10.26/2.82 YES 10.39/2.91 10.39/2.91 10.39/2.91 The system was inverted. 10.39/2.91 10.39/2.91 Remains to prove termination of the 6-rule system 10.39/2.91 { c a a -> c c b , 10.39/2.91 c a b -> c b a , 10.39/2.91 b b a -> b b c , 10.39/2.91 b c b -> a a a , 10.39/2.91 c a a ->= a b a , 10.39/2.91 a b c ->= a a c } 10.39/2.91 10.39/2.91 10.39/2.91 Applying context closure of depth 1 in the following form: System R over Sigma 10.39/2.91 maps to { fold(xly) -> fold(xry) | l -> r in R, x,y in Sigma } over Sigma^2, 10.39/2.91 where fold(a_1,...,a_n) = (a_1,a_2)...(a_{n-1}a_{n}) 10.39/2.91 10.39/2.91 Remains to prove termination of the 54-rule system 10.39/2.91 { [c, c] [c, c] [c, b] [b, c] -> [c, c] [c, a] [a, a] [a, c] , 10.39/2.91 [c, c] [c, b] [b, a] [a, c] -> [c, c] [c, a] [a, b] [b, c] , 10.39/2.91 [c, b] [b, b] [b, c] [c, c] -> [c, b] [b, b] [b, a] [a, c] , 10.39/2.91 [c, a] [a, a] [a, a] [a, c] -> [c, b] [b, c] [c, b] [b, c] , 10.39/2.91 [c, a] [a, b] [b, a] [a, c] ->= [c, c] [c, a] [a, a] [a, c] , 10.39/2.91 [c, a] [a, a] [a, c] [c, c] ->= [c, a] [a, b] [b, c] [c, c] , 10.39/2.91 [c, c] [c, c] [c, b] [b, b] -> [c, c] [c, a] [a, a] [a, b] , 10.39/2.91 [c, c] [c, b] [b, a] [a, b] -> [c, c] [c, a] [a, b] [b, b] , 10.39/2.91 [c, b] [b, b] [b, c] [c, b] -> [c, b] [b, b] [b, a] [a, b] , 10.39/2.91 [c, a] [a, a] [a, a] [a, b] -> [c, b] [b, c] [c, b] [b, b] , 10.39/2.91 [c, a] [a, b] [b, a] [a, b] ->= [c, c] [c, a] [a, a] [a, b] , 10.39/2.91 [c, a] [a, a] [a, c] [c, b] ->= [c, a] [a, b] [b, c] [c, b] , 10.39/2.91 [c, c] [c, c] [c, b] [b, a] -> [c, c] [c, a] [a, a] [a, a] , 10.39/2.91 [c, c] [c, b] [b, a] [a, a] -> [c, c] [c, a] [a, b] [b, a] , 10.39/2.91 [c, b] [b, b] [b, c] [c, a] -> [c, b] [b, b] [b, a] [a, a] , 10.39/2.91 [c, a] [a, a] [a, a] [a, a] -> [c, b] [b, c] [c, b] [b, a] , 10.39/2.91 [c, a] [a, b] [b, a] [a, a] ->= [c, c] [c, a] [a, a] [a, a] , 10.39/2.91 [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.39/2.91 [b, c] [c, c] [c, b] [b, c] -> [b, c] [c, a] [a, a] [a, c] , 10.39/2.91 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.39/2.91 [b, b] [b, b] [b, c] [c, c] -> [b, b] [b, b] [b, a] [a, c] , 10.39/2.91 [b, a] [a, a] [a, a] [a, c] -> [b, b] [b, c] [c, b] [b, c] , 10.39/2.91 [b, a] [a, b] [b, a] [a, c] ->= [b, c] [c, a] [a, a] [a, c] , 10.39/2.91 [b, a] [a, a] [a, c] [c, c] ->= [b, a] [a, b] [b, c] [c, c] , 10.39/2.91 [b, c] [c, c] [c, b] [b, b] -> [b, c] [c, a] [a, a] [a, b] , 10.39/2.91 [b, c] [c, b] [b, a] [a, b] -> [b, c] [c, a] [a, b] [b, b] , 10.39/2.91 [b, b] [b, b] [b, c] [c, b] -> [b, b] [b, b] [b, a] [a, b] , 10.39/2.91 [b, a] [a, a] [a, a] [a, b] -> [b, b] [b, c] [c, b] [b, b] , 10.39/2.91 [b, a] [a, b] [b, a] [a, b] ->= [b, c] [c, a] [a, a] [a, b] , 10.39/2.91 [b, a] [a, a] [a, c] [c, b] ->= [b, a] [a, b] [b, c] [c, b] , 10.39/2.91 [b, c] [c, c] [c, b] [b, a] -> [b, c] [c, a] [a, a] [a, a] , 10.39/2.91 [b, c] [c, b] [b, a] [a, a] -> [b, c] [c, a] [a, b] [b, a] , 10.39/2.91 [b, b] [b, b] [b, c] [c, a] -> [b, b] [b, b] [b, a] [a, a] , 10.39/2.91 [b, a] [a, a] [a, a] [a, a] -> [b, b] [b, c] [c, b] [b, a] , 10.39/2.91 [b, a] [a, b] [b, a] [a, a] ->= [b, c] [c, a] [a, a] [a, a] , 10.39/2.91 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.39/2.91 [a, c] [c, c] [c, b] [b, c] -> [a, c] [c, a] [a, a] [a, c] , 10.39/2.91 [a, c] [c, b] [b, a] [a, c] -> [a, c] [c, a] [a, b] [b, c] , 10.39/2.91 [a, b] [b, b] [b, c] [c, c] -> [a, b] [b, b] [b, a] [a, c] , 10.39/2.91 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.39/2.91 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.39/2.91 [a, a] [a, a] [a, c] [c, c] ->= [a, a] [a, b] [b, c] [c, c] , 10.39/2.91 [a, c] [c, c] [c, b] [b, b] -> [a, c] [c, a] [a, a] [a, b] , 10.39/2.91 [a, c] [c, b] [b, a] [a, b] -> [a, c] [c, a] [a, b] [b, b] , 10.39/2.91 [a, b] [b, b] [b, c] [c, b] -> [a, b] [b, b] [b, a] [a, b] , 10.39/2.91 [a, a] [a, a] [a, a] [a, b] -> [a, b] [b, c] [c, b] [b, b] , 10.39/2.91 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.39/2.91 [a, a] [a, a] [a, c] [c, b] ->= [a, a] [a, b] [b, c] [c, b] , 10.39/2.91 [a, c] [c, c] [c, b] [b, a] -> [a, c] [c, a] [a, a] [a, a] , 10.39/2.91 [a, c] [c, b] [b, a] [a, a] -> [a, c] [c, a] [a, b] [b, a] , 10.39/2.91 [a, b] [b, b] [b, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] , 10.39/2.91 [a, a] [a, a] [a, a] [a, a] -> [a, b] [b, c] [c, b] [b, a] , 10.39/2.91 [a, a] [a, b] [b, a] [a, a] ->= [a, c] [c, a] [a, a] [a, a] , 10.39/2.91 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.39/2.91 10.39/2.91 10.39/2.91 10.39/2.91 The system was filtered by the following matrix interpretation 10.39/2.91 of type E_J with J = {1,...,2} and dimension 5: 10.39/2.91 10.39/2.91 [c, c] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 1 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 1 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [c, b] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 1 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [b, c] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [c, a] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [a, a] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [a, c] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [b, a] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [a, b] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [b, b] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 10.39/2.91 Remains to prove termination of the 53-rule system 10.39/2.91 { [c, c] [c, c] [c, b] [b, c] -> [c, c] [c, a] [a, a] [a, c] , 10.39/2.91 [c, c] [c, b] [b, a] [a, c] -> [c, c] [c, a] [a, b] [b, c] , 10.39/2.91 [c, b] [b, b] [b, c] [c, c] -> [c, b] [b, b] [b, a] [a, c] , 10.39/2.91 [c, a] [a, a] [a, a] [a, c] -> [c, b] [b, c] [c, b] [b, c] , 10.39/2.91 [c, a] [a, b] [b, a] [a, c] ->= [c, c] [c, a] [a, a] [a, c] , 10.39/2.91 [c, a] [a, a] [a, c] [c, c] ->= [c, a] [a, b] [b, c] [c, c] , 10.39/2.91 [c, c] [c, c] [c, b] [b, b] -> [c, c] [c, a] [a, a] [a, b] , 10.39/2.91 [c, c] [c, b] [b, a] [a, b] -> [c, c] [c, a] [a, b] [b, b] , 10.39/2.91 [c, b] [b, b] [b, c] [c, b] -> [c, b] [b, b] [b, a] [a, b] , 10.39/2.91 [c, a] [a, a] [a, a] [a, b] -> [c, b] [b, c] [c, b] [b, b] , 10.39/2.91 [c, a] [a, b] [b, a] [a, b] ->= [c, c] [c, a] [a, a] [a, b] , 10.39/2.91 [c, a] [a, a] [a, c] [c, b] ->= [c, a] [a, b] [b, c] [c, b] , 10.39/2.91 [c, c] [c, b] [b, a] [a, a] -> [c, c] [c, a] [a, b] [b, a] , 10.39/2.91 [c, b] [b, b] [b, c] [c, a] -> [c, b] [b, b] [b, a] [a, a] , 