= 4 4 5 4 7 7 , 7 7 5 ->= 7 7 2 3 5 2 , 7 7 5 ->= 4 5 7 3 7 4 , 1 2 7 1 ->= 2 7 3 1 3 1 , 1 5 7 1 ->= 5 7 4 5 1 1 , 1 5 7 1 ->= 1 7 3 4 5 1 , 7 1 2 1 ->= 1 2 7 4 1 1 , 1 7 2 1 ->= 7 2 3 1 1 , 7 7 2 1 ->= 4 2 1 7 7 5 , 1 7 1 5 ->= 2 7 4 1 1 5 , 1 3 7 5 ->= 3 4 5 1 4 7 , 1 3 7 5 ->= 7 3 3 4 1 5 , 1 4 7 5 ->= 2 3 1 4 5 7 , 1 4 7 5 ->= 1 2 7 3 5 4 , 7 5 7 5 ->= 7 5 7 4 5 , 7 1 2 5 ->= 2 3 5 7 1 , 1 7 2 5 ->= 1 5 2 4 7 , 1 7 2 5 ->= 2 4 1 5 7 , 1 7 2 5 ->= 1 7 2 4 5 , 1 7 2 5 ->= 5 2 4 1 2 7 , 7 7 2 5 ->= 4 2 2 5 7 7 , 1 5 3 7 1 ->= 1 3 1 4 5 7 , 1 3 4 7 1 ->= 1 2 3 4 1 7 , 1 7 5 4 7 ->= 1 7 7 3 4 5 , 1 4 7 1 5 ->= 1 1 4 5 4 7 , 1 1 7 5 5 ->= 1 7 4 1 5 5 } 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 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 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 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 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 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 0 0 0 0 0 0 0 | | 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 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 0 | | 0 0 0 0 1 0 0 0 | \ / 6 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 | \ / 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 1 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 | \ / 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 93-rule system { 0 1 1 -> 0 1 2 3 1 , 0 1 1 -> 0 4 5 1 4 1 , 0 1 1 -> 6 1 7 3 , 0 1 1 -> 6 7 3 , 0 1 1 -> 0 3 , 0 1 1 -> 0 1 4 5 1 4 , 0 7 1 -> 0 4 2 1 7 , 0 7 1 -> 0 7 4 2 1 5 , 0 1 5 -> 0 4 5 1 , 0 1 5 -> 0 1 4 5 3 , 0 1 5 -> 0 3 1 5 , 0 1 5 -> 0 1 , 0 1 5 -> 0 1 2 4 1 5 , 0 7 5 -> 0 7 , 0 7 5 -> 0 7 4 5 , 0 7 5 -> 0 4 2 5 7 , 0 7 5 -> 0 7 2 3 5 2 , 0 7 5 -> 0 3 7 4 , 0 1 2 1 -> 6 2 7 4 1 1 , 0 1 2 1 -> 0 4 1 1 , 0 7 2 1 -> 6 7 7 5 , 0 7 2 1 -> 0 7 5 , 6 3 7 5 -> 6 4 7 , 6 3 7 5 -> 0 , 6 3 7 5 -> 0 3 3 4 1 5 , 6 4 7 5 -> 6 4 5 7 , 6 4 7 5 -> 0 , 6 4 7 5 -> 6 2 7 3 5 4 , 6 4 7 5 -> 0 3 5 4 , 0 5 7 5 -> 0 5 7 4 5 , 0 1 2 5 -> 0 1 , 6 7 2 5 -> 6 5 2 4 7 , 6 7 2 5 -> 0 , 6 7 2 5 -> 6 5 7 , 6 7 2 5 -> 6 7 2 4 5 , 6 7 2 5 -> 0 2 4 5 , 6 7 2 5 -> 6 2 7 , 0 7 2 5 -> 0 7 , 6 4 7 1 5 -> 6 1 4 5 4 7 , 6 4 7 1 5 -> 6 4 5 4 7 , 6 4 7 1 5 -> 0 , 6 1 7 5 5 -> 6 7 4 1 5 5 , 6 1 7 5 5 -> 0 4 1 5 5 , 7 1 1 ->= 7 1 2 3 1 , 7 1 1 ->= 7 4 5 1 4 1 , 7 1 1 ->= 4 2 1 1 7 3 , 7 1 1 ->= 7 1 4 5 1 4 , 1 7 1 ->= 3 7 3 1 1 , 1 7 1 ->= 4 5 1 1 7 , 1 7 1 ->= 7 4 5 3 1 1 , 7 7 1 ->= 7 4 2 1 7 , 7 7 1 ->= 7 7 4 2 1 5 , 7 1 5 ->= 7 4 5 1 , 7 1 5 ->= 7 1 4 5 3 , 7 1 5 ->= 3 7 3 1 5 , 7 1 5 ->= 4 4 5 4 7 1 , 7 1 5 ->= 4 4 7 4 5 1 , 7 1 5 ->= 7 1 2 4 1 5 , 1 7 5 ->= 7 3 3 1 5 , 1 7 5 ->= 7 4 5 1 5 , 1 7 5 ->= 7 3 3 1 5 1 , 1 7 5 ->= 2 3 5 1 4 7 , 1 7 5 ->= 3 4 4 1 5 7 , 1 7 5 ->= 5 4 1 7 4 4 , 7 7 5 ->= 4 5 7 7 , 7 7 5 ->= 7 7 4 5 , 7 7 5 ->= 7 4 2 5 7 , 7 7 5 ->= 4 4 5 4 7 7 , 7 7 5 ->= 7 7 2 3 5 2 , 7 7 5 ->= 4 5 7 3 7 4 , 1 2 7 1 ->= 2 7 3 1 3 1 , 1 5 7 1 ->= 5 7 4 5 1 1 , 1 5 7 1 ->= 1 7 3 4 5 1 , 7 1 2 1 ->= 1 2 7 4 1 1 , 1 7 2 1 ->= 7 2 3 1 1 , 7 7 2 1 ->= 4 2 1 7 7 5 , 1 7 1 5 ->= 2 7 4 1 1 5 , 1 3 7 5 ->= 3 4 5 1 4 7 , 1 3 7 5 ->= 7 3 3 4 1 5 , 1 4 7 5 ->= 2 3 1 4 5 7 , 1 4 7 5 ->= 1 2 7 3 5 4 , 7 5 7 5 ->= 7 5 7 4 5 , 7 1 2 5 ->= 2 3 5 7 1 , 1 7 2 5 ->= 1 5 2 4 7 , 1 7 2 5 ->= 2 4 1 5 7 , 1 7 2 5 ->= 1 7 2 4 5 , 1 7 2 5 ->= 5 2 4 1 2 7 , 7 7 2 5 ->= 4 2 2 5 7 7 , 1 5 3 7 1 ->= 1 3 1 4 5 7 , 1 3 4 7 1 ->= 1 2 3 4 1 7 , 1 7 5 4 7 ->= 1 7 7 3 4 5 , 1 4 7 1 5 ->= 1 1 4 5 4 7 , 1 1 7 5 5 ->= 1 7 4 1 5 5 } 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 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 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 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 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 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 }, it remains to prove termination of the 90-rule system { 0 1 1 -> 0 1 2 3 1 , 0 1 1 -> 0 4 5 1 4 1 , 0 1 1 -> 6 1 7 3 , 0 1 1 -> 6 7 3 , 0 1 1 -> 0 3 , 0 1 1 -> 0 1 4 5 1 4 , 0 7 1 -> 0 4 2 1 7 , 0 7 1 -> 0 7 4 2 1 5 , 0 1 5 -> 0 4 5 1 , 0 1 5 -> 0 1 4 5 3 , 0 1 5 -> 0 3 1 5 , 0 1 5 -> 0 1 , 0 1 5 -> 0 1 2 4 1 5 , 0 7 5 -> 0 7 , 0 7 5 -> 0 7 4 5 , 0 7 5 -> 0 4 2 5 7 , 0 7 5 -> 0 7 2 3 5 2 , 0 7 5 -> 0 3 7 4 , 0 1 2 1 -> 6 2 7 4 1 1 , 0 1 2 1 -> 0 4 1 1 , 0 7 2 1 -> 6 7 7 5 , 0 7 2 1 -> 0 7 5 , 6 4 7 5 -> 6 4 5 7 , 6 4 7 5 -> 0 , 6 4 7 5 -> 6 2 7 3 5 4 , 6 4 7 5 -> 0 3 5 4 , 0 5 7 5 -> 0 5 7 4 5 , 0 1 2 5 -> 0 1 , 6 7 2 5 -> 6 5 2 4 7 , 6 7 2 5 -> 0 , 6 7 2 5 -> 6 5 7 , 6 7 2 5 -> 6 7 2 4 5 , 6 7 2 5 -> 0 2 4 5 , 6 7 2 5 -> 6 2 7 , 0 7 2 5 -> 0 7 , 6 4 7 1 5 -> 6 1 4 5 4 7 , 6 4 7 1 5 -> 6 4 5 4 7 , 6 4 7 1 5 -> 0 , 6 1 7 5 5 -> 6 7 4 1 5 5 , 6 1 7 5 5 -> 0 4 1 5 5 , 7 1 1 ->= 7 1 2 3 1 , 7 1 1 ->= 7 4 5 1 4 1 , 7 1 1 ->= 4 2 1 1 7 3 , 7 1 1 ->= 7 1 4 5 1 4 , 1 7 1 ->= 3 7 3 1 1 , 1 7 1 ->= 4 5 1 1 7 , 1 7 1 ->= 7 4 5 3 1 1 , 7 7 1 ->= 7 4 2 1 7 , 7 7 1 ->= 7 7 4 2 1 5 , 7 1 5 ->= 7 4 5 1 , 7 1 5 ->= 7 1 4 5 3 , 7 1 5 ->= 3 7 3 1 5 , 7 1 5 ->= 4 4 5 4 7 1 , 7 1 5 ->= 4 4 7 4 5 1 , 7 1 5 ->= 7 1 2 4 1 5 , 1 7 5 ->= 7 3 3 1 5 , 1 7 5 ->= 7 4 5 1 5 , 1 7 5 ->= 7 3 3 1 5 1 , 1 7 5 ->= 2 3 5 1 4 7 , 1 7 5 ->= 3 4 4 1 5 7 , 1 7 5 ->= 5 4 1 7 4 4 , 7 7 5 ->= 4 5 7 7 , 7 7 5 ->= 7 7 4 5 , 7 7 5 ->= 7 4 2 5 7 , 7 7 5 ->= 4 4 5 4 7 7 , 7 7 5 ->= 7 7 2 3 5 2 , 7 7 5 ->= 4 5 7 3 7 4 , 1 2 7 1 ->= 2 7 3 1 3 1 , 1 5 7 1 ->= 5 7 4 5 1 1 , 1 5 7 1 ->= 1 7 3 4 5 1 , 7 1 2 1 ->= 1 2 7 4 1 1 , 1 7 2 1 ->= 7 2 3 1 1 , 7 7 2 1 ->= 4 2 1 7 7 5 , 1 7 1 5 ->= 2 7 4 1 1 5 , 1 3 7 5 ->= 3 4 5 1 4 7 , 1 3 7 5 ->= 7 3 3 4 1 5 , 1 4 7 5 ->= 2 3 1 4 5 7 , 1 4 7 5 ->= 1 2 7 3 5 4 , 7 5 7 5 ->= 7 5 7 4 5 , 7 1 2 5 ->= 2 3 5 7 1 , 1 7 2 5 ->= 1 5 2 4 7 , 1 7 2 5 ->= 2 4 1 5 7 , 1 7 2 5 ->= 1 7 2 4 5 , 1 7 2 5 ->= 5 2 4 1 2 7 , 7 7 2 5 ->= 4 2 2 5 7 7 , 1 5 3 7 1 ->= 1 3 1 4 5 7 , 1 3 4 7 1 ->= 1 2 3 4 1 7 , 1 7 5 4 7 ->= 1 7 7 3 4 5 , 1 4 7 1 5 ->= 1 1 4 5 4 7 , 1 1 7 5 5 ->= 1 7 4 1 5 5 } 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 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 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 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 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 }, it remains to prove termination of the 83-rule system { 0 1 1 -> 0 1 2 3 1 , 0 1 1 -> 0 4 5 1 4 1 , 0 1 1 -> 6 1 7 3 , 0 1 1 -> 6 7 3 , 0 1 1 -> 0 3 , 0 1 1 -> 0 1 4 5 1 4 , 0 7 1 -> 0 4 2 1 7 , 0 7 1 -> 0 7 4 2 1 5 , 0 1 5 -> 0 4 5 1 , 0 1 5 -> 0 1 4 5 3 , 0 1 5 -> 0 3 1 5 , 0 1 5 -> 0 1 , 0 1 5 -> 0 1 2 4 1 5 , 0 7 5 -> 0 7 , 0 7 5 -> 0 7 4 5 , 0 7 5 -> 0 4 2 5 7 , 0 7 5 -> 0 7 2 3 5 2 , 0 7 5 -> 0 3 7 4 , 0 1 2 1 -> 6 2 7 4 1 1 , 0 1 2 1 -> 0 4 1 1 , 0 7 2 1 -> 6 7 7 5 , 0 7 2 1 -> 0 7 5 , 0 5 7 5 -> 0 5 7 4 5 , 0 1 2 5 -> 0 1 , 6 7 2 5 -> 6 5 2 4 7 , 6 7 2 5 -> 0 , 6 7 2 5 -> 6 5 7 , 6 7 2 5 -> 6 7 2 4 5 , 6 7 2 5 -> 0 2 4 5 , 6 7 2 5 -> 6 2 7 , 0 7 2 5 -> 0 7 , 6 1 7 5 5 -> 6 7 4 1 5 5 , 6 1 7 5 5 -> 0 4 1 5 5 , 7 1 1 ->= 7 1 2 3 1 , 7 1 1 ->= 7 4 5 1 4 1 , 7 1 1 ->= 4 2 1 1 7 3 , 7 1 1 ->= 7 1 4 5 1 4 , 1 7 1 ->= 3 7 3 1 1 , 1 7 1 ->= 4 5 1 1 7 , 1 7 1 ->= 7 4 5 3 1 1 , 7 7 1 ->= 7 4 2 1 7 , 7 7 1 ->= 7 7 4 2 1 5 , 7 1 5 ->= 7 4 5 1 , 7 1 5 ->= 7 1 4 5 3 , 7 1 5 ->= 3 7 3 1 5 , 7 1 5 ->= 4 4 5 4 7 1 , 7 1 5 ->= 4 4 7 4 5 1 , 7 1 5 ->= 7 1 2 4 1 5 , 1 7 5 ->= 7 3 3 1 5 , 1 7 5 ->= 7 4 5 1 5 , 1 7 5 ->= 7 3 3 1 5 1 , 1 7 5 ->= 2 3 5 1 4 7 , 1 7 5 ->= 3 4 4 1 5 7 , 1 7 5 ->= 5 4 1 7 4 4 , 7 7 5 ->= 4 5 7 7 , 7 7 5 ->= 7 7 4 5 , 7 7 5 ->= 7 4 2 5 7 , 7 7 5 ->= 4 4 5 4 7 7 , 7 7 5 ->= 7 7 2 3 5 2 , 7 7 5 ->= 4 5 7 3 7 4 , 1 2 7 1 ->= 2 7 3 1 3 1 , 1 5 7 1 ->= 5 7 4 5 1 1 , 1 5 7 1 ->= 1 7 3 4 5 1 , 7 1 2 1 ->= 1 2 7 4 1 1 , 1 7 2 1 ->= 7 2 3 1 1 , 7 7 2 1 ->= 4 2 1 7 7 5 , 1 7 1 5 ->= 2 7 4 1 1 5 , 1 3 7 5 ->= 3 4 5 1 4 7 , 1 3 7 5 ->= 7 3 3 4 1 5 , 1 4 7 5 ->= 2 3 1 4 5 7 , 1 4 7 5 ->= 1 2 7 3 5 4 , 7 5 7 5 ->= 7 5 7 4 5 , 7 1 2 5 ->= 2 3 5 7 1 , 1 7 2 5 ->= 1 5 2 4 7 , 1 7 2 5 ->= 2 4 1 5 7 , 1 7 2 5 ->= 1 7 2 4 5 , 1 7 2 5 ->= 5 2 4 1 2 7 , 7 7 2 5 ->= 4 2 2 5 7 7 , 1 5 3 7 1 ->= 1 3 1 4 5 7 , 1 3 4 7 1 ->= 1 2 3 4 1 7 , 1 7 5 4 7 ->= 1 7 7 3 4 5 , 1 4 7 1 5 ->= 1 1 4 5 4 7 , 1 1 7 5 5 ->= 1 7 4 1 5 5 } 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 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 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 0 0 0 0 | \ / 7 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 