0.00/0.38 YES 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 5: 0.00/0.40 0.00/0.40 a is interpreted by 0.00/0.40 / \ 0.00/0.40 | 1 0 1 0 0 | 0.00/0.40 | 0 1 0 0 0 | 0.00/0.40 | 0 0 0 0 0 | 0.00/0.40 | 0 0 0 0 0 | 0.00/0.40 | 0 1 0 1 0 | 0.00/0.40 \ / 0.00/0.40 b is interpreted by 0.00/0.40 / \ 0.00/0.40 | 1 0 0 0 0 | 0.00/0.40 | 0 1 0 0 0 | 0.00/0.40 | 0 0 0 1 0 | 0.00/0.40 | 0 0 0 0 1 | 0.00/0.40 | 0 0 0 0 0 | 0.00/0.40 \ / 0.00/0.40 c is interpreted by 0.00/0.40 / \ 0.00/0.40 | 1 0 0 0 0 | 0.00/0.40 | 0 1 0 0 0 | 0.00/0.40 | 0 0 1 0 0 | 0.00/0.40 | 0 0 0 0 0 | 0.00/0.40 | 0 0 0 0 0 | 0.00/0.40 \ / 0.00/0.40 0.00/0.40 Remains to prove termination of the 2-rule system 0.00/0.40 { a c -> c c a , 0.00/0.40 c c c -> b c b } 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 3: 0.00/0.40 0.00/0.40 a is interpreted by 0.00/0.40 / \ 0.00/0.40 | 1 0 1 | 0.00/0.40 | 0 1 0 | 0.00/0.40 | 0 0 2 | 0.00/0.40 \ / 0.00/0.40 b is interpreted by 0.00/0.40 / \ 0.00/0.40 | 1 0 0 | 0.00/0.40 | 0 1 0 | 0.00/0.40 | 0 0 0 | 0.00/0.40 \ / 0.00/0.40 c is interpreted by 0.00/0.40 / \ 0.00/0.40 | 1 0 0 | 0.00/0.40 | 0 1 0 | 0.00/0.40 | 0 1 1 | 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 { c c c -> b c b } 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 2: 0.00/0.40 0.00/0.40 a is interpreted by 0.00/0.40 / \ 0.00/0.40 | 1 0 | 0.00/0.40 | 0 1 | 0.00/0.40 \ / 0.00/0.40 b is interpreted by 0.00/0.40 / \ 0.00/0.40 | 1 0 | 0.00/0.40 | 0 1 | 0.00/0.40 \ / 0.00/0.40 c is interpreted by 0.00/0.40 / \ 0.00/0.40 | 1 1 | 0.00/0.40 | 0 1 | 0.00/0.40 \ / 0.00/0.40 0.00/0.40 Remains to prove termination of the 0-rule system 0.00/0.40 { } 0.00/0.40 0.00/0.40 0.00/0.40 The system is trivially terminating. 0.00/0.43 EOF