0.00/0.50 YES 1.05/0.52 1.05/0.52 1.05/0.52 The system was reversed. 1.05/0.52 1.05/0.52 Remains to prove termination of the 1-rule system 1.05/0.52 { a a b a b -> a b a b a b b a a } 1.05/0.52 1.05/0.52 1.05/0.52 The dependency pairs transformation was applied. 1.05/0.52 1.05/0.52 Remains to prove termination of the 6-rule system 1.05/0.52 { (a,true) (a,false) (b,false) (a,false) (b,false) -> (a,true) (b,false) (a,false) (b,false) (a,false) (b,false) (b,false) (a,false) (a,false) , 1.05/0.52 (a,true) (a,false) (b,false) (a,false) (b,false) -> (a,true) (b,false) (a,false) (b,false) (b,false) (a,false) (a,false) , 1.05/0.52 (a,true) (a,false) (b,false) (a,false) (b,false) -> (a,true) (b,false) (b,false) (a,false) (a,false) , 1.05/0.52 (a,true) (a,false) (b,false) (a,false) (b,false) -> (a,true) (a,false) , 1.05/0.52 (a,true) (a,false) (b,false) (a,false) (b,false) -> (a,true) , 1.05/0.52 (a,false) (a,false) (b,false) (a,false) (b,false) ->= (a,false) (b,false) (a,false) (b,false) (a,false) (b,false) (b,false) (a,false) (a,false) } 1.05/0.52 1.05/0.52 1.05/0.52 1.05/0.52 1.05/0.52 The system was filtered by the following matrix interpretation 1.05/0.52 of type E_J with J = {1,...,2} and dimension 6: 1.05/0.52 1.05/0.52 (a,true) is interpreted by 1.05/0.52 / \ 1.05/0.52 | 1 0 1 0 0 0 | 1.05/0.52 | 0 1 0 0 0 0 | 1.05/0.52 | 0 0 0 0 0 0 | 1.05/0.52 | 0 0 0 0 0 0 | 1.05/0.52 | 0 0 0 0 0 0 | 1.05/0.52 | 0 0 0 0 0 0 | 1.05/0.52 \ / 1.05/0.52 (a,false) is interpreted by 1.05/0.52 / \ 1.05/0.52 | 1 0 0 0 0 0 | 1.05/0.52 | 0 1 0 0 0 0 | 1.05/0.52 | 0 0 1 1 0 0 | 1.05/0.52 | 0 0 0 0 0 0 | 1.05/0.52 | 0 0 2 0 0 1 | 1.05/0.52 | 0 0 0 0 0 0 | 1.05/0.52 \ / 1.05/0.52 (b,false) is interpreted by 1.05/0.52 / \ 1.05/0.52 | 1 0 0 0 0 0 | 1.05/0.52 | 0 1 0 0 0 0 | 1.05/0.52 | 0 0 0 0 0 0 | 1.05/0.52 | 0 0 0 0 1 0 | 1.05/0.52 | 0 0 0 0 0 0 | 1.05/0.52 | 0 1 1 1 0 0 | 1.05/0.52 \ / 1.05/0.52 1.05/0.52 Remains to prove termination of the 1-rule system 1.05/0.52 { (a,false) (a,false) (b,false) (a,false) (b,false) ->= (a,false) (b,false) (a,false) (b,false) (a,false) (b,false) (b,false) (a,false) (a,false) } 1.05/0.52 1.05/0.52 1.05/0.52 The system is trivially terminating. 1.05/0.55 EOF