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 77-rule system { 0 1 1 -> 0 1 2 3 1 , 0 1 1 -> 0 4 5 1 4 1 , 0 1 1 -> 6 1 7 3 , 0 1 1 -> 6 7 3 , 0 1 1 -> 0 3 , 0 1 1 -> 0 1 4 5 1 4 , 0 7 1 -> 0 4 2 1 7 , 0 7 1 -> 0 7 4 2 1 5 , 0 1 5 -> 0 4 5 1 , 0 1 5 -> 0 1 4 5 3 , 0 1 5 -> 0 3 1 5 , 0 1 5 -> 0 1 , 0 1 5 -> 0 1 2 4 1 5 , 0 7 5 -> 0 7 , 0 7 5 -> 0 7 4 5 , 0 7 5 -> 0 4 2 5 7 , 0 7 5 -> 0 7 2 3 5 2 , 0 7 5 -> 0 3 7 4 , 0 1 2 1 -> 6 2 7 4 1 1 , 0 1 2 1 -> 0 4 1 1 , 0 7 2 1 -> 6 7 7 5 , 0 7 2 1 -> 0 7 5 , 0 5 7 5 -> 0 5 7 4 5 , 0 1 2 5 -> 0 1 , 0 7 2 5 -> 0 7 , 6 1 7 5 5 -> 6 7 4 1 5 5 , 6 1 7 5 5 -> 0 4 1 5 5 , 7 1 1 ->= 7 1 2 3 1 , 7 1 1 ->= 7 4 5 1 4 1 , 7 1 1 ->= 4 2 1 1 7 3 , 7 1 1 ->= 7 1 4 5 1 4 , 1 7 1 ->= 3 7 3 1 1 , 1 7 1 ->= 4 5 1 1 7 , 1 7 1 ->= 7 4 5 3 1 1 , 7 7 1 ->= 7 4 2 1 7 , 7 7 1 ->= 7 7 4 2 1 5 , 7 1 5 ->= 7 4 5 1 , 7 1 5 ->= 7 1 4 5 3 , 7 1 5 ->= 3 7 3 1 5 , 7 1 5 ->= 4 4 5 4 7 1 , 7 1 5 ->= 4 4 7 4 5 1 , 7 1 5 ->= 7 1 2 4 1 5 , 1 7 5 ->= 7 3 3 1 5 , 1 7 5 ->= 7 4 5 1 5 , 1 7 5 ->= 7 3 3 1 5 1 , 1 7 5 ->= 2 3 5 1 4 7 , 1 7 5 ->= 3 4 4 1 5 7 , 1 7 5 ->= 5 4 1 7 4 4 , 7 7 5 ->= 4 5 7 7 , 7 7 5 ->= 7 7 4 5 , 7 7 5 ->= 7 4 2 5 7 , 7 7 5 ->= 4 4 5 4 7 7 , 7 7 5 ->= 7 7 2 3 5 2 , 7 7 5 ->= 4 5 7 3 7 4 , 1 2 7 1 ->= 2 7 3 1 3 1 , 1 5 7 1 ->= 5 7 4 5 1 1 , 1 5 7 1 ->= 1 7 3 4 5 1 , 7 1 2 1 ->= 1 2 7 4 1 1 , 1 7 2 1 ->= 7 2 3 1 1 , 7 7 2 1 ->= 4 2 1 7 7 5 , 1 7 1 5 ->= 2 7 4 1 1 5 , 1 3 7 5 ->= 3 4 5 1 4 7 , 1 3 7 5 ->= 7 3 3 4 1 5 , 1 4 7 5 ->= 2 3 1 4 5 7 , 1 4 7 5 ->= 1 2 7 3 5 4 , 7 5 7 5 ->= 7 5 7 4 5 , 7 1 2 5 ->= 2 3 5 7 1 , 1 7 2 5 ->= 1 5 2 4 7 , 1 7 2 5 ->= 2 4 1 5 7 , 1 7 2 5 ->= 1 7 2 4 5 , 1 7 2 5 ->= 5 2 4 1 2 7 , 7 7 2 5 ->= 4 2 2 5 7 7 , 1 5 3 7 1 ->= 1 3 1 4 5 7 , 1 3 4 7 1 ->= 1 2 3 4 1 7 , 1 7 5 4 7 ->= 1 7 7 3 4 5 , 1 4 7 1 5 ->= 1 1 4 5 4 7 , 1 1 7 5 5 ->= 1 7 4 1 5 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 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 0 0 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 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 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 }, it remains to prove termination of the 76-rule system { 0 1 1 -> 0 1 2 3 1 , 0 1 1 -> 0 4 5 1 4 1 , 0 1 1 -> 6 1 7 3 , 0 1 1 -> 6 7 3 , 0 1 1 -> 0 3 , 0 1 1 -> 0 1 4 5 1 4 , 0 7 1 -> 0 4 2 1 7 , 0 7 1 -> 0 7 4 2 1 5 , 0 1 5 -> 0 4 5 1 , 0 1 5 -> 0 1 4 5 3 , 0 1 5 -> 0 3 1 5 , 0 1 5 -> 0 1 , 0 1 5 -> 0 1 2 4 1 5 , 0 7 5 -> 0 7 , 0 7 5 -> 0 7 4 5 , 0 7 5 -> 0 4 2 5 7 , 0 7 5 -> 0 7 2 3 5 2 , 0 7 5 -> 0 3 7 4 , 0 1 2 1 -> 6 2 7 4 1 1 , 0 1 2 1 -> 0 4 1 1 , 0 7 2 1 -> 6 7 7 5 , 0 7 2 1 -> 0 7 5 , 0 1 2 5 -> 0 1 , 0 7 2 5 -> 0 7 , 6 1 7 5 5 -> 6 7 4 1 5 5 , 6 1 7 5 5 -> 0 4 1 5 5 , 7 1 1 ->= 7 1 2 3 1 , 7 1 1 ->= 7 4 5 1 4 1 , 7 1 1 ->= 4 2 1 1 7 3 , 7 1 1 ->= 7 1 4 5 1 4 , 1 7 1 ->= 3 7 3 1 1 , 1 7 1 ->= 4 5 1 1 7 , 1 7 1 ->= 7 4 5 3 1 1 , 7 7 1 ->= 7 4 2 1 7 , 7 7 1 ->= 7 7 4 2 1 5 , 7 1 5 ->= 7 4 5 1 , 7 1 5 ->= 7 1 4 5 3 , 7 1 5 ->= 3 7 3 1 5 , 7 1 5 ->= 4 4 5 4 7 1 , 7 1 5 ->= 4 4 7 4 5 1 , 7 1 5 ->= 7 1 2 4 1 5 , 1 7 5 ->= 7 3 3 1 5 , 1 7 5 ->= 7 4 5 1 5 , 1 7 5 ->= 7 3 3 1 5 1 , 1 7 5 ->= 2 3 5 1 4 7 , 1 7 5 ->= 3 4 4 1 5 7 , 1 7 5 ->= 5 4 1 7 4 4 , 7 7 5 ->= 4 5 7 7 , 7 7 5 ->= 7 7 4 5 , 7 7 5 ->= 7 4 2 5 7 , 7 7 5 ->= 4 4 5 4 7 7 , 7 7 5 ->= 7 7 2 3 5 2 , 7 7 5 ->= 4 5 7 3 7 4 , 1 2 7 1 ->= 2 7 3 1 3 1 , 1 5 7 1 ->= 5 7 4 5 1 1 , 1 5 7 1 ->= 1 7 3 4 5 1 , 7 1 2 1 ->= 1 2 7 4 1 1 , 1 7 2 1 ->= 7 2 3 1 1 , 7 7 2 1 ->= 4 2 1 7 7 5 , 1 7 1 5 ->= 2 7 4 1 1 5 , 1 3 7 5 ->= 3 4 5 1 4 7 , 1 3 7 5 ->= 7 3 3 4 1 5 , 1 4 7 5 ->= 2 3 1 4 5 7 , 1 4 7 5 ->= 1 2 7 3 5 4 , 7 5 7 5 ->= 7 5 7 4 5 , 7 1 2 5 ->= 2 3 5 7 1 , 1 7 2 5 ->= 1 5 2 4 7 , 1 7 2 5 ->= 2 4 1 5 7 , 1 7 2 5 ->= 1 7 2 4 5 , 1 7 2 5 ->= 5 2 4 1 2 7 , 7 7 2 5 ->= 4 2 2 5 7 7 , 1 5 3 7 1 ->= 1 3 1 4 5 7 , 1 3 4 7 1 ->= 1 2 3 4 1 7 , 1 7 5 4 7 ->= 1 7 7 3 4 5 , 1 4 7 1 5 ->= 1 1 4 5 4 7 , 1 1 7 5 5 ->= 1 7 4 1 5 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 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 1 0 0 0 0 | | 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 1 | | 0 1 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 0 0 | \ / 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 