2.89/0.91 YES 3.33/1.02 3.33/1.02 3.33/1.02 The system was filtered by the following matrix interpretation 3.33/1.02 of type E_J with J = {1,...,2} and dimension 2: 3.33/1.02 3.33/1.02 0 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 1 | 3.33/1.02 | 0 1 | 3.33/1.02 \ / 3.33/1.02 1 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 1 | 3.33/1.02 | 0 1 | 3.33/1.02 \ / 3.33/1.02 2 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 1 | 3.33/1.02 | 0 1 | 3.33/1.02 \ / 3.33/1.02 3 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 1 | 3.33/1.02 | 0 1 | 3.33/1.02 \ / 3.33/1.02 4 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 1 | 3.33/1.02 | 0 1 | 3.33/1.02 \ / 3.33/1.02 5 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 1 | 3.33/1.02 | 0 1 | 3.33/1.02 \ / 3.33/1.02 3.33/1.02 Remains to prove termination of the 13-rule system 3.33/1.02 { 0 3 3 1 1 4 -> 3 2 3 0 1 3 , 3.33/1.02 0 3 2 1 4 0 1 -> 4 0 5 1 3 0 1 , 3.33/1.02 2 2 0 2 5 2 0 -> 2 2 1 2 5 1 3 , 3.33/1.02 4 5 3 2 4 4 2 2 -> 4 0 5 0 0 0 2 2 , 3.33/1.02 1 0 2 5 2 3 0 1 1 -> 1 5 1 2 0 2 4 4 1 , 3.33/1.02 1 3 0 4 3 0 5 3 2 5 3 -> 1 3 0 0 0 3 1 3 3 5 3 , 3.33/1.02 5 1 5 2 0 5 5 5 2 2 5 1 -> 2 2 4 0 0 5 3 0 5 1 0 2 , 3.33/1.02 5 0 5 1 0 3 1 3 1 1 3 1 5 1 -> 5 4 4 1 2 5 5 0 1 0 3 2 2 2 , 3.33/1.02 0 5 5 2 5 4 5 0 5 2 2 3 1 3 3 4 4 2 -> 5 0 2 4 4 3 2 2 5 1 4 4 1 1 4 3 5 2 , 3.33/1.02 1 4 4 3 3 0 0 3 5 2 1 4 4 4 3 0 1 5 -> 3 5 3 3 0 2 5 1 5 4 4 3 1 2 3 4 3 5 , 3.33/1.02 3 5 1 4 5 2 4 1 3 2 4 4 0 5 4 1 0 3 -> 3 0 5 5 4 5 1 4 3 0 0 5 5 3 3 1 2 3 , 3.33/1.02 5 3 5 3 3 1 5 5 2 2 3 3 4 1 5 1 0 5 -> 3 5 0 4 4 3 4 0 5 2 0 0 2 4 1 5 1 5 , 3.33/1.02 4 1 0 2 0 3 5 5 3 2 1 2 4 5 2 2 3 4 3 0 -> 0 0 5 5 4 1 2 2 1 0 0 4 4 5 0 5 3 5 3 0 } 3.33/1.02 3.33/1.02 3.33/1.02 The system was filtered by the following matrix interpretation 3.33/1.02 of type E_J with J = {1,...,2} and dimension 8: 3.33/1.02 3.33/1.02 0 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 1 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 1 | 3.33/1.02 | 0 0 0 0 0 0 0 0 | 3.33/1.02 \ / 3.33/1.02 1 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 1 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 0 | 3.33/1.02 \ / 3.33/1.02 2 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 1 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 | 3.33/1.02 \ / 3.33/1.02 3 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 1 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 | 3.33/1.02 \ / 3.33/1.02 4 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 1 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 | 3.33/1.02 \ / 3.33/1.02 5 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 | 3.33/1.02 \ / 3.33/1.02 3.33/1.02 Remains to prove termination of the 12-rule system 3.33/1.02 { 0 3 3 1 1 4 -> 3 2 3 0 1 3 , 3.33/1.02 