0.00/0.39 YES 0.00/0.40 0.00/0.40 0.00/0.40 The system was reversed. 0.00/0.40 0.00/0.40 Remains to prove termination of the 1-rule system 0.00/0.40 { a c b a a c -> c b a a c c b a a } 0.00/0.40 0.00/0.40 0.00/0.40 The dependency pairs transformation was applied. 0.00/0.40 0.00/0.40 Remains to prove termination of the 5-rule system 0.00/0.40 { (a,true) (c,false) (b,false) (a,false) (a,false) (c,false) -> (a,true) (a,false) (c,false) (c,false) (b,false) (a,false) (a,false) , 0.00/0.40 (a,true) (c,false) (b,false) (a,false) (a,false) (c,false) -> (a,true) (c,false) (c,false) (b,false) (a,false) (a,false) , 0.00/0.40 (a,true) (c,false) (b,false) (a,false) (a,false) (c,false) -> (a,true) (a,false) , 0.00/0.40 (a,true) (c,false) (b,false) (a,false) (a,false) (c,false) -> (a,true) , 0.00/0.40 (a,false) (c,false) (b,false) (a,false) (a,false) (c,false) ->= (c,false) (b,false) (a,false) (a,false) (c,false) (c,false) (b,false) (a,false) (a,false) } 0.00/0.40 0.00/0.40 0.00/0.40 0.00/0.40 0.00/0.40 The system was filtered by the following matrix interpretation 0.00/0.40 of type E_J with J = {1,...,2} and dimension 7: 0.00/0.40 0.00/0.40 (a,true) is interpreted by 0.00/0.40 / \ 0.00/0.40 | 1 0 1 0 0 0 0 | 0.00/0.40 | 0 1 0 0 0 0 0 | 0.00/0.40 | 0 0 0 0 0 0 0 | 0.00/0.40 | 0 0 0 0 0 0 0 | 0.00/0.40 | 0 0 0 0 0 0 0 | 0.00/0.40 | 0 0 0 0 0 0 0 | 0.00/0.40 | 0 0 0 0 0 0 0 | 0.00/0.40 \ / 0.00/0.40 (c,false) is interpreted by 0.00/0.40 / \ 0.00/0.40 | 1 0 0 0 0 0 0 | 0.00/0.40 | 0 1 0 0 0 0 0 | 0.00/0.40 | 0 0 0 2 0 0 0 | 0.00/0.40 | 0 0 0 0 0 0 0 | 0.00/0.40 | 0 0 0 0 0 0 0 | 0.00/0.40 | 0 0 0 0 0 0 0 | 0.00/0.40 | 0 1 1 0 0 0 1 | 0.00/0.40 \ / 0.00/0.40 (b,false) is interpreted by 0.00/0.40 / \ 0.00/0.40 | 1 0 0 0 0 0 0 | 0.00/0.40 | 0 1 0 0 0 0 0 | 0.00/0.40 | 0 0 0 0 0 0 0 | 0.00/0.40 | 0 0 0 0 1 0 0 | 0.00/0.40 | 0 0 0 0 0 0 0 | 0.00/0.40 | 0 0 0 0 0 0 0 | 0.00/0.40 | 0 0 0 0 0 0 0 | 0.00/0.40 \ / 0.00/0.40 (a,false) is interpreted by 0.00/0.40 / \ 0.00/0.40 | 1 0 0 0 0 0 0 | 0.00/0.40 | 0 1 0 0 0 0 0 | 0.00/0.40 | 0 0 2 0 0 0 0 | 0.00/0.40 | 0 0 0 0 0 0 0 | 0.00/0.40 | 0 0 0 0 0 1 0 | 0.00/0.40 | 0 0 0 0 0 0 1 | 0.00/0.40 | 0 0 1 0 0 0 0 | 0.00/0.40 \ / 0.00/0.40 0.00/0.40 Remains to prove termination of the 1-rule system 0.00/0.40 { (a,false) (c,false) (b,false) (a,false) (a,false) (c,false) ->= (c,false) (b,false) (a,false) (a,false) (c,false) (c,false) (b,false) (a,false) (a,false) } 0.00/0.40 0.00/0.40 0.00/0.40 The system is trivially terminating. 0.00/0.43 EOF