0.00/0.47 YES 0.00/0.49 0.00/0.49 0.00/0.49 The system was filtered by the following matrix interpretation 0.00/0.49 of type E_J with J = {1,...,2} and dimension 2: 0.00/0.49 0.00/0.49 a is interpreted by 0.00/0.49 / \ 0.00/0.49 | 1 1 | 0.00/0.49 | 0 1 | 0.00/0.49 \ / 0.00/0.49 c is interpreted by 0.00/0.49 / \ 0.00/0.49 | 1 1 | 0.00/0.49 | 0 1 | 0.00/0.49 \ / 0.00/0.49 b is interpreted by 0.00/0.49 / \ 0.00/0.49 | 1 0 | 0.00/0.49 | 0 1 | 0.00/0.49 \ / 0.00/0.49 0.00/0.49 Remains to prove termination of the 3-rule system 0.00/0.49 { a c a -> c a c , 0.00/0.49 a a b ->= c b a , 0.00/0.49 b c c ->= b c a } 0.00/0.49 0.00/0.49 0.00/0.49 The system was filtered by the following matrix interpretation 0.00/0.49 of type E_J with J = {1,...,2} and dimension 6: 0.00/0.49 0.00/0.49 a is interpreted by 0.00/0.49 / \ 0.00/0.49 | 1 0 1 0 0 0 | 0.00/0.49 | 0 1 0 0 0 0 | 0.00/0.49 | 0 0 0 1 0 0 | 0.00/0.49 | 0 0 0 0 0 0 | 0.00/0.49 | 0 0 0 0 0 0 | 0.00/0.49 | 0 0 0 0 0 0 | 0.00/0.49 \ / 0.00/0.49 c is interpreted by 0.00/0.49 / \ 0.00/0.49 | 1 0 0 0 0 0 | 0.00/0.49 | 0 1 0 0 0 0 | 0.00/0.49 | 0 0 0 0 0 0 | 0.00/0.49 | 0 0 0 0 0 0 | 0.00/0.49 | 0 0 0 0 0 1 | 0.00/0.49 | 0 0 1 0 0 0 | 0.00/0.49 \ / 0.00/0.49 b is interpreted by 0.00/0.49 / \ 0.00/0.49 | 1 0 0 0 1 0 | 0.00/0.49 | 0 1 0 0 0 0 | 0.00/0.49 | 0 0 0 0 0 0 | 0.00/0.49 | 0 1 1 0 0 0 | 0.00/0.49 | 0 0 0 0 0 0 | 0.00/0.49 | 0 0 0 0 0 0 | 0.00/0.49 \ / 0.00/0.49 0.00/0.49 Remains to prove termination of the 2-rule system 0.00/0.49 { a c a -> c a c , 0.00/0.49 b c c ->= b c a } 0.00/0.49 0.00/0.49 0.00/0.49 The system was filtered by the following matrix interpretation 0.00/0.49 of type E_J with J = {1,...,2} and dimension 4: 0.00/0.49 0.00/0.49 a is interpreted by 0.00/0.49 / \ 0.00/0.49 | 1 0 1 0 | 0.00/0.49 | 0 1 0 0 | 0.00/0.49 | 0 0 0 1 | 0.00/0.49 | 0 1 0 1 | 0.00/0.49 \ / 0.00/0.49 c is interpreted by 0.00/0.49 / \ 0.00/0.49 | 1 0 1 0 | 0.00/0.49 | 0 1 0 0 | 0.00/0.49 | 0 0 0 1 | 0.00/0.49 | 0 0 0 1 | 0.00/0.49 \ / 0.00/0.49 b is interpreted by 0.00/0.49 / \ 0.00/0.49 | 1 0 0 0 | 0.00/0.49 | 0 1 0 0 | 0.00/0.49 | 0 0 0 0 | 0.00/0.49 | 0 0 0 0 | 0.00/0.49 \ / 0.00/0.49 0.00/0.49 Remains to prove termination of the 1-rule system 0.00/0.49 { b c c ->= b c a } 0.00/0.49 0.00/0.49 0.00/0.49 The system is trivially terminating. 1.26/0.53 EOF