10.39/2.91 [c, a] [a, a] [a, a] [a, a] -> [c, b] [b, c] [c, b] [b, a] , 10.39/2.91 [c, a] [a, b] [b, a] [a, a] ->= [c, c] [c, a] [a, a] [a, a] , 10.39/2.91 [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.39/2.91 [b, c] [c, c] [c, b] [b, c] -> [b, c] [c, a] [a, a] [a, c] , 10.39/2.91 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.39/2.91 [b, b] [b, b] [b, c] [c, c] -> [b, b] [b, b] [b, a] [a, c] , 10.39/2.91 [b, a] [a, a] [a, a] [a, c] -> [b, b] [b, c] [c, b] [b, c] , 10.39/2.91 [b, a] [a, b] [b, a] [a, c] ->= [b, c] [c, a] [a, a] [a, c] , 10.39/2.91 [b, a] [a, a] [a, c] [c, c] ->= [b, a] [a, b] [b, c] [c, c] , 10.39/2.91 [b, c] [c, c] [c, b] [b, b] -> [b, c] [c, a] [a, a] [a, b] , 10.39/2.91 [b, c] [c, b] [b, a] [a, b] -> [b, c] [c, a] [a, b] [b, b] , 10.39/2.91 [b, b] [b, b] [b, c] [c, b] -> [b, b] [b, b] [b, a] [a, b] , 10.39/2.91 [b, a] [a, a] [a, a] [a, b] -> [b, b] [b, c] [c, b] [b, b] , 10.39/2.91 [b, a] [a, b] [b, a] [a, b] ->= [b, c] [c, a] [a, a] [a, b] , 10.39/2.91 [b, a] [a, a] [a, c] [c, b] ->= [b, a] [a, b] [b, c] [c, b] , 10.39/2.91 [b, c] [c, c] [c, b] [b, a] -> [b, c] [c, a] [a, a] [a, a] , 10.39/2.91 [b, c] [c, b] [b, a] [a, a] -> [b, c] [c, a] [a, b] [b, a] , 10.39/2.91 [b, b] [b, b] [b, c] [c, a] -> [b, b] [b, b] [b, a] [a, a] , 10.39/2.91 [b, a] [a, a] [a, a] [a, a] -> [b, b] [b, c] [c, b] [b, a] , 10.39/2.91 [b, a] [a, b] [b, a] [a, a] ->= [b, c] [c, a] [a, a] [a, a] , 10.39/2.91 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.39/2.91 [a, c] [c, c] [c, b] [b, c] -> [a, c] [c, a] [a, a] [a, c] , 10.39/2.91 [a, c] [c, b] [b, a] [a, c] -> [a, c] [c, a] [a, b] [b, c] , 10.39/2.91 [a, b] [b, b] [b, c] [c, c] -> [a, b] [b, b] [b, a] [a, c] , 10.39/2.91 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.39/2.91 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.39/2.91 [a, a] [a, a] [a, c] [c, c] ->= [a, a] [a, b] [b, c] [c, c] , 10.39/2.91 [a, c] [c, c] [c, b] [b, b] -> [a, c] [c, a] [a, a] [a, b] , 10.39/2.91 [a, c] [c, b] [b, a] [a, b] -> [a, c] [c, a] [a, b] [b, b] , 10.39/2.91 [a, b] [b, b] [b, c] [c, b] -> [a, b] [b, b] [b, a] [a, b] , 10.39/2.91 [a, a] [a, a] [a, a] [a, b] -> [a, b] [b, c] [c, b] [b, b] , 10.39/2.91 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.39/2.91 [a, a] [a, a] [a, c] [c, b] ->= [a, a] [a, b] [b, c] [c, b] , 10.39/2.91 [a, c] [c, c] [c, b] [b, a] -> [a, c] [c, a] [a, a] [a, a] , 10.39/2.91 [a, c] [c, b] [b, a] [a, a] -> [a, c] [c, a] [a, b] [b, a] , 10.39/2.91 [a, b] [b, b] [b, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] , 10.39/2.91 [a, a] [a, a] [a, a] [a, a] -> [a, b] [b, c] [c, b] [b, a] , 10.39/2.91 [a, a] [a, b] [b, a] [a, a] ->= [a, c] [c, a] [a, a] [a, a] , 10.39/2.91 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.39/2.91 10.39/2.91 10.39/2.91 The system was filtered by the following matrix interpretation 10.39/2.91 of type E_J with J = {1,...,2} and dimension 5: 10.39/2.91 10.39/2.91 [c, c] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 1 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [c, b] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 1 