2 2 0 2 5 2 0 -> 2 2 1 2 5 1 3 , 3.33/1.02 4 5 3 2 4 4 2 2 -> 4 0 5 0 0 0 2 2 , 3.33/1.02 1 0 2 5 2 3 0 1 1 -> 1 5 1 2 0 2 4 4 1 , 3.33/1.02 1 3 0 4 3 0 5 3 2 5 3 -> 1 3 0 0 0 3 1 3 3 5 3 , 3.33/1.02 5 1 5 2 0 5 5 5 2 2 5 1 -> 2 2 4 0 0 5 3 0 5 1 0 2 , 3.33/1.02 5 0 5 1 0 3 1 3 1 1 3 1 5 1 -> 5 4 4 1 2 5 5 0 1 0 3 2 2 2 , 3.33/1.02 0 5 5 2 5 4 5 0 5 2 2 3 1 3 3 4 4 2 -> 5 0 2 4 4 3 2 2 5 1 4 4 1 1 4 3 5 2 , 3.33/1.02 1 4 4 3 3 0 0 3 5 2 1 4 4 4 3 0 1 5 -> 3 5 3 3 0 2 5 1 5 4 4 3 1 2 3 4 3 5 , 3.33/1.02 3 5 1 4 5 2 4 1 3 2 4 4 0 5 4 1 0 3 -> 3 0 5 5 4 5 1 4 3 0 0 5 5 3 3 1 2 3 , 3.33/1.02 5 3 5 3 3 1 5 5 2 2 3 3 4 1 5 1 0 5 -> 3 5 0 4 4 3 4 0 5 2 0 0 2 4 1 5 1 5 , 3.33/1.02 4 1 0 2 0 3 5 5 3 2 1 2 4 5 2 2 3 4 3 0 -> 0 0 5 5 4 1 2 2 1 0 0 4 4 5 0 5 3 5 3 0 } 3.33/1.02 3.33/1.02 3.33/1.02 The system was filtered by the following matrix interpretation 3.33/1.02 of type E_J with J = {1,...,2} and dimension 7: 3.33/1.02 3.33/1.02 0 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 1 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 | 3.33/1.02 \ / 3.33/1.02 1 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 1 0 | 3.33/1.02 | 0 0 0 0 0 0 1 | 3.33/1.02 | 0 0 0 0 0 0 0 | 3.33/1.02 \ / 3.33/1.02 2 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 | 3.33/1.02 \ / 3.33/1.02 3 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 | 3.33/1.02 | 0 0 0 1 0 0 0 | 3.33/1.02 | 0 0 0 0 1 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 | 3.33/1.02 \ / 3.33/1.02 4 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 | 3.33/1.02 \ / 3.33/1.02 5 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 | 3.33/1.02 \ / 3.33/1.02 3.33/1.02 Remains to prove termination of the 11-rule system 3.33/1.02 { 2 2 0 2 5 2 0 -> 2 2 1 2 5 1 3 , 3.33/1.02 4 5 3 2 4 4 2 2 -> 4 0 5 0 0 0 2 2 , 3.33/1.02 1 0 2 5 2 3 0 1 1 -> 1 5 1 2 0 2 4 4 1 , 3.33/1.02 1 3 0 4 3 0 5 3 2 5 3 -> 1 3 0 0 0 3 1 3 3 5 3 , 3.33/1.02 5 1 5 2 0 5 5 5 2 2 5 1 -> 2 2 4 0 0 5 3 0 5 1 0 2 , 3.33/1.02 5 0 5 1 0 3 1 3 1 1 3 1 5 1 -> 5 4 4 1 2 5 5 0 1 0 3 2 2 2 , 3.33/1.02 0 5 5 2 5 4 5 0 5 2 2 3 1 3 3 4 4 2 -> 5 0 2 4 4 3 2 2 5 1 4 4 1 1 4 3 5 2 , 3.33/1.02 1 4 4 3 3 0 0 3 5 2 1 4 4 4 3 0 1 5 -> 3 5 3 3 0 2 5 1 5 4 4 3 1 2 3 4 3 5 , 3.33/1.02 3 5 1 4 5 2 4 1 3 2 4 4 0 5 4 1 0 3 -> 3 0 5 5 4 5 1 4 3 0 0 5 5 3 3 1 2 3 , 3.33/1.02 5 3 5 3 3 1 5 5 2 2 3 3 4 1 5 1 0 5 -> 3 5 0 4 4 3 4 0 5 2 0 0 2 4 1 5 1 5 , 3.33/1.02 4 1 0 2 0 3 5 5 3 2 1 2 4 5 2 2 3 4 3 0 -> 0 0 5 5 4 1 2 2 1 0 0 4 4 5 0 5 3 5 3 0 } 3.33/1.02 3.33/1.02 3.33/1.02 The system was filtered by the following matrix interpretation 3.33/1.02 of type E_J with J = {1,...,2} and dimension 13: 3.33/1.02 3.33/1.02 0 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 0 1 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 1 