1 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 }, it remains to prove termination of the 74-rule system { 0 1 1 -> 0 1 2 3 1 , 0 1 1 -> 0 4 5 1 4 1 , 0 1 1 -> 6 1 7 3 , 0 1 1 -> 6 7 3 , 0 1 1 -> 0 3 , 0 1 1 -> 0 1 4 5 1 4 , 0 7 1 -> 0 4 2 1 7 , 0 7 1 -> 0 7 4 2 1 5 , 0 1 5 -> 0 4 5 1 , 0 1 5 -> 0 1 4 5 3 , 0 1 5 -> 0 3 1 5 , 0 1 5 -> 0 1 , 0 1 5 -> 0 1 2 4 1 5 , 0 7 5 -> 0 7 , 0 7 5 -> 0 7 4 5 , 0 7 5 -> 0 4 2 5 7 , 0 7 5 -> 0 7 2 3 5 2 , 0 7 5 -> 0 3 7 4 , 0 1 2 1 -> 6 2 7 4 1 1 , 0 1 2 1 -> 0 4 1 1 , 0 7 2 1 -> 6 7 7 5 , 0 7 2 1 -> 0 7 5 , 0 1 2 5 -> 0 1 , 0 7 2 5 -> 0 7 , 7 1 1 ->= 7 1 2 3 1 , 7 1 1 ->= 7 4 5 1 4 1 , 7 1 1 ->= 4 2 1 1 7 3 , 7 1 1 ->= 7 1 4 5 1 4 , 1 7 1 ->= 3 7 3 1 1 , 1 7 1 ->= 4 5 1 1 7 , 1 7 1 ->= 7 4 5 3 1 1 , 7 7 1 ->= 7 4 2 1 7 , 7 7 1 ->= 7 7 4 2 1 5 , 7 1 5 ->= 7 4 5 1 , 7 1 5 ->= 7 1 4 5 3 , 7 1 5 ->= 3 7 3 1 5 , 7 1 5 ->= 4 4 5 4 7 1 , 7 1 5 ->= 4 4 7 4 5 1 , 7 1 5 ->= 7 1 2 4 1 5 , 1 7 5 ->= 7 3 3 1 5 , 1 7 5 ->= 7 4 5 1 5 , 1 7 5 ->= 7 3 3 1 5 1 , 1 7 5 ->= 2 3 5 1 4 7 , 1 7 5 ->= 3 4 4 1 5 7 , 1 7 5 ->= 5 4 1 7 4 4 , 7 7 5 ->= 4 5 7 7 , 7 7 5 ->= 7 7 4 5 , 7 7 5 ->= 7 4 2 5 7 , 7 7 5 ->= 4 4 5 4 7 7 , 7 7 5 ->= 7 7 2 3 5 2 , 7 7 5 ->= 4 5 7 3 7 4 , 1 2 7 1 ->= 2 7 3 1 3 1 , 1 5 7 1 ->= 5 7 4 5 1 1 , 1 5 7 1 ->= 1 7 3 4 5 1 , 7 1 2 1 ->= 1 2 7 4 1 1 , 1 7 2 1 ->= 7 2 3 1 1 , 7 7 2 1 ->= 4 2 1 7 7 5 , 1 7 1 5 ->= 2 7 4 1 1 5 , 1 3 7 5 ->= 3 4 5 1 4 7 , 1 3 7 5 ->= 7 3 3 4 1 5 , 1 4 7 5 ->= 2 3 1 4 5 7 , 1 4 7 5 ->= 1 2 7 3 5 4 , 7 5 7 5 ->= 7 5 7 4 5 , 7 1 2 5 ->= 2 3 5 7 1 , 1 7 2 5 ->= 1 5 2 4 7 , 1 7 2 5 ->= 2 4 1 5 7 , 1 7 2 5 ->= 1 7 2 4 5 , 1 7 2 5 ->= 5 2 4 1 2 7 , 7 7 2 5 ->= 4 2 2 5 7 7 , 1 5 3 7 1 ->= 1 3 1 4 5 7 , 1 3 4 7 1 ->= 1 2 3 4 1 7 , 1 7 5 4 7 ->= 1 7 7 3 4 5 , 1 4 7 1 5 ->= 1 1 4 5 4 7 , 1 1 7 5 5 ->= 1 7 4 1 5 5 } 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 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 7->6 }, it remains to prove termination of the 70-rule system { 0 1 1 -> 0 1 2 3 1 , 0 1 1 -> 0 4 5 1 4 1 , 0 1 1 -> 0 3 , 0 1 1 -> 0 1 4 5 1 4 , 0 6 1 -> 0 4 2 1 6 , 0 6 1 -> 0 6 4 2 1 5 , 0 1 5 -> 0 4 5 1 , 0 1 5 -> 0 1 4 5 3 , 0 1 5 -> 0 3 1 5 , 0 1 5 -> 0 1 , 0 1 5 -> 0 1 2 4 1 5 , 0 6 5 -> 0 6 , 0 6 5 -> 0 6 4 5 , 0 6 5 -> 0 4 2 5 6 , 0 6 5 -> 0 6 2 3 5 2 , 0 6 5 -> 0 3 6 4 , 0 1 2 1 -> 0 4 1 1 , 0 6 2 1 -> 0 6 5 , 0 1 2 5 -> 0 1 , 0 6 2 5 -> 0 6 , 6 1 1 ->= 6 1 2 3 1 , 6 1 1 ->= 6 4 5 1 4 1 , 6 1 1 ->= 4 2 1 1 6 3 , 6 1 1 ->= 6 1 4 5 1 4 , 1 6 1 ->= 3 6 3 1 1 , 1 6 1 ->= 4 5 1 1 6 , 1 6 1 ->= 6 4 5 3 1 1 , 6 6 1 ->= 6 4 2 1 6 , 6 6 1 ->= 6 6 4 2 1 5 , 6 1 5 ->= 6 4 5 1 , 6 1 5 ->= 6 1 4 5 3 , 6 1 5 ->= 3 6 3 1 5 , 6 1 5 ->= 4 4 5 4 6 1 , 6 1 5 ->= 4 4 6 4 5 1 , 6 1 5 ->= 6 1 2 4 1 5 , 1 6 5 ->= 6 3 3 1 5 , 1 6 5 ->= 6 4 5 1 5 , 1 6 5 ->= 6 3 3 1 5 1 , 1 6 5 ->= 2 3 5 1 4 6 , 1 6 5 ->= 3 4 4 1 5 6 , 1 6 5 ->= 5 4 1 6 4 4 , 6 6 5 ->= 4 5 6 6 , 6 6 5 ->= 6 6 4 5 , 6 6 5 ->= 6 4 2 5 6 , 6 6 5 ->= 4 4 5 4 6 6 , 6 6 5 ->= 6 6 2 3 5 2 , 6 6 5 ->= 4 5 6 3 6 4 , 1 2 6 1 ->= 2 6 3 1 3 1 , 1 5 6 1 ->= 5 6 4 5 1 1 , 1 5 6 1 ->= 1 6 3 4 5 1 , 6 1 2 1 ->= 1 2 6 4 1 1 , 1 6 2 1 ->= 6 2 3 1 1 , 6 6 2 1 ->= 4 2 1 6 6 5 , 1 6 1 5 ->= 2 6 4 1 1 5 , 1 3 6 5 ->= 3 4 5 1 4 6 , 1 3 6 5 ->= 6 3 3 4 1 5 , 1 4 6 5 ->= 2 3 1 4 5 6 , 1 4 6 5 ->= 1 2 6 3 5 4 , 6 5 6 5 ->= 6 5 6 4 5 , 6 1 2 5 ->= 2 3 5 6 1 , 1 6 2 5 ->= 1 5 2 4 6 , 1 6 2 5 ->= 2 4 1 5 6 , 1 6 2 5 ->= 1 6 2 4 5 , 1 6 2 5 ->= 5 2 4 1 2 6 , 6 6 2 5 ->= 4 2 2 5 6 6 , 1 5 3 6 1 ->= 1 3 1 4 5 6 , 1 3 4 6 1 ->= 1 2 3 4 1 6 , 1 6 5 4 6 ->= 1 6 6 3 4 5 , 1 4 6 1 5 ->= 1 1 4 5 4 6 , 1 1 6 5 5 ->= 1 6 4 1 5 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 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 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 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 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 1 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 69-rule system { 0 1 1 -> 0 1 2 3 1 , 0 1 1 -> 0 4 5 1 4 1 , 0 1 1 -> 0 3 , 0 1 1 -> 0 1 4 5 1 4 , 0 6 1 -> 0 4 2 1 6 , 0 6 1 -> 0 6 4 2 1 5 , 0 1 5 -> 0 4 5 1 , 0 1 5 -> 0 1 4 5 3 , 0 1 5 -> 0 3 1 5 , 0 1 5 -> 0 1 , 0 1 5 -> 0 1 2 4 1 5 , 0 6 5 -> 0 6 , 0 6 5 -> 0 6 4 5 , 0 6 