0.00/0.41 YES 0.00/0.44 0.00/0.44 0.00/0.44 The system was filtered by the following matrix interpretation 0.00/0.44 of type E_J with J = {1,...,2} and dimension 2: 0.00/0.44 0.00/0.44 0 is interpreted by 0.00/0.44 / \ 0.00/0.44 | 1 1 | 0.00/0.44 | 0 1 | 0.00/0.44 \ / 0.00/0.44 1 is interpreted by 0.00/0.44 / \ 0.00/0.44 | 1 0 | 0.00/0.44 | 0 1 | 0.00/0.44 \ / 0.00/0.44 2 is interpreted by 0.00/0.44 / \ 0.00/0.44 | 1 0 | 0.00/0.44 | 0 1 | 0.00/0.44 \ / 0.00/0.44 3 is interpreted by 0.00/0.44 / \ 0.00/0.44 | 1 0 | 0.00/0.44 | 0 1 | 0.00/0.44 \ / 0.00/0.44 4 is interpreted by 0.00/0.44 / \ 0.00/0.44 | 1 0 | 0.00/0.44 | 0 1 | 0.00/0.44 \ / 0.00/0.44 5 is interpreted by 0.00/0.44 / \ 0.00/0.44 | 1 0 | 0.00/0.44 | 0 1 | 0.00/0.44 \ / 0.00/0.44 0.00/0.44 Remains to prove termination of the 2-rule system 0.00/0.44 { 2 -> 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 , 0.00/0.44 0 1 2 3 4 5 4 5 -> 0 1 2 3 4 4 5 5 } 0.00/0.44 0.00/0.44 0.00/0.44 The system was filtered by the following matrix interpretation 0.00/0.44 of type E_J with J = {1,...,2} and dimension 2: 0.00/0.44 0.00/0.44 0 is interpreted by 0.00/0.44 / \ 0.00/0.44 | 1 0 | 0.00/0.44 | 0 1 | 0.00/0.44 \ / 0.00/0.44 1 is interpreted by 0.00/0.44 / \ 0.00/0.44 | 1 0 | 0.00/0.44 | 0 1 | 0.00/0.44 \ / 0.00/0.44 2 is interpreted by 0.00/0.44 / \ 0.00/0.44 | 1 1 | 0.00/0.44 | 0 1 | 0.00/0.44 \ / 0.00/0.44 3 is interpreted by 0.00/0.44 / \ 0.00/0.44 | 1 0 | 0.00/0.44 | 0 1 | 0.00/0.44 \ / 0.00/0.44 4 is interpreted by 0.00/0.44 / \ 0.00/0.44 | 1 0 | 0.00/0.44 | 0 1 | 0.00/0.44 \ / 0.00/0.44 5 is interpreted by 0.00/0.44 / \ 0.00/0.44 | 1 0 | 0.00/0.44 | 0 1 | 0.00/0.44 \ / 0.00/0.44 0.00/0.44 Remains to prove termination of the 1-rule system 0.00/0.44 { 0 1 2 3 4 5 4 5 -> 0 1 2 3 4 4 5 5 } 0.00/0.44 0.00/0.44 0.00/0.44 The system was filtered by the following matrix interpretation 0.00/0.44 of type E_J with J = {1,...,2} and dimension 9: 0.00/0.44 0.00/0.44 0 is interpreted by 0.00/0.44 / \ 0.00/0.44 | 1 0 1 0 0 0 0 0 0 | 0.00/0.44 | 0 1 0 0 0 0 0 0 0 | 0.00/0.44 | 0 0 0 0 0 0 0 0 0 | 0.00/0.44 | 