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 \ / 3.33/1.02 1 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 1 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 \ / 3.33/1.02 2 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 1 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 1 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 1 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 \ / 3.33/1.02 3 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 \ / 3.33/1.02 4 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 \ / 3.33/1.02 5 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 1 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 1 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 1 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 1 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 1 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 1 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 \ / 3.33/1.02 3.33/1.02 Remains to prove termination of the 10-rule system 3.33/1.02 { 2 2 0 2 5 2 0 -> 2 2 1 2 5 1 3 , 3.33/1.02 4 5 3 2 4 4 2 2 -> 4 0 5 0 0 0 2 2 , 3.33/1.02 1 0 2 5 2 3 0 1 1 -> 1 5 1 2 0 2 4 4 1 , 3.33/1.02 1 3 0 4 3 0 5 3 2 5 3 -> 1 3 0 0 0 3 1 3 3 5 3 , 3.33/1.02 5 0 5 1 0 3 1 3 1 1 3 1 5 1 -> 5 4 4 1 2 5 5 0 1 0 3 2 2 2 , 3.33/1.02 0 5 5 2 5 4 5 0 5 2 2 3 1 3 3 4 4 2 -> 5 0 2 4 4 3 2 2 5 1 4 4 1 1 4 3 5 2 , 3.33/1.02 1 4 4 3 3 0 0 3 5 2 1 4 4 4 3 0 1 5 -> 3 5 3 3 0 2 5 1 5 4 4 3 1 2 3 4 3 5 , 3.33/1.02 3 5 1 4 5 2 4 1 3 2 4 4 0 5 4 1 0 3 -> 3 0 5 5 4 5 1 4 3 0 0 5 5 3 3 1 2 3 , 3.33/1.02 5 3 5 3 3 1 5 5 2 2 3 3 4 1 5 1 0 5 -> 3 5 0 4 4 3 4 0 5 2 0 0 2 4 1 5 1 5 , 3.33/1.02 4 1 0 2 0 3 5 5 3 2 1 2 4 5 2 2 3 4 3 0 -> 0 0 5 5 4 1 2 2 1 0 0 4 4 5 0 5 3 5 3 0 } 3.33/1.02 3.33/1.02 3.33/1.02 The system was filtered by the following matrix interpretation 3.33/1.02 of type E_J with J = {1,...,2} and dimension 9: 3.33/1.02 3.33/1.02 0 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 | 3.33/1.02 \ / 3.33/1.02 1 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 | 3.33/1.02 \ / 3.33/1.02 2 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 1 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 1 | 3.33/1.02 | 0 1 0 0 0 0 0 0 0 | 3.33/1.02 \ / 3.33/1.02 3 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 1 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 | 3.33/1.02 \ / 3.33/1.02 4 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 1 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 1 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 1 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 | 3.33/1.02 \ / 3.33/1.02 5 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 1 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 | 3.33/1.02 \ / 3.33/1.02 3.33/1.02 Remains to prove termination of the 