5.12/1.60 YES 5.46/1.65 5.46/1.65 5.46/1.65 The system was filtered by the following matrix interpretation 5.46/1.65 of type E_J with J = {1,...,2} and dimension 2: 5.46/1.65 5.46/1.65 g is interpreted by 5.46/1.65 / \ 5.46/1.65 | 1 0 | 5.46/1.65 | 0 1 | 5.46/1.65 \ / 5.46/1.65 h is interpreted by 5.46/1.65 / \ 5.46/1.65 | 1 0 | 5.46/1.65 | 0 1 | 5.46/1.65 \ / 5.46/1.65 f is interpreted by 5.46/1.65 / \ 5.46/1.65 | 1 0 | 5.46/1.65 | 0 1 | 5.46/1.65 \ / 5.46/1.65 s is interpreted by 5.46/1.65 / \ 5.46/1.65 | 1 0 | 5.46/1.65 | 0 1 | 5.46/1.65 \ / 5.46/1.65 b is interpreted by 5.46/1.65 / \ 5.46/1.65 | 1 1 | 5.46/1.65 | 0 1 | 5.46/1.65 \ / 5.46/1.65 a is interpreted by 5.46/1.65 / \ 5.46/1.65 | 1 3 | 5.46/1.65 | 0 1 | 5.46/1.65 \ / 5.46/1.65 5.46/1.65 Remains to prove termination of the 6-rule system 5.46/1.65 { g h -> g f s , 5.46/1.65 f s s s -> h f s h , 5.46/1.65 f h -> h f s h , 5.46/1.65 h -> , 5.46/1.65 f f s s -> s s s f f , 5.46/1.65 b a -> a b } 5.46/1.65 5.46/1.65 5.46/1.65 The system was filtered by the following matrix interpretation 5.46/1.65 of type E_J with J = {1,...,2} and dimension 3: 5.46/1.65 5.46/1.65 g is interpreted by 5.46/1.65 / \ 5.46/1.65 | 1 0 0 | 5.46/1.65 | 0 1 0 | 5.46/1.65 | 0 0 0 | 5.46/1.65 \ / 5.46/1.65 h is interpreted by 5.46/1.65 / \ 5.46/1.65 | 1 0 0 | 5.46/1.65 | 0 1 0 | 5.46/1.65 | 0 0 1 | 5.46/1.65 \ / 5.46/1.65 f is interpreted by 5.46/1.65 / \ 5.46/1.65 | 1 0 0 | 5.46/1.65 | 0 1 0 | 5.46/1.65 | 0 0 0 | 5.46/1.65 \ / 5.46/1.65 s is interpreted by 5.46/1.65 / \ 5.46/1.65 | 1 0 0 | 5.46/1.65 | 0 1 0 | 5.46/1.65 | 0 0 0 | 5.46/1.65 \ / 5.46/1.65 b is interpreted by 5.46/1.65 / \ 5.46/1.65 | 1 0 1 | 5.46/1.65 | 0 1 0 | 5.46/1.65 | 0 0 1 | 5.46/1.65 \ / 5.46/1.65 a is interpreted by 5.46/1.65 / \ 5.46/1.65 | 1 0 0 | 5.46/1.65 | 0 1 0 | 5.46/1.65 | 0 1 1 | 5.46/1.65 \ / 5.46/1.65 5.46/1.65 Remains to prove termination of the 5-rule system 5.46/1.65 { g h -> g f s , 5.46/1.65 f s s s -> h f s h , 5.46/1.65 f h -> h f s h , 5.46/1.65 h -> , 5.46/1.65 f f s s -> s s s f f } 5.46/1.65 5.46/1.65 5.46/1.65 The system was filtered by the following matrix interpretation 5.46/1.65 of type E_J with J = {1,...,2} and dimension 5: 5.46/1.65 5.46/1.65 g is interpreted by 5.46/1.65 / \ 5.46/1.65 | 1 0 0 0 0 | 5.46/1.65 | 0 1 0 0 0 | 5.46/1.65 | 0 0 0 0 0 | 5.46/1.65 | 0 0 0 0 0 | 5.46/1.65 | 0 0 0 0 0 | 5.46/1.65 \ / 5.46/1.65 h is interpreted by 5.46/1.65 / \ 5.46/1.65 | 1 0 0 0 0 | 5.46/1.65 | 0 1 0 0 0 | 5.46/1.65 | 0 0 1 0 0 | 5.46/1.65 | 0 0 0 1 1 | 5.46/1.65 | 0 0 0 0 1 | 5.46/1.65 \ / 5.46/1.65 f is interpreted by 5.46/1.65 / \ 5.46/1.65 | 1 0 1 0 0 | 5.46/1.65 | 0 1 0 0 0 | 5.46/1.65 | 0 0 0 2 0 | 