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [b, c] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [c, a] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [a, a] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [a, c] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [b, a] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 1 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [a, b] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [b, b] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 10.39/2.91 Remains to prove termination of the 52-rule system 10.39/2.91 { [c, c] [c, c] [c, b] [b, c] -> [c, c] [c, a] [a, a] [a, c] , 10.39/2.91 [c, c] [c, b] [b, a] [a, c] -> [c, c] [c, a] [a, b] [b, c] , 10.39/2.91 [c, b] [b, b] [b, c] [c, c] -> [c, b] [b, b] [b, a] [a, c] , 10.39/2.91 [c, a] [a, a] [a, a] [a, c] -> [c, b] [b, c] [c, b] [b, c] , 10.39/2.91 [c, a] [a, b] [b, a] [a, c] ->= [c, c] [c, a] [a, a] [a, c] , 10.39/2.91 [c, a] [a, a] [a, c] [c, c] ->= [c, a] [a, b] [b, c] [c, c] , 10.39/2.91 [c, c] [c, c] [c, b] [b, b] -> [c, c] [c, a] [a, a] [a, b] , 10.39/2.91 [c, c] [c, b] [b, a] [a, b] -> [c, c] [c, a] [a, b] [b, b] , 10.39/2.91 [c, b] [b, b] [b, c] [c, b] -> [c, b] [b, b] [b, a] [a, b] , 10.39/2.91 [c, a] [a, a] [a, a] [a, b] -> [c, b] [b, c] [c, b] [b, b] , 10.39/2.91 [c, a] [a, b] [b, a] [a, b] ->= [c, c] [c, a] [a, a] [a, b] , 10.39/2.91 [c, a] [a, a] [a, c] [c, b] ->= [c, a] [a, b] [b, c] [c, b] , 10.39/2.91 [c, b] [b, b] [b, c] [c, a] -> [c, b] [b, b] [b, a] [a, a] , 10.39/2.91 [c, a] [a, a] [a, a] [a, a] -> [c, b] [b, c] [c, b] [b, a] , 10.39/2.91 [c, a] [a, b] [b, a] [a, a] ->= [c, c] [c, a] [a, a] [a, a] , 10.39/2.91 [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.39/2.91 [b, c] [c, c] [c, b] [b, c] -> [b, c] [c, a] [a, a] [a, c] , 10.39/2.91 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.39/2.91 [b, b] [b, b] [b, c] [c, c] -> [b, b] [b, b] [b, a] [a, c] , 10.39/2.91 [b, a] [a, a] [a, a] [a, c] -> [b, b] [b, c] [c, b] [b, c] , 10.39/2.91 [b, a] [a, b] [b, a] [a, c] ->= [b, c] [c, a] [a, a] [a, c] , 10.39/2.91 [b, a] [a, a] [a, c] [c, c] ->= [b, a] [a, b] [b, c] [c, c] , 10.39/2.91 [b, c] [c, c] [c, b] [b, b] -> [b, c] [c, a] [a, a] [a, b] , 10.39/2.91 [b, c] [c, b] [b, a] [a, b] -> [b, c] [c, a] [a, b] [b, b] , 10.39/2.91 [b, b] [b, b] [b, c] [c, b] -> [b, b] [b, b] [b, a] [a, b] , 10.39/2.91 [b, a] [a, a] [a, a] [a, b] -> [b, b] [b, c] [c, b] [b, b] , 10.39/2.91 [b, a] [a, b] [b, a] [a, b] ->= [b, c] [c, a] [a, a] [a, b] , 10.39/2.91 [b, a] [a, a] [a, c] [c, b] ->= [b, a] [a, b] [b, c] [c, b] , 10.39/2.91 [b, c] [c, c] [c, b] [b, a] -> [b, c] [c, a] [a, a] [a, a] , 10.39/2.91 [b, c] [c, b] [b, a] [a, a] -> [b, c] [c, a] [a, b] [b, a] , 10.39/2.91 [b, b] [b, b] [b, c] [c, a] -> [b, b] [b, b] [b, a] [a, a] , 10.39/2.91 [b, a] [a, a] [a, a] [a, a] -> [b, b] [b, c] [c, b] [b, a] , 10.39/2.91 [b, a] [a, b] [b, a] [a, a] ->= [b, c] [c, a] [a, a] [a, a] , 10.39/2.91 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.39/2.91 [a, c] [c, c] [c, b] [b, c] -> [a, c] [c, a] [a, a] [a, c] , 10.39/2.91 [a, c] [c, b] [b, a] [a, c] -> [a, c] [c, a] [a, b] [b, c] , 10.39/2.91 [a, b] [b, b] [b, c] [c, c] -> [a, b] [b, b] [b, a] [a, c] , 10.39/2.91 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.39/2.91 