9-rule system 3.33/1.02 { 2 2 0 2 5 2 0 -> 2 2 1 2 5 1 3 , 3.33/1.02 1 0 2 5 2 3 0 1 1 -> 1 5 1 2 0 2 4 4 1 , 3.33/1.02 1 3 0 4 3 0 5 3 2 5 3 -> 1 3 0 0 0 3 1 3 3 5 3 , 3.33/1.02 5 0 5 1 0 3 1 3 1 1 3 1 5 1 -> 5 4 4 1 2 5 5 0 1 0 3 2 2 2 , 3.33/1.02 0 5 5 2 5 4 5 0 5 2 2 3 1 3 3 4 4 2 -> 5 0 2 4 4 3 2 2 5 1 4 4 1 1 4 3 5 2 , 3.33/1.02 1 4 4 3 3 0 0 3 5 2 1 4 4 4 3 0 1 5 -> 3 5 3 3 0 2 5 1 5 4 4 3 1 2 3 4 3 5 , 3.33/1.02 3 5 1 4 5 2 4 1 3 2 4 4 0 5 4 1 0 3 -> 3 0 5 5 4 5 1 4 3 0 0 5 5 3 3 1 2 3 , 3.33/1.02 5 3 5 3 3 1 5 5 2 2 3 3 4 1 5 1 0 5 -> 3 5 0 4 4 3 4 0 5 2 0 0 2 4 1 5 1 5 , 3.33/1.02 4 1 0 2 0 3 5 5 3 2 1 2 4 5 2 2 3 4 3 0 -> 0 0 5 5 4 1 2 2 1 0 0 4 4 5 0 5 3 5 3 0 } 3.33/1.02 3.33/1.02 3.33/1.02 The system was filtered by the following matrix interpretation 3.33/1.02 of type E_J with J = {1,...,2} and dimension 10: 3.33/1.02 3.33/1.02 0 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 1 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 1 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 \ / 3.33/1.02 1 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 1 0 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 1 | 3.33/1.02 | 0 1 0 0 0 0 0 0 0 0 | 3.33/1.02 \ / 3.33/1.02 2 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 1 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 1 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 \ / 3.33/1.02 3 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 1 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 \ / 3.33/1.02 4 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 \ / 3.33/1.02 5 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 1 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 \ / 3.33/1.02 3.33/1.02 Remains to prove termination of the 8-rule system 3.33/1.02 { 2 2 0 2 5 2 0 -> 2 2 1 2 5 1 3 , 3.33/1.02 1 3 0 4 3 0 5 3 2 5 3 -> 1 3 0 0 0 3 1 3 3 5 3 , 3.33/1.02 5 0 5 1 0 3 1 3 1 1 3 1 5 1 -> 5 4 4 1 2 5 5 0 1 0 3 2 2 2 , 3.33/1.02 0 5 5 2 5 4 5 0 5 2 2 3 1 3 3 4 4 2 -> 5 0 2 4 4 3 2 2 5 1 4 4 1 1 4 3 5 2 , 3.33/1.02 1 4 4 3 3 0 0 3 5 2 1 4 4 4 3 0 1 5 -> 3 5 3 3 0 2 5 1 5 4 4 3 1 2 3 4 3 5 , 3.33/1.02 3 5 1 4 5 2 4 1 3 2 4 4 0 5 4 1 0 3 -> 3 0 5 5 4 5 1 4 3 0 0 5 5 3 3 1 2 3 , 3.33/1.02 5 3 5 3 3 1 5 5 2 2 3 3 4 1 5 1 0 5 -> 3 5 0 4 4 3 4 0 5 2 0 0 2 4 1 5 1 5 , 3.33/1.02 4 1 0 2 0 3 5 5 3 2 1 2 4 5 2 2 3 4 3 0 -> 0 0 5 5 4 1 2 2 1 0 0 4 4 5 0 5 3 5 3 0 } 3.33/1.02 3.33/1.02 3.33/1.02 The system was filtered by the following matrix interpretation 3.33/1.02 of type E_J with J = {1,...,2} and dimension 15: 3.33/1.02 3.33/1.02 0 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 \ / 3.33/1.02 1 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 \ / 3.33/1.02 2 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 \ / 3.33/1.02 3 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 \ / 3.33/1.02 4 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 \ / 3.33/1.02 5 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | 3.33/1.02 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3.33/1.02 \ / 3.33/1.02 3.33/1.02 Remains to prove termination of the 7-rule system 3.33/1.02 { 2 2 0 2 5 2 0 -> 2 2 1 2 5 1 3 , 3.33/1.02 1 3 0 4 3 0 5 3 2 5 3 -> 1 3 0 0 0 3 1 3 3 5 3 , 3.33/1.02 0 5 5 2 5 4 5 0 5 2 2 3 1 3 3 4 4 2 -> 5 0 2 4 4 3 2 2 5 1 4 4 1 1 4 3 5 2 , 3.33/1.02 1 4 4 3 3 0 0 3 5 2 1 4 4 4 3 0 1 5 -> 3 5 3 3 0 2 5 1 5 4 4 3 1 2 3 4 3 5 , 3.33/1.02 3 5 1 4 5 2 4 1 3 2 4 4 0 5 4 1 0 3 -> 3 0 5 5 4 5 1 4 3 0 0 5 5 3 3 1 2 3 , 3.33/1.02 5 3 5 3 3 1 5 5 2 2 3 3 4 1 5 1 0 5 -> 3 5 0 4 4 3 4 0 5 2 0 0 2 4 1 5 1 5 , 3.33/1.02 4 1 0 2 0 3 5 5 3 2 1 2 4 5 2 2 3 4 3 0 -> 0 0 5 5 4 1 2 2 1 0 0 4 4 5 0 5 3 5 3 0 } 3.33/1.02 3.33/1.02 3.33/1.02 The system was filtered by the following matrix interpretation 3.33/1.02 of type E_J with J = {1,...,2} and dimension 2: 3.33/1.02 3.33/1.02 0 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 46 | 3.33/1.02 | 0 1 | 3.33/1.02 \ / 3.33/1.02 1 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 50 | 3.33/1.02 | 0 1 | 3.33/1.02 \ / 3.33/1.02 2 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 53 | 3.33/1.02 | 0 1 | 3.33/1.02 \ / 3.33/1.02 3 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 34 | 3.33/1.02 | 0 1 | 3.33/1.02 \ / 3.33/1.02 4 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 34 | 3.33/1.02 | 0 1 | 3.33/1.02 \ / 3.33/1.02 5 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 44 | 3.33/1.02 | 0 1 | 3.33/1.02 \ / 3.33/1.02 3.33/1.02 Remains to prove termination of the 2-rule system 3.33/1.02 { 0 5 5 2 5 4 5 0 5 2 2 3 1 3 3 4 4 2 -> 5 0 2 4 4 3 2 2 5 1 4 4 1 1 4 3 5 2 , 3.33/1.02 5 3 5 3 3 1 5 5 2 2 3 3 4 1 5 1 0 5 -> 3 5 0 4 4 3 4 0 5 2 0 0 2 4 1 5 1 5 } 3.33/1.02 3.33/1.02 3.33/1.02 The system was filtered by the following matrix interpretation 3.33/1.02 of type E_J with J = {1,...,2} and dimension 2: 3.33/1.02 3.33/1.02 0 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 | 3.33/1.02 | 0 1 | 3.33/1.02 \ / 3.33/1.02 1 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 | 3.33/1.02 | 0 1 | 3.33/1.02 \ / 3.33/1.02 2 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 | 3.33/1.02 | 0 1 | 3.33/1.02 \ / 3.33/1.02 3 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 1 | 3.33/1.02 | 0 1 | 3.33/1.02 \ / 3.33/1.02 4 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 | 3.33/1.02 | 0 1 | 3.33/1.02 \ / 3.33/1.02 5 is interpreted by 3.33/1.02 / \ 3.33/1.02 | 1 0 | 3.33/1.02 | 0 1 | 3.33/1.02 \ / 3.33/1.02 3.33/1.02 Remains to prove termination of the 0-rule system 3.33/1.02 { } 3.33/1.02 3.33/1.02 3.33/1.02 The system is trivially terminating. 3.46/1.09 EOF