5 -> 0 4 2 5 6 , 0 6 5 -> 0 6 2 3 5 2 , 0 6 5 -> 0 3 6 4 , 0 6 2 1 -> 0 6 5 , 0 1 2 5 -> 0 1 , 0 6 2 5 -> 0 6 , 6 1 1 ->= 6 1 2 3 1 , 6 1 1 ->= 6 4 5 1 4 1 , 6 1 1 ->= 4 2 1 1 6 3 , 6 1 1 ->= 6 1 4 5 1 4 , 1 6 1 ->= 3 6 3 1 1 , 1 6 1 ->= 4 5 1 1 6 , 1 6 1 ->= 6 4 5 3 1 1 , 6 6 1 ->= 6 4 2 1 6 , 6 6 1 ->= 6 6 4 2 1 5 , 6 1 5 ->= 6 4 5 1 , 6 1 5 ->= 6 1 4 5 3 , 6 1 5 ->= 3 6 3 1 5 , 6 1 5 ->= 4 4 5 4 6 1 , 6 1 5 ->= 4 4 6 4 5 1 , 6 1 5 ->= 6 1 2 4 1 5 , 1 6 5 ->= 6 3 3 1 5 , 1 6 5 ->= 6 4 5 1 5 , 1 6 5 ->= 6 3 3 1 5 1 , 1 6 5 ->= 2 3 5 1 4 6 , 1 6 5 ->= 3 4 4 1 5 6 , 1 6 5 ->= 5 4 1 6 4 4 , 6 6 5 ->= 4 5 6 6 , 6 6 5 ->= 6 6 4 5 , 6 6 5 ->= 6 4 2 5 6 , 6 6 5 ->= 4 4 5 4 6 6 , 6 6 5 ->= 6 6 2 3 5 2 , 6 6 5 ->= 4 5 6 3 6 4 , 1 2 6 1 ->= 2 6 3 1 3 1 , 1 5 6 1 ->= 5 6 4 5 1 1 , 1 5 6 1 ->= 1 6 3 4 5 1 , 6 1 2 1 ->= 1 2 6 4 1 1 , 1 6 2 1 ->= 6 2 3 1 1 , 6 6 2 1 ->= 4 2 1 6 6 5 , 1 6 1 5 ->= 2 6 4 1 1 5 , 1 3 6 5 ->= 3 4 5 1 4 6 , 1 3 6 5 ->= 6 3 3 4 1 5 , 1 4 6 5 ->= 2 3 1 4 5 6 , 1 4 6 5 ->= 1 2 6 3 5 4 , 6 5 6 5 ->= 6 5 6 4 5 , 6 1 2 5 ->= 2 3 5 6 1 , 1 6 2 5 ->= 1 5 2 4 6 , 1 6 2 5 ->= 2 4 1 5 6 , 1 6 2 5 ->= 1 6 2 4 5 , 1 6 2 5 ->= 5 2 4 1 2 6 , 6 6 2 5 ->= 4 2 2 5 6 6 , 1 5 3 6 1 ->= 1 3 1 4 5 6 , 1 3 4 6 1 ->= 1 2 3 4 1 6 , 1 6 5 4 6 ->= 1 6 6 3 4 5 , 1 4 6 1 5 ->= 1 1 4 5 4 6 , 1 1 6 5 5 ->= 1 6 4 1 5 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 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 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 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 1 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 }, it remains to prove termination of the 68-rule system { 0 1 1 -> 0 1 2 3 1 , 0 1 1 -> 0 4 5 1 4 1 , 0 1 1 -> 0 3 , 0 1 1 -> 0 1 4 5 1 4 , 0 6 1 -> 0 4 2 1 6 , 0 6 1 -> 0 6 4 2 1 5 , 0 1 5 -> 0 4 5 1 , 0 1 5 -> 0 1 4 5 3 , 0 1 5 -> 0 3 1 5 , 0 1 5 -> 0 1 , 0 1 5 -> 0 1 2 4 1 5 , 0 6 5 -> 0 6 , 0 6 5 -> 0 6 4 5 , 0 6 5 -> 0 4 2 5 6 , 0 6 5 -> 0 6 2 3 5 2 , 0 6 5 -> 0 3 6 4 , 0 1 2 5 -> 0 1 , 0 6 2 5 -> 0 6 , 6 1 1 ->= 6 1 2 3 1 , 6 1 1 ->= 6 4 5 1 4 1 , 6 1 1 ->= 4 2 1 1 6 3 , 6 1 1 ->= 6 1 4 5 1 4 , 1 6 1 ->= 3 6 3 1 1 , 1 6 1 ->= 4 5 1 1 6 , 1 6 1 ->= 6 4 5 3 1 1 , 6 6 1 ->= 6 4 2 1 6 , 6 6 1 ->= 6 6 4 2 1 5 , 6 1 5 ->= 6 4 5 1 , 6 1 5 ->= 6 1 4 5 3 , 6 1 5 ->= 3 6 3 1 5 , 6 1 5 ->= 4 4 5 4 6 1 , 6 1 5 ->= 4 4 6 4 5 1 , 6 1 5 ->= 6 1 2 4 1 5 , 1 6 5 ->= 6 3 3 1 5 , 1 6 5 ->= 6 4 5 1 5 , 1 6 5 ->= 6 3 3 1 5 1 , 1 6 5 ->= 2 3 5 1 4 6 , 1 6 5 ->= 3 4 4 1 5 6 , 1 6 5 ->= 5 4 1 6 4 4 , 6 6 5 ->= 4 5 6 6 , 6 6 5 ->= 6 6 4 5 , 6 6 5 ->= 6 4 2 5 6 , 6 6 5 ->= 4 4 5 4 6 6 , 6 6 5 ->= 6 6 2 3 5 2 , 6 6 5 ->= 4 5 6 3 6 4 , 1 2 6 1 ->= 2 6 3 1 3 1 , 1 5 6 1 ->= 5 6 4 5 1 1 , 1 5 6 1 ->= 1 6 3 4 5 1 , 6 1 2 1 ->= 1 2 6 4 1 1 , 1 6 2 1 ->= 6 2 3 1 1 , 6 6 2 1 ->= 4 2 1 6 6 5 , 1 6 1 5 ->= 2 6 4 1 1 5 , 1 3 6 5 ->= 3 4 5 1 4 6 , 1 3 6 5 ->= 6 3 3 4 1 5 , 1 4 6 5 ->= 2 3 1 4 5 6 , 1 4 6 5 ->= 1 2 6 3 5 4 , 6 5 6 5 ->= 6 5 6 4 5 , 6 1 2 5 ->= 2 3 5 6 1 , 1 6 2 5 ->= 1 5 2 4 6 , 1 6 2 5 ->= 2 4 1 5 6 , 1 6 2 5 ->= 1 6 2 4 5 , 1 6 2 5 ->= 5 2 4 1 2 6 , 6 6 2 5 ->= 4 2 2 5 6 6 , 1 5 3 6 1 ->= 1 3 1 4 5 6 , 1 3 4 6 1 ->= 1 2 3 4 1 6 , 1 6 5 4 6 ->= 1 6 6 3 4 5 , 1 4 6 1 5 ->= 1 1 4 5 4 6 , 1 1 6 5 5 ->= 1 6 4 1 5 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 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 0 | | 0 1 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 1 | \ / 3 is interpreted by / \ | 1 0 0 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 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 1 | \ / 6 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 1 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 66-rule system { 0 1 1 -> 0 1 2 3 1 , 0 1 1 -> 0 4 5 1 4 1 , 0 1 1 -> 0 3 , 0 1 1 -> 0 1 4 5 1 4 , 0 1 5 -> 0 4 5 1 , 0 1 5 -> 0 1 4 5 3 , 0 1 5 -> 0 3 1 5 , 0 1 5 -> 0 1 , 0 1 5 -> 0 1 2 4 1 5 , 0 6 5 -> 0 6 , 0 6 5 -> 0 6 4 5 , 0 6 5 -> 0 4 2 5 6 , 0 6 5 -> 0 6 2 3 5 2 , 0 6 5 -> 0 3 6 4 , 0 1 2 5 -> 0 1 , 0 6 2 5 -> 0 6 , 6 1 1 ->= 6 1 2 3 1 , 6 1 1 ->= 6 4 5 1 4 1 , 6 1 1 ->= 4 2 1 1 6 3 , 6 1 1 ->= 6 1 4 5 1 4 , 1 6 1 ->= 3 6 3 1 1 , 1 6 1 ->= 4 5 1 1 6 , 1 6 1 ->= 6 4 5 3 1 1 , 6 6 1 ->= 6 4 2 1 6 , 6 6 1 ->= 6 6 4 2 