4.65/1.45 YES 4.97/1.50 4.97/1.50 4.97/1.50 The dependency pairs transformation was applied. 4.97/1.50 4.97/1.50 Remains to prove termination of the 5-rule system 4.97/1.50 { (0,true) (1,false) (2,false) (3,false) (4,false) (5,false) (1,false) -> (0,true) (1,false) (2,false) (3,false) (4,false) (5,false) (0,false) (1,false) (2,false) (3,false) (4,false) (5,false) , 4.97/1.50 (0,true) (1,false) (2,false) (3,false) (4,false) (5,false) (1,false) -> (0,true) (1,false) (2,false) (3,false) (4,false) (5,false) , 4.97/1.50 (0,true) (1,false) (2,false) (3,false) (4,false) (5,false) (1,false) -> (0,true) (1,false) (2,false) (3,false) (4,false) (5,false) (0,false) (1,false) (2,false) (3,false) (4,false) (5,false) (0,false) (1,false) (2,false) (3,false) (4,false) (5,false) , 4.97/1.50 (0,false) (1,false) (2,false) (3,false) (4,false) (5,false) (1,false) ->= (1,false) (2,false) (3,false) (4,false) (5,false) (1,false) (1,false) (0,false) (1,false) (2,false) (3,false) (4,false) (5,false) (0,false) (1,false) (2,false) (3,false) (4,false) (5,false) , 4.97/1.50 (0,false) (1,false) (2,false) (3,false) (4,false) (5,false) (1,false) ->= (1,false) (2,false) (3,false) (4,false) (5,false) (1,false) (1,false) (0,false) (1,false) (2,false) (3,false) (4,false) (5,false) (0,false) (1,false) (2,false) (3,false) (4,false) (5,false) (0,false) (1,false) (2,false) (3,false) (4,false) (5,false) } 4.97/1.50 4.97/1.50 4.97/1.50 4.97/1.50 4.97/1.50 The system was filtered by the following matrix interpretation 4.97/1.50 of type E_J with J = {1,...,2} and dimension 8: 4.97/1.50 4.97/1.50 (0,true) is interpreted by 4.97/1.50 / \ 4.97/1.50 | 1 0 1 0 0 0 0 0 | 4.97/1.50 | 0 1 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 | 4.97/1.50 \ / 4.97/1.50 (1,false) is interpreted by 4.97/1.50 / \ 4.97/1.50 | 1 0 0 0 0 0 0 0 | 4.97/1.50 | 0 1 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 1 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 1 0 0 0 0 0 1 | 4.97/1.50 \ / 4.97/1.50 (2,false) is interpreted by 4.97/1.50 / \ 4.97/1.50 | 1 0 0 0 0 0 0 0 | 4.97/1.50 | 0 1 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 1 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 | 4.97/1.50 \ / 4.97/1.50 (3,false) is interpreted by 4.97/1.50 / \ 4.97/1.50 | 1 0 0 0 0 0 0 0 | 4.97/1.50 | 0 1 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 1 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 | 4.97/1.50 \ / 4.97/1.50 (4,false) is interpreted by 4.97/1.50 / \ 4.97/1.50 | 1 0 0 0 0 0 0 0 | 4.97/1.50 | 0 1 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 1 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 | 4.97/1.50 \ / 4.97/1.50 (5,false) is interpreted by 4.97/1.50 / \ 4.97/1.50 | 1 0 0 0 0 0 0 0 | 4.97/1.50 | 0 1 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 1 | 4.97/1.50 | 0 0 0 0 0 0 0 0 | 4.97/1.50 \ / 4.97/1.50 (0,false) is interpreted by 4.97/1.50 / \ 4.97/1.50 | 1 0 0 0 0 0 0 0 | 4.97/1.50 | 0 1 0 0 0 0 0 0 | 4.97/1.50 | 0 1 1 0 0 0 0 1 | 4.97/1.50 | 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 1 0 0 0 0 0 0 | 4.97/1.50 \ / 4.97/1.50 4.97/1.50 Remains to prove termination of the 4-rule system 4.97/1.50 { (0,true) (1,false) (2,false) (3,false) (4,false) (5,false) (1,false) -> (0,true) (1,false) (2,false) (3,false) (4,false) (5,false) (0,false) (1,false) (2,false) (3,false) (4,false) (5,false) , 4.97/1.50 (0,true) (1,false) (2,false) (3,false) (4,false) (5,false) (1,false) -> (0,true) (1,false) (2,false) (3,false) (4,false) (5,false) (0,false) (1,false) (2,false) (3,false) (4,false) (5,false) (0,false) (1,false) (2,false) (3,false) (4,false) (5,false) , 4.97/1.50 (0,false) (1,false) (2,false) (3,false) (4,false) (5,false) (1,false) ->= (1,false) (2,false) (3,false) (4,false) (5,false) (1,false) (1,false) (0,false) (1,false) (2,false) (3,false) (4,false) (5,false) (0,false) (1,false) (2,false) (3,false) (4,false) (5,false) , 4.97/1.50 (0,false) (1,false) (2,false) (3,false) (4,false) (5,false) (1,false) ->= (1,false) (2,false) (3,false) (4,false) (5,false) (1,false) (1,false) (0,false) (1,false) (2,false) (3,false) (4,false) (5,false) (0,false) (1,false) (2,false) (3,false) (4,false) (5,false) (0,false) (1,false) (2,false) (3,false) (4,false) (5,false) } 4.97/1.50 4.97/1.50 4.97/1.50 The system was filtered by the following matrix interpretation 4.97/1.50 of type E_J with J = {1,...,2} and dimension 14: 4.97/1.50 4.97/1.50 (0,true) is interpreted by 4.97/1.50 / \ 4.97/1.50 | 1 0 1 0 0 0 0 0 1 0 0 0 0 0 | 4.97/1.50 | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 \ / 4.97/1.50 (1,false) is interpreted by 4.97/1.50 / \ 4.97/1.50 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | 4.97/1.50 \ / 4.97/1.50 (2,false) is interpreted by 4.97/1.50 / \ 4.97/1.50 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 \ / 4.97/1.50 (3,false) is interpreted by 4.97/1.50 / \ 4.97/1.50 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 \ / 4.97/1.50 (4,false) is interpreted by 4.97/1.50 / \ 4.97/1.50 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 \ / 4.97/1.50 (5,false) is interpreted by 4.97/1.50 / \ 4.97/1.50 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 \ / 4.97/1.50 (0,false) is interpreted by 4.97/1.50 / \ 4.97/1.50 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4.97/1.50 \ / 4.97/1.50 4.97/1.50 Remains to prove termination of the 2-rule system 4.97/1.50 { (0,false) (1,false) (2,false) (3,false) (4,false) (5,false) (1,false) ->= (1,false) (2,false) (3,false) (4,false) (5,false) (1,false) (1,false) (0,false) (1,false) (2,false) (3,false) (4,false) (5,false) (0,false) (1,false) (2,false) (3,false) (4,false) (5,false) , 4.97/1.50 (0,false) (1,false) (2,false) (3,false) (4,false) (5,false) (1,false) ->= (1,false) (2,false) (3,false) (4,false) (5,false) (1,false) (1,false) (0,false) (1,false) (2,false) (3,false) (4,false) (5,false) (0,false) (1,false) (2,false) (3,false) (4,false) (5,false) (0,false) (1,false) (2,false) (3,false) (4,false) (5,false) } 4.97/1.50 4.97/1.50 4.97/1.50 The system is trivially terminating. 5.07/1.53 EOF