19.09/5.17 YES 19.09/5.19 19.09/5.19 19.09/5.19 The system was reversed. 19.09/5.19 19.09/5.19 Remains to prove termination of the 1-rule system 19.09/5.19 { b a a b b a a b a a -> a a b b a a b a a b b a a } 19.09/5.19 19.09/5.19 19.09/5.19 The dependency pairs transformation was applied. 19.09/5.19 19.09/5.19 Remains to prove termination of the 6-rule system 19.09/5.19 { (b,true) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) (b,false) (a,false) (a,false) -> (b,true) (b,false) (a,false) (a,false) (b,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) , 19.09/5.19 (b,true) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) (b,false) (a,false) (a,false) -> (b,true) (a,false) (a,false) (b,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) , 19.09/5.19 (b,true) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) (b,false) (a,false) (a,false) -> (b,true) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) , 19.09/5.19 (b,true) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) (b,false) (a,false) (a,false) -> (b,true) (b,false) (a,false) (a,false) , 19.09/5.19 (b,true) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) (b,false) (a,false) (a,false) -> (b,true) (a,false) (a,false) , 19.09/5.19 (b,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) (b,false) (a,false) (a,false) ->= (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) (b,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) } 19.09/5.19 19.09/5.19 19.09/5.19 19.09/5.19 19.09/5.19 The system was filtered by the following matrix interpretation 19.09/5.19 of type E_J with J = {1,...,2} and dimension 11: 19.09/5.19 19.09/5.19 (b,true) is interpreted by 19.09/5.19 / \ 19.09/5.19 | 1 0 1 0 0 0 0 0 0 0 0 | 19.09/5.19 | 0 1 0 0 0 0 0 0 0 0 0 | 19.09/5.19 | 0 0 0 0 0 0 0 0 0 0 0 | 19.09/5.19 | 0 0 0 0 0 0 0 0 0 0 0 | 19.09/5.19 | 0 0 0 0 0 0 0 0 0 0 0 | 19.09/5.19 | 0 0 0 0 0 0 0 0 0 0 0 | 19.09/5.19 | 0 0 0 0 0 0 0 0 0 0 0 | 19.09/5.19 | 0 0 0 0 0 0 0 0 0 0 0 | 19.09/5.19 | 0 0 0 0 0 0 0 0 0 0 0 | 19.09/5.19 | 0 0 0 0 0 0 0 0 0 0 0 | 19.09/5.19 | 0 0 0 0 0 0 0 0 0 0 0 | 19.09/5.19 \ / 19.09/5.19 (a,false) is interpreted by 19.09/5.19 / \ 19.09/5.19 | 1 0 0 0 0 0 0 0 0 0 0 | 19.09/5.19 | 0 1 0 0 0 0 0 0 0 0 0 | 19.09/5.19 | 0 0 0 1 0 0 0 0 0 0 0 | 19.09/5.19 | 0 0 0 0 2 0 0 0 0 0 0 | 19.09/5.19 | 0 0 0 0 0 0 0 0 0 0 0 | 19.09/5.19 | 0 0 0 0 0 0 0 0 0 0 0 | 19.09/5.19 | 0 0 0 0 0 0 0 1 0 0 0 | 19.09/5.19 | 0 0 0 0 0 0 0 0 1 0 0 | 19.09/5.19 | 0 0 0 0 0 0 0 0 0 0 0 | 19.09/5.19 | 0 0 0 1 0 0 0 0 0 0 1 | 19.09/5.19 | 0 1 0 0 0 0 0 0 0 0 0 | 19.09/5.19 \ / 19.09/5.19 (b,false) is interpreted by 19.09/5.19 / \ 19.09/5.19 | 1 0 0 0 0 0 0 0 0 0 0 | 19.09/5.19 | 0 1 0 0 0 0 0 0 0 0 0 | 19.09/5.19 | 0 0 1 0 0 0 0 0 0 1 0 | 19.09/5.19 | 0 0 0 0 0 0 0 0 0 0 0 | 19.09/5.19 | 0 0 0 0 0 1 0 0 0 0 0 | 19.09/5.19 | 0 0 0 0 0 0 1 0 0 0 0 | 19.09/5.19 | 0 0 0 0 0 0 0 0 0 0 0 | 19.09/5.19 | 0 0 0 0 0 0 0 0 0 0 0 | 19.09/5.19 | 0 0 0 0 0 0 1 0 0 1 0 | 19.09/5.19 | 0 0 2 0 0 0 0 0 0 0 0 | 19.09/5.19 | 0 0 0 0 0 0 0 0 0 0 1 | 19.09/5.19 \ / 19.09/5.19 19.09/5.19 Remains to prove termination of the 1-rule system 19.09/5.19 { (b,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) (b,false) (a,false) (a,false) ->= (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) (b,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) } 19.09/5.19 19.09/5.19 19.09/5.19 The system is trivially terminating. 19.31/5.23 EOF