3.60/1.15 YES 3.60/1.18 3.60/1.18 3.60/1.18 The system was reversed. 3.60/1.18 3.60/1.18 Remains to prove termination of the 1-rule system 3.60/1.18 { a a a a b c b a a -> b c b a a b c b a a a a a a } 3.60/1.18 3.60/1.18 3.60/1.18 The dependency pairs transformation was applied. 3.60/1.18 3.60/1.18 Remains to prove termination of the 9-rule system 3.60/1.18 { (a,true) (a,false) (a,false) (a,false) (b,false) (c,false) (b,false) (a,false) (a,false) -> (a,true) (a,false) (b,false) (c,false) (b,false) (a,false) (a,false) (a,false) (a,false) (a,false) (a,false) , 3.60/1.18 (a,true) (a,false) (a,false) (a,false) (b,false) (c,false) (b,false) (a,false) (a,false) -> (a,true) (b,false) (c,false) (b,false) (a,false) (a,false) (a,false) (a,false) (a,false) (a,false) , 3.60/1.18 (a,true) (a,false) (a,false) (a,false) (b,false) (c,false) (b,false) (a,false) (a,false) -> (a,true) (a,false) (a,false) (a,false) (a,false) (a,false) , 3.60/1.18 (a,true) (a,false) (a,false) (a,false) (b,false) (c,false) (b,false) (a,false) (a,false) -> (a,true) (a,false) (a,false) (a,false) (a,false) , 3.60/1.18 (a,true) (a,false) (a,false) (a,false) (b,false) (c,false) (b,false) (a,false) (a,false) -> (a,true) (a,false) (a,false) (a,false) , 3.60/1.18 (a,true) (a,false) (a,false) (a,false) (b,false) (c,false) (b,false) (a,false) (a,false) -> (a,true) (a,false) (a,false) , 3.60/1.18 (a,true) (a,false) (a,false) (a,false) (b,false) (c,false) (b,false) (a,false) (a,false) -> (a,true) (a,false) , 3.60/1.18 (a,true) (a,false) (a,false) (a,false) (b,false) (c,false) (b,false) (a,false) (a,false) -> (a,true) , 3.60/1.18 (a,false) (a,false) (a,false) (a,false) (b,false) (c,false) (b,false) (a,false) (a,false) ->= (b,false) (c,false) (b,false) (a,false) (a,false) (b,false) (c,false) (b,false) (a,false) (a,false) (a,false) (a,false) (a,false) (a,false) } 3.60/1.18 3.60/1.18 3.60/1.18 3.60/1.18 3.60/1.18 The system was filtered by the following matrix interpretation 3.60/1.18 of type E_J with J = {1,...,2} and dimension 10: 3.60/1.18 3.60/1.18 (a,true) is interpreted by 3.60/1.18 / \ 3.60/1.18 | 1 0 1 0 0 0 0 0 0 0 | 3.60/1.18 | 0 1 0 0 0 0 0 0 0 0 | 3.60/1.18 | 0 0 0 0 0 0 0 0 0 0 | 3.60/1.18 | 0 0 0 0 0 0 0 0 0 0 | 3.60/1.18 | 0 0 0 0 0 0 0 0 0 0 | 3.60/1.18 | 0 0 0 0 0 0 0 0 0 0 | 3.60/1.18 | 0 0 0 0 0 0 0 0 0 0 | 3.60/1.18 | 0 0 0 0 0 0 0 0 0 0 | 3.60/1.18 | 0 0 0 0 0 0 0 0 0 0 | 3.60/1.18 | 0 0 0 0 0 0 0 0 0 0 | 3.60/1.18 \ / 3.60/1.18 (a,false) is interpreted by 3.60/1.18 / \ 3.60/1.18 | 1 0 0 0 0 0 0 0 0 0 | 3.60/1.18 | 0 1 0 0 0 0 0 0 0 0 | 3.60/1.18 | 0 0 0 2 0 0 0 0 0 0 | 3.60/1.18 | 0 0 0 0 1 0 0 0 0 0 | 3.60/1.18 | 0 0 0 0 0 1 0 0 0 0 | 3.60/1.18 | 0 0 1 0 0 0 0 0 0 0 | 3.60/1.18 | 0 0 0 0 0 0 0 0 0 0 | 3.60/1.18 | 0 0 0 0 0 0 0 0 0 0 | 3.60/1.18 | 0 0 1 0 0 0 0 0 0 1 | 3.60/1.18 | 0 1 1 0 1 0 0 0 0 0 | 3.60/1.18 \ / 3.60/1.18 (b,false) is interpreted by 3.60/1.18 / \ 3.60/1.18 | 1 0 0 0 0 0 0 0 0 0 | 3.60/1.18 | 0 1 0 0 0 0 0 0 0 0 | 3.60/1.18 | 0 0 0 0 0 0 0 0 0 0 | 3.60/1.18 | 0 0 0 0 0 0 0 0 0 0 | 3.60/1.18 | 0 0 0 0 0 0 0 0 0 0 | 3.60/1.18 | 0 0 0 0 0 0 1 0 0 0 | 3.60/1.18 | 0 0 0 0 0 0 0 0 0 0 | 3.60/1.18 | 0 0 0 1 0 0 0 0 1 0 | 3.60/1.18 | 0 0 0 0 0 0 0 0 0 0 | 3.60/1.18 | 0 0 0 0 0 0 0 0 0 0 | 3.60/1.18 \ / 3.60/1.18 (c,false) is interpreted by 3.60/1.18 / \ 3.60/1.18 | 1 0 0 0 0 0 0 0 0 0 | 3.60/1.18 | 0 1 0 0 0 0 0 0 0 0 | 3.60/1.18 | 0 0 0 0 0 0 0 0 0 0 | 3.60/1.18 | 0 0 0 0 0 0 0 0 0 0 | 3.60/1.18 | 0 0 0 0 0 0 0 0 0 0 | 3.60/1.18 | 0 0 0 0 0 0 0 0 0 0 | 3.60/1.18 | 0 0 0 0 0 0 0 1 0 0 | 3.60/1.18 | 0 0 0 0 0 0 0 0 0 0 | 3.60/1.18 | 0 0 0 0 0 0 0 0 0 0 | 3.60/1.18 | 0 0 0 0 0 0 0 0 0 0 | 3.60/1.18 \ / 3.60/1.18 3.60/1.18 Remains to prove termination of the 1-rule system 3.60/1.18 { (a,false) (a,false) (a,false) (a,false) (b,false) (c,false) (b,false) (a,false) (a,false) ->= (b,false) (c,false) (b,false) (a,false) (a,false) (b,false) (c,false) (b,false) (a,false) (a,false) (a,false) (a,false) (a,false) (a,false) } 3.60/1.18 3.60/1.18 3.60/1.18 The system is trivially terminating. 3.83/1.27 EOF