5.46/1.65 | 0 0 1 0 0 | 5.46/1.65 | 0 0 1 0 0 | 5.46/1.65 \ / 5.46/1.65 s is interpreted by 5.46/1.65 / \ 5.46/1.65 | 1 0 0 0 0 | 5.46/1.65 | 0 1 0 0 0 | 5.46/1.65 | 0 0 0 0 0 | 5.46/1.65 | 0 0 0 0 1 | 5.46/1.65 | 0 1 1 1 0 | 5.46/1.65 \ / 5.46/1.65 b is interpreted by 5.46/1.65 / \ 5.46/1.65 | 1 0 0 0 0 | 5.46/1.65 | 0 1 0 0 0 | 5.46/1.65 | 0 0 0 0 0 | 5.46/1.65 | 0 0 0 0 0 | 5.46/1.65 | 0 0 0 0 0 | 5.46/1.65 \ / 5.46/1.65 a is interpreted by 5.46/1.65 / \ 5.46/1.65 | 1 0 0 0 0 | 5.46/1.65 | 0 1 0 0 0 | 5.46/1.65 | 0 0 0 0 0 | 5.46/1.65 | 0 0 0 0 0 | 5.46/1.65 | 0 0 0 0 0 | 5.46/1.65 \ / 5.46/1.65 5.46/1.65 Remains to prove termination of the 4-rule system 5.46/1.65 { g h -> g f s , 5.46/1.65 f s s s -> h f s h , 5.46/1.65 f h -> h f s h , 5.46/1.65 h -> } 5.46/1.65 5.46/1.65 5.46/1.65 The system was filtered by the following matrix interpretation 5.46/1.65 of type E_J with J = {1,...,2} and dimension 3: 5.46/1.65 5.46/1.65 g is interpreted by 5.46/1.65 / \ 5.46/1.65 | 1 0 0 | 5.46/1.65 | 0 1 0 | 5.46/1.65 | 0 0 0 | 5.46/1.65 \ / 5.46/1.65 h is interpreted by 5.46/1.65 / \ 5.46/1.65 | 1 1 0 | 5.46/1.65 | 0 1 0 | 5.46/1.65 | 0 1 1 | 5.46/1.65 \ / 5.46/1.65 f is interpreted by 5.46/1.65 / \ 5.46/1.65 | 1 0 2 | 5.46/1.65 | 0 1 0 | 5.46/1.65 | 1 1 2 | 5.46/1.65 \ / 5.46/1.65 s is interpreted by 5.46/1.65 / \ 5.46/1.65 | 1 1 0 | 5.46/1.65 | 0 1 0 | 5.46/1.65 | 0 0 0 | 5.46/1.65 \ / 5.46/1.65 b is interpreted by 5.46/1.65 / \ 5.46/1.65 | 1 0 0 | 5.46/1.65 | 0 1 0 | 5.46/1.65 | 0 0 0 | 5.46/1.65 \ / 5.46/1.65 a is interpreted by 5.46/1.65 / \ 5.46/1.65 | 1 0 0 | 5.46/1.65 | 0 1 0 | 5.46/1.65 | 0 0 0 | 5.46/1.65 \ / 5.46/1.65 5.46/1.65 Remains to prove termination of the 3-rule system 5.46/1.65 { g h -> g f s , 5.46/1.65 f s s s -> h f s h , 5.46/1.65 f h -> h f s h } 5.46/1.65 5.46/1.65 5.46/1.65 The system was filtered by the following matrix interpretation 5.46/1.65 of type E_J with J = {1,...,2} and dimension 6: 5.46/1.65 5.46/1.65 g is interpreted by 5.46/1.65 / \ 5.46/1.65 | 1 0 0 0 0 1 | 5.46/1.65 | 0 1 0 0 0 0 | 5.46/1.65 | 0 0 0 0 0 0 | 5.46/1.65 | 0 0 0 0 0 0 | 5.46/1.65 | 0 0 0 0 0 0 | 5.46/1.65 | 0 0 0 0 0 0 | 5.46/1.65 \ / 5.46/1.65 h is interpreted by 5.46/1.66 / \ 5.46/1.66 | 1 0 0 0 0 0 | 5.46/1.66 | 0 1 0 0 0 0 | 5.46/1.66 | 0 0 0 0 0 0 | 5.46/1.66 | 0 0 0 0 0 0 | 5.46/1.66 | 0 0 0 0 0 0 | 5.46/1.66 | 0 0 0 1 0 0 | 5.46/1.66 \ / 5.46/1.66 f is interpreted by 5.46/1.66 / \ 5.46/1.66 | 1 0 1 0 0 0 | 5.46/1.66 | 0 1 0 0 0 0 | 5.46/1.66 | 0 0 0 0 0 0 | 5.46/1.66 | 0 0 0 0 0 0 | 5.46/1.66 | 0 0 0 0 0 0 | 5.46/1.66 | 0 0 0 0 0 0 | 5.46/1.66 \ / 5.46/1.66 s is interpreted by 5.46/1.66 / \ 5.46/1.66 | 1 0 0 0 0 0 | 5.46/1.66 | 0 1 0 