0 0 0 0 0 0 0 0 0 | 0.00/0.44 | 0 0 0 0 0 0 0 0 0 | 0.00/0.44 | 0 0 0 0 0 0 0 0 0 | 0.00/0.44 | 0 0 0 0 0 0 0 0 0 | 0.00/0.44 | 0 0 0 0 0 0 0 0 0 | 0.00/0.44 | 0 0 0 0 0 0 0 0 0 | 0.00/0.44 \ / 0.00/0.44 1 is interpreted by 0.00/0.44 / \ 0.00/0.44 | 1 0 0 0 0 0 0 0 0 | 0.00/0.44 | 0 1 0 0 0 0 0 0 0 | 0.00/0.44 | 0 0 0 1 0 0 0 0 0 | 0.00/0.44 | 0 0 0 0 0 0 0 0 0 | 0.00/0.44 | 0 0 0 0 0 0 0 0 0 | 0.00/0.44 | 0 0 0 0 0 0 0 0 0 | 0.00/0.44 | 0 0 0 0 0 0 0 0 0 | 0.00/0.44 | 0 0 0 0 0 0 0 0 0 | 0.00/0.44 | 0 0 0 0 0 0 0 0 0 | 0.00/0.44 \ / 0.00/0.44 2 is interpreted by 0.00/0.44 / \ 0.00/0.44 | 1 0 0 0 0 0 0 0 0 | 0.00/0.44 | 0 1 0 0 0 0 0 0 0 | 0.00/0.44 | 0 0 0 0 0 0 0 0 0 | 0.00/0.44 | 0 0 0 0 1 0 0 0 0 | 0.00/0.44 | 0 0 0 0 0 0 0 0 0 | 0.00/0.44 | 0 0 0 0 0 0 0 0 0 | 0.00/0.44 | 0 0 0 0 0 0 0 0 0 | 0.00/0.44 | 0 0 0 0 0 0 0 0 0 | 0.00/0.44 | 0 0 0 0 0 0 0 0 0 | 0.00/0.44 \ / 0.00/0.44 3 is interpreted by 0.00/0.44 / \ 0.00/0.44 | 1 0 0 0 0 0 0 0 0 | 0.00/0.44 | 0 1 0 0 0 0 0 0 0 | 0.00/0.44 | 0 0 0 0 0 0 0 0 0 | 0.00/0.44 | 0 0 0 0 0 0 0 0 0 | 0.00/0.44 | 0 0 0 0 0 1 0 0 0 | 0.00/0.44 | 0 0 0 0 0 0 0 0 0 | 0.00/0.44 | 0 0 0 0 0 0 0 0 0 | 0.00/0.44 | 0 0 0 0 0 0 0 0 0 | 0.00/0.44 | 0 0 0 0 0 0 0 0 0 | 0.00/0.44 \ / 0.00/0.44 4 is interpreted by 0.00/0.44 / \ 0.00/0.44 | 1 0 0 0 0 0 0 0 0 | 0.00/0.44 | 0 1 0 0 0 0 0 0 0 | 0.00/0.44 | 0 0 0 0 0 0 0 0 0 | 0.00/0.44 | 0 0 0 0 0 0 0 0 0 | 0.00/0.44 | 0 0 0 0 0 0 0 0 0 | 0.00/0.44 | 0 0 0 0 0 0 1 0 0 | 0.00/0.44 | 0 0 0 0 0 0 0 0 0 | 0.00/0.44 | 0 0 0 0 0 0 0 0 1 | 0.00/0.44 | 0 0 0 0 0 0 0 0 0 | 0.00/0.44 \ / 0.00/0.44 5 is interpreted by 0.00/0.44 / \ 0.00/0.44 | 1 0 0 0 0 0 0 0 0 | 0.00/0.44 | 0 1 0 0 0 0 0 0 0 | 0.00/0.44 | 0 0 0 0 0 0 0 0 0 | 0.00/0.44 | 0 0 0 0 0 0 0 0 0 | 0.00/0.44 | 0 0 0 0 0 0 0 0 0 | 0.00/0.44 | 0 0 0 0 0 0 0 0 0 | 0.00/0.44 | 0 0 0 0 0 0 0 1 0 | 0.00/0.44 | 0 0 0 0 0 0 0 0 0 | 0.00/0.44 | 0 1 0 0 0 0 0 0 0 | 0.00/0.44 \ / 0.00/0.44 0.00/0.44 Remains to prove termination of the 0-rule system 0.00/0.44 { } 0.00/0.44 0.00/0.44 0.00/0.44 The system is trivially terminating. 0.00/0.47 EOF