3.16/1.00 YES 3.16/1.02 3.16/1.02 3.16/1.02 The system was reversed. 3.16/1.02 3.16/1.02 Remains to prove termination of the 1-rule system 3.16/1.02 { a a a a c c b a a -> c c b a a c c b a a a a a a } 3.16/1.02 3.16/1.02 3.16/1.02 The dependency pairs transformation was applied. 3.16/1.02 3.16/1.02 Remains to prove termination of the 9-rule system 3.16/1.02 { (a,true) (a,false) (a,false) (a,false) (c,false) (c,false) (b,false) (a,false) (a,false) -> (a,true) (a,false) (c,false) (c,false) (b,false) (a,false) (a,false) (a,false) (a,false) (a,false) (a,false) , 3.16/1.02 (a,true) (a,false) (a,false) (a,false) (c,false) (c,false) (b,false) (a,false) (a,false) -> (a,true) (c,false) (c,false) (b,false) (a,false) (a,false) (a,false) (a,false) (a,false) (a,false) , 3.16/1.02 (a,true) (a,false) (a,false) (a,false) (c,false) (c,false) (b,false) (a,false) (a,false) -> (a,true) (a,false) (a,false) (a,false) (a,false) (a,false) , 3.16/1.02 (a,true) (a,false) (a,false) (a,false) (c,false) (c,false) (b,false) (a,false) (a,false) -> (a,true) (a,false) (a,false) (a,false) (a,false) , 3.16/1.02 (a,true) (a,false) (a,false) (a,false) (c,false) (c,false) (b,false) (a,false) (a,false) -> (a,true) (a,false) (a,false) (a,false) , 3.16/1.02 (a,true) (a,false) (a,false) (a,false) (c,false) (c,false) (b,false) (a,false) (a,false) -> (a,true) (a,false) (a,false) , 3.16/1.02 (a,true) (a,false) (a,false) (a,false) (c,false) (c,false) (b,false) (a,false) (a,false) -> (a,true) (a,false) , 3.16/1.02 (a,true) (a,false) (a,false) (a,false) (c,false) (c,false) (b,false) (a,false) (a,false) -> (a,true) , 3.16/1.02 (a,false) (a,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) (c,false) (c,false) (b,false) (a,false) (a,false) (a,false) (a,false) (a,false) (a,false) } 3.16/1.02 3.16/1.02 3.16/1.02 3.16/1.02 3.16/1.02 The system was filtered by the following matrix interpretation 3.16/1.02 of type E_J with J = {1,...,2} and dimension 10: 3.16/1.02 3.16/1.02 (a,true) is interpreted by 3.16/1.02 / \ 3.16/1.02 | 1 0 1 0 0 0 0 0 0 0 | 3.16/1.02 | 0 1 0 0 0 0 0 0 0 0 | 3.16/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.16/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.16/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.16/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.16/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.16/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.16/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.16/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.16/1.02 \ / 3.16/1.02 (a,false) is interpreted by 3.16/1.02 / \ 3.16/1.02 | 1 0 0 0 0 0 0 0 0 0 | 3.16/1.02 | 0 1 0 0 0 0 0 0 0 0 | 3.16/1.02 | 0 0 0 2 0 0 0 0 0 0 | 3.16/1.02 | 0 0 0 0 1 0 0 0 0 0 | 3.16/1.02 | 0 0 0 0 0 1 0 0 0 0 | 3.16/1.02 | 0 0 1 0 0 0 0 0 0 0 | 3.16/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.16/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.16/1.02 | 0 0 1 0 0 0 0 0 0 1 | 3.16/1.02 | 0 1 1 0 1 0 0 0 0 0 | 3.16/1.02 \ / 3.16/1.02 (c,false) is interpreted by 3.16/1.02 / \ 3.16/1.02 | 1 0 0 0 0 0 0 0 0 0 | 3.16/1.02 | 0 1 0 0 0 0 0 0 0 0 | 3.16/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.16/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.16/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.16/1.02 | 0 0 0 0 0 0 1 0 0 0 | 3.16/1.02 | 0 0 0 0 0 0 0 1 0 0 | 3.16/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.16/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.16/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.16/1.02 \ / 3.16/1.02 (b,false) is interpreted by 3.16/1.02 / \ 3.16/1.02 | 1 0 0 0 0 0 0 0 0 0 | 3.16/1.02 | 0 1 0 0 0 0 0 0 0 0 | 3.16/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.16/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.16/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.16/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.16/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.16/1.02 | 0 0 0 1 0 0 0 0 1 0 | 3.16/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.16/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.16/1.02 \ / 3.16/1.02 3.16/1.02 Remains to prove termination of the 1-rule system 3.16/1.02 { (a,false) (a,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) (c,false) (c,false) (b,false) (a,false) (a,false) (a,false) (a,false) (a,false) (a,false) } 3.16/1.02 3.16/1.02 3.16/1.02 The system is trivially terminating. 3.16/1.05 EOF