4.55/1.36 YES 4.65/1.37 4.65/1.37 4.65/1.37 The dependency pairs transformation was applied. 4.65/1.37 4.65/1.37 Remains to prove termination of the 6-rule system 4.65/1.37 { (a,true) (a,false) (b,false) (b,false) -> (a,true) (a,false) (a,false) (a,false) (a,false) , 4.65/1.37 (a,true) (a,false) (b,false) (b,false) -> (a,true) (a,false) (a,false) (a,false) , 4.65/1.37 (a,true) (a,false) (b,false) (b,false) -> (a,true) (a,false) (a,false) , 4.65/1.37 (a,true) (a,false) (b,false) (b,false) -> (a,true) (a,false) , 4.65/1.37 (a,true) (a,false) (b,false) (b,false) -> (a,true) , 4.65/1.37 (a,false) (a,false) (b,false) (b,false) ->= (b,false) (b,false) (b,false) (a,false) (a,false) (a,false) (a,false) (a,false) } 4.65/1.37 4.65/1.37 4.65/1.37 4.65/1.37 4.65/1.37 The system was filtered by the following matrix interpretation 4.65/1.37 of type E_J with J = {1,...,2} and dimension 5: 4.65/1.37 4.65/1.37 (a,true) is interpreted by 4.65/1.37 / \ 4.65/1.37 | 1 0 1 0 0 | 4.65/1.37 | 0 1 0 0 0 | 4.65/1.37 | 0 0 0 0 0 | 4.65/1.37 | 0 0 0 0 0 | 4.65/1.37 | 0 0 0 0 0 | 4.65/1.37 \ / 4.65/1.37 (a,false) is interpreted by 4.65/1.37 / \ 4.65/1.37 | 1 0 0 0 0 | 4.65/1.37 | 0 1 0 0 0 | 4.65/1.37 | 0 0 0 1 0 | 4.65/1.37 | 0 0 1 0 0 | 4.65/1.37 | 0 0 2 0 0 | 4.65/1.37 \ / 4.65/1.37 (b,false) is interpreted by 4.65/1.37 / \ 4.65/1.37 | 1 0 0 0 0 | 4.65/1.37 | 0 1 0 0 0 | 4.65/1.37 | 0 0 0 0 0 | 4.65/1.37 | 0 0 0 0 1 | 4.65/1.37 | 0 1 2 1 0 | 4.65/1.37 \ / 4.65/1.37 4.65/1.37 Remains to prove termination of the 1-rule system 4.65/1.37 { (a,false) (a,false) (b,false) (b,false) ->= (b,false) (b,false) (b,false) (a,false) (a,false) (a,false) (a,false) (a,false) } 4.65/1.37 4.65/1.37 4.65/1.37 The system is trivially terminating. 4.65/1.41 EOF