1 5 , 6 1 5 ->= 6 4 5 1 , 6 1 5 ->= 6 1 4 5 3 , 6 1 5 ->= 3 6 3 1 5 , 6 1 5 ->= 4 4 5 4 6 1 , 6 1 5 ->= 4 4 6 4 5 1 , 6 1 5 ->= 6 1 2 4 1 5 , 1 6 5 ->= 6 3 3 1 5 , 1 6 5 ->= 6 4 5 1 5 , 1 6 5 ->= 6 3 3 1 5 1 , 1 6 5 ->= 2 3 5 1 4 6 , 1 6 5 ->= 3 4 4 1 5 6 , 1 6 5 ->= 5 4 1 6 4 4 , 6 6 5 ->= 4 5 6 6 , 6 6 5 ->= 6 6 4 5 , 6 6 5 ->= 6 4 2 5 6 , 6 6 5 ->= 4 4 5 4 6 6 , 6 6 5 ->= 6 6 2 3 5 2 , 6 6 5 ->= 4 5 6 3 6 4 , 1 2 6 1 ->= 2 6 3 1 3 1 , 1 5 6 1 ->= 5 6 4 5 1 1 , 1 5 6 1 ->= 1 6 3 4 5 1 , 6 1 2 1 ->= 1 2 6 4 1 1 , 1 6 2 1 ->= 6 2 3 1 1 , 6 6 2 1 ->= 4 2 1 6 6 5 , 1 6 1 5 ->= 2 6 4 1 1 5 , 1 3 6 5 ->= 3 4 5 1 4 6 , 1 3 6 5 ->= 6 3 3 4 1 5 , 1 4 6 5 ->= 2 3 1 4 5 6 , 1 4 6 5 ->= 1 2 6 3 5 4 , 6 5 6 5 ->= 6 5 6 4 5 , 6 1 2 5 ->= 2 3 5 6 1 , 1 6 2 5 ->= 1 5 2 4 6 , 1 6 2 5 ->= 2 4 1 5 6 , 1 6 2 5 ->= 1 6 2 4 5 , 1 6 2 5 ->= 5 2 4 1 2 6 , 6 6 2 5 ->= 4 2 2 5 6 6 , 1 5 3 6 1 ->= 1 3 1 4 5 6 , 1 3 4 6 1 ->= 1 2 3 4 1 6 , 1 6 5 4 6 ->= 1 6 6 3 4 5 , 1 4 6 1 5 ->= 1 1 4 5 4 6 , 1 1 6 5 5 ->= 1 6 4 1 5 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 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 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 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 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 1 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 65-rule system { 0 1 1 -> 0 1 2 3 1 , 0 1 1 -> 0 4 5 1 4 1 , 0 1 1 -> 0 3 , 0 1 1 -> 0 1 4 5 1 4 , 0 1 5 -> 0 4 5 1 , 0 1 5 -> 0 1 4 5 3 , 0 1 5 -> 0 3 1 5 , 0 1 5 -> 0 1 , 0 1 5 -> 0 1 2 4 1 5 , 0 6 5 -> 0 6 , 0 6 5 -> 0 6 4 5 , 0 6 5 -> 0 4 2 5 6 , 0 6 5 -> 0 6 2 3 5 2 , 0 6 5 -> 0 3 6 4 , 0 6 2 5 -> 0 6 , 6 1 1 ->= 6 1 2 3 1 , 6 1 1 ->= 6 4 5 1 4 1 , 6 1 1 ->= 4 2 1 1 6 3 , 6 1 1 ->= 6 1 4 5 1 4 , 1 6 1 ->= 3 6 3 1 1 , 1 6 1 ->= 4 5 1 1 6 , 1 6 1 ->= 6 4 5 3 1 1 , 6 6 1 ->= 6 4 2 1 6 , 6 6 1 ->= 6 6 4 2 1 5 , 6 1 5 ->= 6 4 5 1 , 6 1 5 ->= 6 1 4 5 3 , 6 1 5 ->= 3 6 3 1 5 , 6 1 5 ->= 4 4 5 4 6 1 , 6 1 5 ->= 4 4 6 4 5 1 , 6 1 5 ->= 6 1 2 4 1 5 , 1 6 5 ->= 6 3 3 1 5 , 1 6 5 ->= 6 4 5 1 5 , 1 6 5 ->= 6 3 3 1 5 1 , 1 6 5 ->= 2 3 5 1 4 6 , 1 6 5 ->= 3 4 4 1 5 6 , 1 6 5 ->= 5 4 1 6 4 4 , 6 6 5 ->= 4 5 6 6 , 6 6 5 ->= 6 6 4 5 , 6 6 5 ->= 6 4 2 5 6 , 6 6 5 ->= 4 4 5 4 6 6 , 6 6 5 ->= 6 6 2 3 5 2 , 6 6 5 ->= 4 5 6 3 6 4 , 1 2 6 1 ->= 2 6 3 1 3 1 , 1 5 6 1 ->= 5 6 4 5 1 1 , 1 5 6 1 ->= 1 6 3 4 5 1 , 6 1 2 1 ->= 1 2 6 4 1 1 , 1 6 2 1 ->= 6 2 3 1 1 , 6 6 2 1 ->= 4 2 1 6 6 5 , 1 6 1 5 ->= 2 6 4 1 1 5 , 1 3 6 5 ->= 3 4 5 1 4 6 , 1 3 6 5 ->= 6 3 3 4 1 5 , 1 4 6 5 ->= 2 3 1 4 5 6 , 1 4 6 5 ->= 1 2 6 3 5 4 , 6 5 6 5 ->= 6 5 6 4 5 , 6 1 2 5 ->= 2 3 5 6 1 , 1 6 2 5 ->= 1 5 2 4 6 , 1 6 2 5 ->= 2 4 1 5 6 , 1 6 2 5 ->= 1 6 2 4 5 , 1 6 2 5 ->= 5 2 4 1 2 6 , 6 6 2 5 ->= 4 2 2 5 6 6 , 1 5 3 6 1 ->= 1 3 1 4 5 6 , 1 3 4 6 1 ->= 1 2 3 4 1 6 , 1 6 5 4 6 ->= 1 6 6 3 4 5 , 1 4 6 1 5 ->= 1 1 4 5 4 6 , 1 1 6 5 5 ->= 1 6 4 1 5 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 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 0 0 0 | | 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 1 | \ / 5 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 1 | \ / 6 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 1 | \ / After renaming modulo { 0->0, 1->1, 4->2, 5->3, 3->4, 2->5, 6->6 }, it remains to prove termination of the 62-rule system { 0 1 1 -> 0 1 2 3 1 2 , 0 1 3 -> 0 2 3 1 , 0 1 3 -> 0 1 2 3 4 , 0 1 3 -> 0 4 1 3 , 0 1 3 -> 0 1 , 0 1 3 -> 0 1 5 2 1 3 , 0 6 3 -> 0 6 , 0 6 3 -> 0 6 2 3 , 0 6 3 -> 0 2 5 3 6 , 0 6 3 -> 0 6 5 4 3 5 , 0 6 3 -> 0 4 6 2 , 0 6 5 3 -> 0 6 , 6 1 1 ->= 6 1 5 4 1 , 6 1 1 ->= 6 2 3 1 2 1 , 6 1 1 ->= 2 5 1 1 6 4 , 6 1 1 ->= 6 1 2 3 1 2 , 1 6 1 ->= 4 6 4 1 1 , 1 6 1 ->= 2 3 1 1 6 , 1 6 1 ->= 6 2 3 4 1 1 , 6 6 1 ->= 6 2 5 1 6 , 6 6 1 ->= 6 6 2 5 1 3 , 6 1 3 ->= 6 2 3 1 , 6 1 3 ->= 6 1 2 3 4 , 6 1 3 ->= 4 6 4 1 3 , 6 1 3 ->= 2 2 3 2 6 1 , 6 1 3 ->= 2 2 6 2 3 1 , 6 1 3 ->= 6 1 5 2 1 3 , 1 6 3 ->= 6 4 4 1 3 , 1 6 3 ->= 6 2 3 1 3 , 1 6 3 ->= 6 4 4 1 3 1 , 1 6 3 ->= 5 4 3 1 2 6 , 1 6 3 ->= 4 2 2 1 3 6 , 1 6 3 ->= 3 2 1 6 2 2 , 6 6 3 ->= 2 3 6 6 , 6 6 3 ->= 6 6 2 3 , 6 6 3 ->= 6 2 5 3 6 , 6 6 3 ->= 2 2 3 2 6 6 , 6 6 3 ->= 6 6 5 4 3 5 , 6 6 3 ->= 2 3 6 4 6 2 , 1 5 6 1 ->= 5 6 4 1 4 1 , 1 3 6 1 ->= 3 6 2 3 