2.17/0.77 YES 2.17/0.78 2.17/0.78 2.17/0.78 The system was reversed. 2.17/0.78 2.17/0.78 Remains to prove termination of the 1-rule system 2.17/0.78 { a a a a b a -> b a a b a a b a a a a a } 2.17/0.78 2.17/0.78 2.17/0.78 The dependency pairs transformation was applied. 2.17/0.78 2.17/0.78 Remains to prove termination of the 10-rule system 2.17/0.78 { (a,true) (a,false) (a,false) (a,false) (b,false) (a,false) -> (a,true) (a,false) (b,false) (a,false) (a,false) (b,false) (a,false) (a,false) (a,false) (a,false) (a,false) , 2.17/0.78 (a,true) (a,false) (a,false) (a,false) (b,false) (a,false) -> (a,true) (b,false) (a,false) (a,false) (b,false) (a,false) (a,false) (a,false) (a,false) (a,false) , 2.17/0.78 (a,true) (a,false) (a,false) (a,false) (b,false) (a,false) -> (a,true) (a,false) (b,false) (a,false) (a,false) (a,false) (a,false) (a,false) , 2.17/0.78 (a,true) (a,false) (a,false) (a,false) (b,false) (a,false) -> (a,true) (b,false) (a,false) (a,false) (a,false) (a,false) (a,false) , 2.17/0.78 (a,true) (a,false) (a,false) (a,false) (b,false) (a,false) -> (a,true) (a,false) (a,false) (a,false) (a,false) , 2.17/0.78 (a,true) (a,false) (a,false) (a,false) (b,false) (a,false) -> (a,true) (a,false) (a,false) (a,false) , 2.17/0.78 (a,true) (a,false) (a,false) (a,false) (b,false) (a,false) -> (a,true) (a,false) (a,false) , 2.17/0.78 (a,true) (a,false) (a,false) (a,false) (b,false) (a,false) -> (a,true) (a,false) , 2.17/0.78 (a,true) (a,false) (a,false) (a,false) (b,false) (a,false) -> (a,true) , 2.17/0.78 (a,false) (a,false) (a,false) (a,false) (b,false) (a,false) ->= (b,false) (a,false) (a,false) (b,false) (a,false) (a,false) (b,false) (a,false) (a,false) (a,false) (a,false) (a,false) } 2.17/0.78 2.17/0.78 2.17/0.78 2.17/0.78 2.17/0.78 The system was filtered by the following matrix interpretation 2.17/0.78 of type E_J with J = {1,...,2} and dimension 7: 2.17/0.78 2.17/0.78 (a,true) is interpreted by 2.17/0.78 / \ 2.17/0.78 | 1 0 1 0 0 0 0 | 2.17/0.78 | 0 1 0 0 0 0 0 | 2.17/0.78 | 0 0 0 0 0 0 0 | 2.17/0.78 | 0 0 0 0 0 0 0 | 2.17/0.78 | 0 0 0 0 0 0 0 | 2.17/0.78 | 0 0 0 0 0 0 0 | 2.17/0.78 | 0 0 0 0 0 0 0 | 2.17/0.78 \ / 2.17/0.78 (a,false) is interpreted by 2.17/0.78 / \ 2.17/0.78 | 1 0 0 0 0 0 0 | 2.17/0.78 | 0 1 0 0 0 0 0 | 2.17/0.78 | 0 0 0 3 0 0 0 | 2.17/0.78 | 0 0 0 0 1 0 0 | 2.17/0.78 | 0 0 0 0 0 1 0 | 2.17/0.78 | 0 0 1 0 0 0 0 | 2.17/0.78 | 0 1 1 0 0 0 0 | 2.17/0.78 \ / 2.17/0.78 (b,false) is interpreted by 2.17/0.78 / \ 2.17/0.78 | 1 0 0 0 0 0 0 | 2.17/0.78 | 0 1 0 0 0 0 0 | 2.17/0.78 | 0 0 0 0 0 0 0 | 2.17/0.78 | 0 0 0 0 0 0 0 | 2.17/0.78 | 0 0 0 0 0 0 0 | 2.17/0.78 | 0 0 1 1 1 0 1 | 2.17/0.78 | 0 0 0 0 0 0 0 | 2.17/0.78 \ / 2.17/0.78 2.17/0.78 Remains to prove termination of the 1-rule system 2.17/0.78 { (a,false) (a,false) (a,false) (a,false) (b,false) (a,false) ->= (b,false) (a,false) (a,false) (b,false) (a,false) (a,false) (b,false) (a,false) (a,false) (a,false) (a,false) (a,false) } 2.17/0.78 2.17/0.78 2.17/0.78 The system is trivially terminating. 2.17/0.81 EOF