6.93/2.02 YES 6.93/2.04 6.93/2.04 6.93/2.04 The dependency pairs transformation was applied. 6.93/2.04 6.93/2.04 Remains to prove termination of the 12-rule system 6.93/2.04 { (a,true) (b,false) (a,false) (a,false) (a,false) (b,false) (a,false) (a,false) (a,false) (a,false) -> (a,true) (a,false) (a,false) (a,false) (a,false) (b,false) (a,false) (a,false) (a,false) (b,false) (a,false) (a,false) (a,false) (b,false) , 6.93/2.04 (a,true) (b,false) (a,false) (a,false) (a,false) (b,false) (a,false) (a,false) (a,false) (a,false) -> (a,true) (a,false) (a,false) (a,false) (b,false) (a,false) (a,false) (a,false) (b,false) (a,false) (a,false) (a,false) (b,false) , 6.93/2.04 (a,true) (b,false) (a,false) (a,false) (a,false) (b,false) (a,false) (a,false) (a,false) (a,false) -> (a,true) (a,false) (a,false) (b,false) (a,false) (a,false) (a,false) (b,false) (a,false) (a,false) (a,false) (b,false) , 6.93/2.04 (a,true) (b,false) (a,false) (a,false) (a,false) (b,false) (a,false) (a,false) (a,false) (a,false) -> (a,true) (a,false) (b,false) (a,false) (a,false) (a,false) (b,false) (a,false) (a,false) (a,false) (b,false) , 6.93/2.04 (a,true) (b,false) (a,false) (a,false) (a,false) (b,false) (a,false) (a,false) (a,false) (a,false) -> (a,true) (b,false) (a,false) (a,false) (a,false) (b,false) (a,false) (a,false) (a,false) (b,false) , 6.93/2.04 (a,true) (b,false) (a,false) (a,false) (a,false) (b,false) (a,false) (a,false) (a,false) (a,false) -> (a,true) (a,false) (a,false) (b,false) (a,false) (a,false) (a,false) (b,false) , 6.93/2.04 (a,true) (b,false) (a,false) (a,false) (a,false) (b,false) (a,false) (a,false) (a,false) (a,false) -> (a,true) (a,false) (b,false) (a,false) (a,false) (a,false) (b,false) , 6.93/2.04 (a,true) (b,false) (a,false) (a,false) (a,false) (b,false) (a,false) (a,false) (a,false) (a,false) -> (a,true) (b,false) (a,false) (a,false) (a,false) (b,false) , 6.93/2.04 (a,true) (b,false) (a,false) (a,false) (a,false) (b,false) (a,false) (a,false) (a,false) (a,false) -> (a,true) (a,false) (a,false) (b,false) , 6.93/2.04 (a,true) (b,false) (a,false) (a,false) (a,false) (b,false) (a,false) (a,false) (a,false) (a,false) -> (a,true) (a,false) (b,false) , 6.93/2.04 (a,true) (b,false) (a,false) (a,false) (a,false) (b,false) (a,false) (a,false) (a,false) (a,false) -> (a,true) (b,false) , 6.93/2.04 (a,false) (b,false) (a,false) (a,false) (a,false) (b,false) (a,false) (a,false) (a,false) (a,false) ->= (a,false) (a,false) (a,false) (a,false) (a,false) (b,false) (a,false) (a,false) (a,false) (b,false) (a,false) (a,false) (a,false) (b,false) } 6.93/2.04 6.93/2.04 6.93/2.04 6.93/2.04 6.93/2.04 The system was filtered by the following matrix interpretation 6.93/2.04 of type E_J with J = {1,...,2} and dimension 11: 6.93/2.04 6.93/2.04 (a,true) is interpreted by 6.93/2.04 / \ 6.93/2.04 | 1 0 1 0 0 0 0 0 0 0 0 | 6.93/2.04 | 0 1 0 0 0 0 0 0 0 0 0 | 6.93/2.04 | 0 0 0 0 0 0 0 0 0 0 0 | 6.93/2.04 | 0 0 0 0 0 0 0 0 0 0 0 | 6.93/2.04 | 0 0 0 0 0 0 0 0 0 0 0 | 6.93/2.04 | 0 0 0 0 0 0 0 0 0 0 0 | 6.93/2.04 | 0 0 0 0 0 0 0 0 0 0 0 | 6.93/2.04 | 0 0 0 0 0 0 0 0 0 0 0 | 6.93/2.04 | 0 0 0 0 0 0 0 0 0 0 0 | 6.93/2.04 | 0 0 0 0 0 0 0 0 0 0 0 | 6.93/2.04 | 0 0 0 0 0 0 0 0 0 0 0 | 6.93/2.04 \ / 6.93/2.04 (b,false) is interpreted by 6.93/2.04 / \ 6.93/2.04 | 1 0 0 0 0 0 0 0 0 0 0 | 6.93/2.04 | 0 1 0 0 0 0 0 0 0 0 0 | 6.93/2.04 | 0 0 0 1 0 0 0 0 0 0 0 | 6.93/2.04 | 0 0 0 0 0 0 0 0 0 0 0 | 6.93/2.04 | 0 0 0 0 0 0 0 0 0 0 0 | 6.93/2.04 | 0 0 0 0 0 0 0 0 0 0 0 | 6.93/2.04 | 0 0 0 0 0 0 0 1 0 0 0 | 6.93/2.04 | 0 0 0 0 0 0 0 0 0 0 0 | 6.93/2.04 | 0 0 0 0 0 0 0 0 0 0 0 | 6.93/2.04 | 0 0 0 1 0 0 0 0 0 0 0 | 6.93/2.04 | 0 0 0 0 0 0 0 0 0 0 0 | 6.93/2.04 \ / 6.93/2.04 (a,false) is interpreted by 6.93/2.04 / \ 6.93/2.04 | 1 0 0 0 0 0 0 0 0 0 0 | 6.93/2.04 | 0 1 0 0 0 0 0 0 0 0 0 | 6.93/2.04 | 0 0 0 0 0 0 0 0 0 0 0 | 6.93/2.04 | 0 0 0 0 1 0 0 0 0 0 0 | 6.93/2.04 | 0 0 0 0 0 1 0 0 0 0 0 | 6.93/2.04 | 0 0 0 0 0 0 1 0 0 0 0 | 6.93/2.04 | 0 0 0 0 0 0 0 0 0 0 0 | 6.93/2.04 | 0 0 1 0 0 0 0 0 1 0 0 | 6.93/2.04 | 0 0 0 0 0 0 0 0 0 1 0 | 6.93/2.04 | 0 0 1 0 0 0 0 0 0 0 1 | 6.93/2.04 | 0 1 1 1 0 0 0 1 0 0 0 | 6.93/2.04 \ / 6.93/2.04 6.93/2.04 Remains to prove termination of the 1-rule system 6.93/2.04 { (a,false) (b,false) (a,false) (a,false) (a,false) (b,false) (a,false) (a,false) (a,false) (a,false) ->= (a,false) (a,false) (a,false) (a,false) (a,false) (b,false) (a,false) (a,false) (a,false) (b,false) (a,false) (a,false) (a,false) (b,false) } 6.93/2.04 6.93/2.04 6.93/2.04 The system is trivially terminating. 7.16/2.10 EOF