1 1 , 1 3 6 1 ->= 1 6 4 2 3 1 , 6 1 5 1 ->= 1 5 6 2 1 1 , 1 6 5 1 ->= 6 5 4 1 1 , 6 6 5 1 ->= 2 5 1 6 6 3 , 1 6 1 3 ->= 5 6 2 1 1 3 , 1 4 6 3 ->= 4 2 3 1 2 6 , 1 4 6 3 ->= 6 4 4 2 1 3 , 1 2 6 3 ->= 5 4 1 2 3 6 , 1 2 6 3 ->= 1 5 6 4 3 2 , 6 3 6 3 ->= 6 3 6 2 3 , 6 1 5 3 ->= 5 4 3 6 1 , 1 6 5 3 ->= 1 3 5 2 6 , 1 6 5 3 ->= 5 2 1 3 6 , 1 6 5 3 ->= 1 6 5 2 3 , 1 6 5 3 ->= 3 5 2 1 5 6 , 6 6 5 3 ->= 2 5 5 3 6 6 , 1 3 4 6 1 ->= 1 4 1 2 3 6 , 1 4 2 6 1 ->= 1 5 4 2 1 6 , 1 6 3 2 6 ->= 1 6 6 4 2 3 , 1 2 6 1 3 ->= 1 1 2 3 2 6 , 1 1 6 3 3 ->= 1 6 2 1 3 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 is interpreted by / \ | 1 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 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 1 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 1 0 0 0 0 0 | \ / 2 is interpreted by / \ | 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 1 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 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 | \ / 4 is interpreted by / \ | 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 | \ / 5 is interpreted by / \ | 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 1 | | 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 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 1 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, 3->2, 2->3, 4->4, 5->5, 6->6 }, it remains to prove termination of the 61-rule system { 0 1 2 -> 0 3 2 1 , 0 1 2 -> 0 1 3 2 4 , 0 1 2 -> 0 4 1 2 , 0 1 2 -> 0 1 , 0 1 2 -> 0 1 5 3 1 2 , 0 6 2 -> 0 6 , 0 6 2 -> 0 6 3 2 , 0 6 2 -> 0 3 5 2 6 , 0 6 2 -> 0 6 5 4 2 5 , 0 6 2 -> 0 4 6 3 , 0 6 5 2 -> 0 6 , 6 1 1 ->= 6 1 5 4 1 , 6 1 1 ->= 6 3 2 1 3 1 , 6 1 1 ->= 3 5 1 1 6 4 , 6 1 1 ->= 6 1 3 2 1 3 , 1 6 1 ->= 4 6 4 1 1 , 1 6 1 ->= 3 2 1 1 6 , 1 6 1 ->= 6 3 2 4 1 1 , 6 6 1 ->= 6 3 5 1 6 , 6 6 1 ->= 6 6 3 5 1 2 , 6 1 2 ->= 6 3 2 1 , 6 1 2 ->= 6 1 3 2 4 , 6 1 2 ->= 4 6 4 1 2 , 6 1 2 ->= 3 3 2 3 6 1 , 6 1 2 ->= 3 3 6 3 2 1 , 6 1 2 ->= 6 1 5 3 1 2 , 1 6 2 ->= 6 4 4 1 2 , 1 6 2 ->= 6 3 2 1 2 , 1 6 2 ->= 6 4 4 1 2 1 , 1 6 2 ->= 5 4 2 1 3 6 , 1 6 2 ->= 4 3 3 1 2 6 , 1 6 2 ->= 2 3 1 6 3 3 , 6 6 2 ->= 3 2 6 6 , 6 6 2 ->= 6 6 3 2 , 6 6 2 ->= 6 3 5 2 6 , 6 6 2 ->= 3 3 2 3 6 6 , 6 6 2 ->= 6 6 5 4 2 5 , 6 6 2 ->= 3 2 6 4 6 3 , 1 5 6 1 ->= 5 6 4 1 4 1 , 1 2 6 1 ->= 2 6 3 2 1 1 , 1 2 6 1 ->= 1 6 4 3 2 1 , 6 1 5 1 ->= 1 5 6 3 1 1 , 1 6 5 1 ->= 6 5 4 1 1 , 6 6 5 1 ->= 3 5 1 6 6 2 , 1 6 1 2 ->= 5 6 3 1 1 2 , 1 4 6 2 ->= 4 3 2 1 3 6 , 1 4 6 2 ->= 6 4 4 3 1 2 , 1 3 6 2 ->= 5 4 1 3 2 6 , 1 3 6 2 ->= 1 5 6 4 2 3 , 6 2 6 2 ->= 6 2 6 3 2 , 6 1 5 2 ->= 5 4 2 6 1 , 1 6 5 2 ->= 1 2 5 3 6 , 1 6 5 2 ->= 5 3 1 2 6 , 1 6 5 2 ->= 1 6 5 3 2 , 1 6 5 2 ->= 2 5 3 1 5 6 , 6 6 5 2 ->= 3 5 5 2 6 6 , 1 2 4 6 1 ->= 1 4 1 3 2 6 , 1 4 3 6 1 ->= 1 5 4 3 1 6 , 1 6 2 3 6 ->= 1 6 6 4 3 2 , 1 3 6 1 2 ->= 1 1 3 2 3 6 , 1 1 6 2 2 ->= 1 6 3 1 2 2 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 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 1 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 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 1 | | 0 0 0 0 0 | \ / 6 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 1 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6 }, it remains to prove termination of the 60-rule system { 0 1 2 -> 0 3 2 1 , 0 1 2 -> 0 1 3 2 4 , 0 1 2 -> 0 4 1 2 , 0 1 2 -> 0 1 , 0 1 2 -> 0 1 5 3 1 2 , 0 6 2 -> 0 6 , 0 6 2 -> 0 6 3 2 , 0 6 2 -> 0 3 5 2 6 , 0 6 2 -> 0 6 5 4 2 5 , 0 6 2 -> 0 4 6 3 , 6 1 1 ->= 6 1 5 4 1 , 6 1 1 ->= 6 3 2 1 3 1 , 6 1 1 ->= 3 5 1 1 6 4 , 6 1 1 ->= 6 1 3 2 1 3 , 1 6 1 ->= 4 6 4 1 1 , 1 6 1 ->= 3 2 1 1 6 , 1 6 1 ->= 6 3 2 4 1 1 , 6 6 1 ->= 6 3 5 1 6 , 6 6 1 ->= 6 6 3 5 1 2 , 6 1 2 ->= 6 3 2 1 , 6 1 2 ->= 6 1 3 2 4 , 6 1 2 ->= 4 6 4 1 2 , 6 1 2 ->= 3 3 2 3 6 1 , 6 1 2 ->= 3 3 6 3 2 1 , 6 1 2 ->= 6 1 5 3 1 2 , 1 6 2 ->= 6 4 4 1 2 , 1 6 2 ->= 6 3 2 1 2 , 1 6 2 ->= 6 4 4 1 2 1 , 1 6 2 ->= 5 4 2 1 3 6 , 1 6 2 ->= 4 3 3 1 2 6 , 1 6 2 ->= 2 3 1 6 3 3 , 6 6 2 ->= 3 2 6 6 , 6 6 2 ->= 6 6 3 2 , 6 6 2 ->= 6 3 5 2 6 , 6 6 2 ->= 3 3 2 3 6 6 , 6 6 2 ->= 6 6 5 4 2 5 , 6 6 2 ->= 3 2 6 4 6 3 , 1 5 6 1 ->= 5 6 4 1 4 1 , 1 2 6 1 ->= 2 6 3 2 1 1 , 1 2 6 1 ->= 1 6 4 3 2 1 , 6 1 5 1 ->= 1 5 6 3 1 1 , 1 6 5 