0.00/0.40 YES 0.00/0.41 0.00/0.41 0.00/0.41 The system was reversed. 0.00/0.41 0.00/0.41 Remains to prove termination of the 1-rule system 0.00/0.41 { b b a a -> a a a b b b } 0.00/0.41 0.00/0.41 0.00/0.41 The dependency pairs transformation was applied. 0.00/0.41 0.00/0.41 Remains to prove termination of the 4-rule system 0.00/0.41 { (b,true) (b,false) (a,false) (a,false) -> (b,true) (b,false) (b,false) , 0.00/0.41 (b,true) (b,false) (a,false) (a,false) -> (b,true) (b,false) , 0.00/0.41 (b,true) (b,false) (a,false) (a,false) -> (b,true) , 0.00/0.41 (b,false) (b,false) (a,false) (a,false) ->= (a,false) (a,false) (a,false) (b,false) (b,false) (b,false) } 0.00/0.41 0.00/0.41 0.00/0.41 0.00/0.41 0.00/0.41 The system was filtered by the following matrix interpretation 0.00/0.41 of type E_J with J = {1,...,2} and dimension 5: 0.00/0.41 0.00/0.41 (b,true) is interpreted by 0.00/0.41 / \ 0.00/0.41 | 1 0 1 0 0 | 0.00/0.41 | 0 1 0 0 0 | 0.00/0.41 | 0 0 0 0 0 | 0.00/0.41 | 0 0 0 0 0 | 0.00/0.41 | 0 0 0 0 0 | 0.00/0.41 \ / 0.00/0.41 (b,false) is interpreted by 0.00/0.41 / \ 0.00/0.41 | 1 0 0 0 0 | 0.00/0.41 | 0 1 0 0 0 | 0.00/0.41 | 0 0 0 1 0 | 0.00/0.41 | 0 0 1 0 0 | 0.00/0.41 | 0 0 2 0 0 | 0.00/0.41 \ / 0.00/0.41 (a,false) is interpreted by 0.00/0.41 / \ 0.00/0.41 | 1 0 0 0 0 | 0.00/0.41 | 0 1 0 0 0 | 0.00/0.41 | 0 0 0 0 0 | 0.00/0.41 | 0 0 0 0 1 | 0.00/0.41 | 0 1 2 1 0 | 0.00/0.41 \ / 0.00/0.41 0.00/0.41 Remains to prove termination of the 1-rule system 0.00/0.41 { (b,false) (b,false) (a,false) (a,false) ->= (a,false) (a,false) (a,false) (b,false) (b,false) (b,false) } 0.00/0.41 0.00/0.41 0.00/0.41 The system is trivially terminating. 0.00/0.44 EOF