0.00/0.32 YES 0.00/0.33 0.00/0.33 0.00/0.33 The system was filtered by the following matrix interpretation 0.00/0.33 of type E_J with J = {1,...,2} and dimension 3: 0.00/0.33 0.00/0.33 a is interpreted by 0.00/0.33 / \ 0.00/0.33 | 1 0 0 | 0.00/0.33 | 0 1 0 | 0.00/0.33 | 0 0 0 | 0.00/0.33 \ / 0.00/0.33 b is interpreted by 0.00/0.33 / \ 0.00/0.33 | 1 0 0 | 0.00/0.33 | 0 1 0 | 0.00/0.33 | 0 0 0 | 0.00/0.33 \ / 0.00/0.33 d is interpreted by 0.00/0.33 / \ 0.00/0.33 | 1 0 1 | 0.00/0.33 | 0 1 0 | 0.00/0.33 | 0 0 0 | 0.00/0.33 \ / 0.00/0.33 c is interpreted by 0.00/0.33 / \ 0.00/0.33 | 1 0 0 | 0.00/0.33 | 0 1 0 | 0.00/0.33 | 0 1 0 | 0.00/0.33 \ / 0.00/0.33 0.00/0.33 Remains to prove termination of the 3-rule system 0.00/0.33 { a b -> b a , 0.00/0.33 a ->= b c , 0.00/0.33 b c ->= a c } 0.00/0.33 0.00/0.33 0.00/0.33 The system was filtered by the following matrix interpretation 0.00/0.33 of type E_J with J = {1,...,2} and dimension 3: 0.00/0.33 0.00/0.33 a is interpreted by 0.00/0.33 / \ 0.00/0.33 | 1 0 1 | 0.00/0.33 | 0 1 0 | 0.00/0.33 | 0 1 1 | 0.00/0.33 \ / 0.00/0.33 b is interpreted by 0.00/0.33 / \ 0.00/0.33 | 1 0 0 | 0.00/0.33 | 0 1 0 | 0.00/0.33 | 0 1 1 | 0.00/0.33 \ / 0.00/0.33 d is interpreted by 0.00/0.33 / \ 0.00/0.33 | 1 0 0 | 0.00/0.33 | 0 1 0 | 0.00/0.33 | 0 0 0 | 0.00/0.33 \ / 0.00/0.33 c is interpreted by 0.00/0.33 / \ 0.00/0.33 | 1 0 0 | 0.00/0.33 | 0 1 0 | 0.00/0.33 | 0 0 0 | 0.00/0.33 \ / 0.00/0.33 0.00/0.33 Remains to prove termination of the 2-rule system 0.00/0.33 { a ->= b c , 0.00/0.33 b c ->= a c } 0.00/0.33 0.00/0.33 0.00/0.33 The system is trivially terminating. 0.00/0.36 EOF