1 ->= 6 5 4 1 1 , 6 6 5 1 ->= 3 5 1 6 6 2 , 1 6 1 2 ->= 5 6 3 1 1 2 , 1 4 6 2 ->= 4 3 2 1 3 6 , 1 4 6 2 ->= 6 4 4 3 1 2 , 1 3 6 2 ->= 5 4 1 3 2 6 , 1 3 6 2 ->= 1 5 6 4 2 3 , 6 2 6 2 ->= 6 2 6 3 2 , 6 1 5 2 ->= 5 4 2 6 1 , 1 6 5 2 ->= 1 2 5 3 6 , 1 6 5 2 ->= 5 3 1 2 6 , 1 6 5 2 ->= 1 6 5 3 2 , 1 6 5 2 ->= 2 5 3 1 5 6 , 6 6 5 2 ->= 3 5 5 2 6 6 , 1 2 4 6 1 ->= 1 4 1 3 2 6 , 1 4 3 6 1 ->= 1 5 4 3 1 6 , 1 6 2 3 6 ->= 1 6 6 4 3 2 , 1 3 6 1 2 ->= 1 1 3 2 3 6 , 1 1 6 2 2 ->= 1 6 3 1 2 2 } 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 0 | | 0 1 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 1 | \ / 3 is interpreted by / \ | 1 0 0 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 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 1 | | 0 0 0 1 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6 }, it remains to prove termination of the 55-rule system { 0 1 2 -> 0 3 2 1 , 0 1 2 -> 0 1 3 2 4 , 0 1 2 -> 0 4 1 2 , 0 1 2 -> 0 1 , 0 1 2 -> 0 1 5 3 1 2 , 6 1 1 ->= 6 1 5 4 1 , 6 1 1 ->= 6 3 2 1 3 1 , 6 1 1 ->= 3 5 1 1 6 4 , 6 1 1 ->= 6 1 3 2 1 3 , 1 6 1 ->= 4 6 4 1 1 , 1 6 1 ->= 3 2 1 1 6 , 1 6 1 ->= 6 3 2 4 1 1 , 6 6 1 ->= 6 3 5 1 6 , 6 6 1 ->= 6 6 3 5 1 2 , 6 1 2 ->= 6 3 2 1 , 6 1 2 ->= 6 1 3 2 4 , 6 1 2 ->= 4 6 4 1 2 , 6 1 2 ->= 3 3 2 3 6 1 , 6 1 2 ->= 3 3 6 3 2 1 , 6 1 2 ->= 6 1 5 3 1 2 , 1 6 2 ->= 6 4 4 1 2 , 1 6 2 ->= 6 3 2 1 2 , 1 6 2 ->= 6 4 4 1 2 1 , 1 6 2 ->= 5 4 2 1 3 6 , 1 6 2 ->= 4 3 3 1 2 6 , 1 6 2 ->= 2 3 1 6 3 3 , 6 6 2 ->= 3 2 6 6 , 6 6 2 ->= 6 6 3 2 , 6 6 2 ->= 6 3 5 2 6 , 6 6 2 ->= 3 3 2 3 6 6 , 6 6 2 ->= 6 6 5 4 2 5 , 6 6 2 ->= 3 2 6 4 6 3 , 1 5 6 1 ->= 5 6 4 1 4 1 , 1 2 6 1 ->= 2 6 3 2 1 1 , 1 2 6 1 ->= 1 6 4 3 2 1 , 6 1 5 1 ->= 1 5 6 3 1 1 , 1 6 5 1 ->= 6 5 4 1 1 , 6 6 5 1 ->= 3 5 1 6 6 2 , 1 6 1 2 ->= 5 6 3 1 1 2 , 1 4 6 2 ->= 4 3 2 1 3 6 , 1 4 6 2 ->= 6 4 4 3 1 2 , 1 3 6 2 ->= 5 4 1 3 2 6 , 1 3 6 2 ->= 1 5 6 4 2 3 , 6 2 6 2 ->= 6 2 6 3 2 , 6 1 5 2 ->= 5 4 2 6 1 , 1 6 5 2 ->= 1 2 5 3 6 , 1 6 5 2 ->= 5 3 1 2 6 , 1 6 5 2 ->= 1 6 5 3 2 , 1 6 5 2 ->= 2 5 3 1 5 6 , 6 6 5 2 ->= 3 5 5 2 6 6 , 1 2 4 6 1 ->= 1 4 1 3 2 6 , 1 4 3 6 1 ->= 1 5 4 3 1 6 , 1 6 2 3 6 ->= 1 6 6 4 3 2 , 1 3 6 1 2 ->= 1 1 3 2 3 6 , 1 1 6 2 2 ->= 1 6 3 1 2 2 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 is interpreted by / \ | 1 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 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 1 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 1 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 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 | \ / 3 is interpreted by / \ | 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 1 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 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 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 | | 0 1 0 0 0 0 0 | \ / After renaming modulo { 6->0, 1->1, 5->2, 4->3, 3->4, 2->5 }, it remains to prove termination of the 50-rule system { 0 1 1 ->= 0 1 2 3 1 , 0 1 1 ->= 0 4 5 1 4 1 , 0 1 1 ->= 4 2 1 1 0 3 , 0 1 1 ->= 0 1 4 5 1 4 , 1 0 1 ->= 3 0 3 1 1 , 1 0 1 ->= 4 5 1 1 0 , 1 0 1 ->= 0 4 5 3 1 1 , 0 0 1 ->= 0 4 2 1 0 , 0 0 1 ->= 0 0 4 2 1 5 , 0 1 5 ->= 0 4 5 1 , 0 1 5 ->= 0 1 4 5 3 , 0 1 5 ->= 3 0 3 1 5 , 0 1 5 ->= 4 4 5 4 0 1 , 0 1 5 ->= 4 4 0 4 5 1 , 0 1 5 ->= 0 1 2 4 1 5 , 1 0 5 ->= 0 3 3 1 5 , 1 0 5 ->= 0 4 5 1 5 , 1 0 5 ->= 0 3 3 1 5 1 , 1 0 5 ->= 2 3 5 1 4 0 , 1 0 5 ->= 3 4 4 1 5 0 , 1 0 5 ->= 5 4 1 0 4 4 , 0 0 5 ->= 4 5 0 0 , 0 0 5 ->= 0 0 4 5 , 0 0 5 ->= 0 4 2 5 0 , 0 0 5 ->= 4 4 5 4 0 0 , 0 0 5 ->= 0 0 2 3 5 2 , 0 0 5 ->= 4 5 0 3 0 4 , 1 2 0 1 ->= 2 0 3 1 3 1 , 1 5 0 1 ->= 5 0 4 5 1 1 , 1 5 0 1 ->= 1 0 3 4 5 1 , 0 1 2 1 ->= 1 2 0 4 1 1 , 1 0 2 1 ->= 0 2 3 1 1 , 0 0 2 1 ->= 4 2 1 0 0 5 , 1 0 1 5 ->= 2 0 4 1 1 5 , 1 3 0 5 ->= 3 4 5 1 4 0 , 1 3 0 5 ->= 0 3 3 4 1 5 , 1 4 0 5 ->= 2 3 1 4 5 0 , 1 4 0 5 ->= 1 2 0 3 5 4 , 0 5 0 5 ->= 0 5 0 4 5 , 0 1 2 5 ->= 2 3 5 0 1 , 1 0 2 5 ->= 1 5 2 4 0 , 1 0 2 5 ->= 2 4 1 5 0 , 1 0 2 5 ->= 1 0 2 4 5 , 1 0 2 5 ->= 5 2 4 1 2 0 , 0 0 2 5 ->= 4 2 2 5 0 0 , 1 5 3 0 1 ->= 1 3 1 4 5 0 , 1 3 4 0 1 ->= 1 2 3 4 1 0 , 1 0 5 4 0 ->= 1 0 0 3 4 5 , 1 4 0 1 5 ->= 1 1 4 5 4 0 , 1 1 0 5 5 ->= 1 0 4 1 5 5 } The system is trivially terminating.