0 0 0 | 5.46/1.66 | 0 0 0 1 0 0 | 5.46/1.66 | 0 0 0 0 1 0 | 5.46/1.66 | 0 1 0 0 0 0 | 5.46/1.66 | 0 0 0 0 0 0 | 5.46/1.66 \ / 5.46/1.66 b is interpreted by 5.46/1.66 / \ 5.46/1.66 | 1 0 0 0 0 0 | 5.46/1.66 | 0 1 0 0 0 0 | 5.46/1.66 | 0 0 0 0 0 0 | 5.46/1.66 | 0 0 0 0 0 0 | 5.46/1.66 | 0 0 0 0 0 0 | 5.46/1.66 | 0 0 0 0 0 0 | 5.46/1.66 \ / 5.46/1.66 a is interpreted by 5.46/1.66 / \ 5.46/1.66 | 1 0 0 0 0 0 | 5.46/1.66 | 0 1 0 0 0 0 | 5.46/1.66 | 0 0 0 0 0 0 | 5.46/1.66 | 0 0 0 0 0 0 | 5.46/1.66 | 0 0 0 0 0 0 | 5.46/1.66 | 0 0 0 0 0 0 | 5.46/1.66 \ / 5.46/1.66 5.46/1.66 Remains to prove termination of the 2-rule system 5.46/1.66 { g h -> g f s , 5.46/1.66 f h -> h f s h } 5.46/1.66 5.46/1.66 5.46/1.66 The system was filtered by the following matrix interpretation 5.46/1.66 of type E_J with J = {1,...,2} and dimension 3: 5.46/1.66 5.46/1.66 g is interpreted by 5.46/1.66 / \ 5.46/1.66 | 1 0 1 | 5.46/1.66 | 0 1 0 | 5.46/1.66 | 0 0 0 | 5.46/1.66 \ / 5.46/1.66 h is interpreted by 5.46/1.66 / \ 5.46/1.66 | 1 0 0 | 5.46/1.66 | 0 1 0 | 5.46/1.66 | 0 1 0 | 5.46/1.66 \ / 5.46/1.66 f is interpreted by 5.46/1.66 / \ 5.46/1.66 | 1 0 0 | 5.46/1.66 | 0 1 0 | 5.46/1.66 | 0 0 1 | 5.46/1.66 \ / 5.46/1.66 s is interpreted by 5.46/1.66 / \ 5.46/1.66 | 1 0 0 | 5.46/1.66 | 0 1 0 | 5.46/1.66 | 0 0 0 | 5.46/1.66 \ / 5.46/1.66 b is interpreted by 5.46/1.66 / \ 5.46/1.66 | 1 0 0 | 5.46/1.66 | 0 1 0 | 5.46/1.66 | 0 0 0 | 5.46/1.66 \ / 5.46/1.66 a is interpreted by 5.46/1.66 / \ 5.46/1.66 | 1 0 0 | 5.46/1.66 | 0 1 0 | 5.46/1.66 | 0 0 0 | 5.46/1.66 \ / 5.46/1.66 5.46/1.66 Remains to prove termination of the 1-rule system 5.46/1.66 { f h -> h f s h } 5.46/1.66 5.46/1.66 5.46/1.66 The system was filtered by the following matrix interpretation 5.46/1.66 of type E_J with J = {1,...,2} and dimension 3: 5.46/1.66 5.46/1.66 g is interpreted by 5.46/1.66 / \ 5.46/1.66 | 1 0 0 | 5.46/1.66 | 0 1 0 | 5.46/1.66 | 0 0 0 | 5.46/1.66 \ / 5.46/1.66 h is interpreted by 5.46/1.66 / \ 5.46/1.66 | 1 0 0 | 5.46/1.66 | 0 1 0 | 5.46/1.66 | 0 1 0 | 5.46/1.66 \ / 5.46/1.66 f is interpreted by 5.46/1.66 / \ 5.46/1.66 | 1 0 1 | 5.46/1.66 | 0 1 0 | 5.46/1.66 | 0 1 0 | 5.46/1.66 \ / 5.46/1.66 s is interpreted by 5.46/1.66 / \ 5.46/1.66 | 1 0 0 | 5.46/1.66 | 0 1 0 | 5.46/1.66 | 0 0 0 | 5.46/1.66 \ / 5.46/1.66 b is interpreted by 5.46/1.66 / \ 5.46/1.66 | 1 0 0 | 5.46/1.66 | 0 1 0 | 5.46/1.66 | 0 0 0 | 5.46/1.66 \ / 5.46/1.66 a is interpreted by 5.46/1.66 / \ 5.46/1.66 | 1 0 0 | 5.46/1.66 | 0 1 0 | 5.46/1.66 | 0 0 0 | 5.46/1.66 \ / 5.46/1.66 5.46/1.66 Remains to prove termination of the 0-rule system 5.46/1.66 { } 5.46/1.66 5.46/1.66 5.46/1.66 The system is trivially terminating. 5.46/1.67 EOF