4.08/1.26 YES 4.08/1.28 4.08/1.28 4.08/1.28 The system was reversed. 4.08/1.28 4.08/1.28 Remains to prove termination of the 1-rule system 4.08/1.28 { b a a b a b a b a -> b a b a b a b a a b a a } 4.08/1.28 4.08/1.28 4.08/1.28 The dependency pairs transformation was applied. 4.08/1.28 4.08/1.28 Remains to prove termination of the 6-rule system 4.08/1.28 { (b,true) (a,false) (a,false) (b,false) (a,false) (b,false) (a,false) (b,false) (a,false) -> (b,true) (a,false) (b,false) (a,false) (b,false) (a,false) (b,false) (a,false) (a,false) (b,false) (a,false) (a,false) , 4.08/1.28 (b,true) (a,false) (a,false) (b,false) (a,false) (b,false) (a,false) (b,false) (a,false) -> (b,true) (a,false) (b,false) (a,false) (b,false) (a,false) (a,false) (b,false) (a,false) (a,false) , 4.08/1.28 (b,true) (a,false) (a,false) (b,false) (a,false) (b,false) (a,false) (b,false) (a,false) -> (b,true) (a,false) (b,false) (a,false) (a,false) (b,false) (a,false) (a,false) , 4.08/1.28 (b,true) (a,false) (a,false) (b,false) (a,false) (b,false) (a,false) (b,false) (a,false) -> (b,true) (a,false) (a,false) (b,false) (a,false) (a,false) , 4.08/1.28 (b,true) (a,false) (a,false) (b,false) (a,false) (b,false) (a,false) (b,false) (a,false) -> (b,true) (a,false) (a,false) , 4.08/1.28 (b,false) (a,false) (a,false) (b,false) (a,false) (b,false) (a,false) (b,false) (a,false) ->= (b,false) (a,false) (b,false) (a,false) (b,false) (a,false) (b,false) (a,false) (a,false) (b,false) (a,false) (a,false) } 4.08/1.28 4.08/1.28 4.08/1.28 4.08/1.28 4.08/1.28 The system was filtered by the following matrix interpretation 4.08/1.28 of type E_J with J = {1,...,2} and dimension 10: 4.08/1.28 4.08/1.28 (b,true) is interpreted by 4.08/1.28 / \ 4.08/1.28 | 1 0 1 0 0 0 0 0 0 0 | 4.08/1.28 | 0 1 0 0 0 0 0 0 0 0 | 4.08/1.28 | 0 0 0 0 0 0 0 0 0 0 | 4.08/1.28 | 0 0 0 0 0 0 0 0 0 0 | 4.08/1.28 | 0 0 0 0 0 0 0 0 0 0 | 4.08/1.28 | 0 0 0 0 0 0 0 0 0 0 | 4.08/1.28 | 0 0 0 0 0 0 0 0 0 0 | 4.08/1.28 | 0 0 0 0 0 0 0 0 0 0 | 4.08/1.28 | 0 0 0 0 0 0 0 0 0 0 | 4.08/1.28 | 0 0 0 0 0 0 0 0 0 0 | 4.08/1.28 \ / 4.08/1.28 (a,false) is interpreted by 4.08/1.28 / \ 4.08/1.28 | 1 0 0 0 0 0 0 0 0 0 | 4.08/1.28 | 0 1 0 0 0 0 0 0 0 0 | 4.08/1.28 | 0 0 0 1 0 0 0 0 0 0 | 4.08/1.28 | 0 0 0 0 1 0 0 0 0 0 | 4.08/1.28 | 0 0 0 0 1 0 0 0 0 0 | 4.08/1.28 | 0 0 0 0 0 0 1 0 0 0 | 4.08/1.28 | 0 0 0 0 1 0 0 0 0 0 | 4.08/1.28 | 0 0 0 0 0 0 0 0 1 0 | 4.08/1.28 | 0 0 0 0 0 0 0 0 0 0 | 4.08/1.28 | 0 1 0 0 0 0 0 0 0 0 | 4.08/1.28 \ / 4.08/1.28 (b,false) is interpreted by 4.08/1.28 / \ 4.08/1.28 | 1 0 0 0 0 0 0 0 0 0 | 4.08/1.28 | 0 1 0 0 0 0 0 0 0 0 | 4.08/1.28 | 0 0 0 0 0 0 0 0 0 0 | 4.08/1.28 | 0 0 0 1 0 0 0 0 0 0 | 4.08/1.28 | 0 0 0 0 0 1 0 0 0 0 | 4.08/1.28 | 0 0 0 0 0 0 0 0 0 0 | 4.08/1.28 | 0 0 1 0 0 0 0 1 0 0 | 4.08/1.28 | 0 0 0 0 0 0 0 0 0 0 | 4.08/1.28 | 0 0 0 0 0 0 0 0 0 1 | 4.08/1.28 | 0 0 0 0 0 0 0 0 0 0 | 4.08/1.28 \ / 4.08/1.28 4.08/1.28 Remains to prove termination of the 1-rule system 4.08/1.28 { (b,false) (a,false) (a,false) (b,false) (a,false) (b,false) (a,false) (b,false) (a,false) ->= (b,false) (a,false) (b,false) (a,false) (b,false) (a,false) (b,false) (a,false) (a,false) (b,false) (a,false) (a,false) } 4.08/1.28 4.08/1.28 4.08/1.28 The system is trivially terminating. 4.22/1.33 EOF