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.39/2.91 [a, a] [a, a] [a, c] [c, c] ->= [a, a] [a, b] [b, c] [c, c] , 10.39/2.91 [a, c] [c, c] [c, b] [b, b] -> [a, c] [c, a] [a, a] [a, b] , 10.39/2.91 [a, c] [c, b] [b, a] [a, b] -> [a, c] [c, a] [a, b] [b, b] , 10.39/2.91 [a, b] [b, b] [b, c] [c, b] -> [a, b] [b, b] [b, a] [a, b] , 10.39/2.91 [a, a] [a, a] [a, a] [a, b] -> [a, b] [b, c] [c, b] [b, b] , 10.39/2.91 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.39/2.91 [a, a] [a, a] [a, c] [c, b] ->= [a, a] [a, b] [b, c] [c, b] , 10.39/2.91 [a, c] [c, c] [c, b] [b, a] -> [a, c] [c, a] [a, a] [a, a] , 10.39/2.91 [a, c] [c, b] [b, a] [a, a] -> [a, c] [c, a] [a, b] [b, a] , 10.39/2.91 [a, b] [b, b] [b, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] , 10.39/2.91 [a, a] [a, a] [a, a] [a, a] -> [a, b] [b, c] [c, b] [b, a] , 10.39/2.91 [a, a] [a, b] [b, a] [a, a] ->= [a, c] [c, a] [a, a] [a, a] , 10.39/2.91 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.39/2.91 10.39/2.91 10.39/2.91 The system was filtered by the following matrix interpretation 10.39/2.91 of type E_J with J = {1,...,2} and dimension 5: 10.39/2.91 10.39/2.91 [c, c] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 1 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [c, b] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 1 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [b, c] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [c, a] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [a, a] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [a, c] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [b, a] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 1 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [a, b] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [b, b] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 10.39/2.91 Remains to prove termination of the 51-rule system 10.39/2.91 { [c, c] [c, c] [c, b] [b, c] -> [c, c] [c, a] [a, a] [a, c] , 10.39/2.91 [c, b] [b, b] [b, c] [c, c] -> [c, b] [b, b] [b, a] [a, c] , 10.39/2.91 [c, a] [a, a] [a, a] [a, c] -> [c, b] [b, c] [c, b] [b, c] , 10.39/2.91 [c, a] [a, b] [b, a] [a, c] ->= [c, c] [c, a] [a, a] [a, c] , 10.39/2.91 [c, a] [a, a] [a, c] [c, c] ->= [c, a] [a, b] [b, c] [c, c] , 10.39/2.91 [c, c] [c, c] [c, b] [b, b] -> [c, c] [c, a] [a, a] [a, b] , 10.39/2.91 [c, c] [c, b] [b, a] [a, b] -> [c, c] [c, a] [a, b] [b, b] , 10.39/2.91 [c, b] [b, b] [b, c] [c, b] -> [c, b] [b, b] [b, a] [a, b] , 10.39/2.91 [c, a] [a, a] [a, a] [a, b] -> [c, b] [b, c] [c, b] [b, b] , 10.39/2.91 [c, a] [a, b] [b, a] [a, b] ->= [c, c] [c, a] [a, a] [a, b] , 10.39/2.91 [c, a] [a, a] [a, c] [c, b] ->= [c, a] [a, b] [b, c] [c, b] , 10.39/2.91 [c, b] [b, b] [b, c] [c, a] -> [c, b] [b, b] [b, a] [a, a] , 10.39/2.91 [c, a] [a, a] [a, a] [a, a] -> [c, b] [b, c] [c, b] [b, a] , 10.39/2.91 [c, a] [a, b] [b, a] [a, a] ->= [c, c] [c, a] [a, a] [a, a] , 10.39/2.91 [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.39/2.91 [b, c] [c, c] [c, b] [b, c] -> [b, c] [c, a] [a, a] [a, c] , 10.39/2.91 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.39/2.91 [b, b] [b, b] [b, c] [c, c] -> [b, b] [b, b] [b, a] [a, c] , 10.39/2.91 [b, a] [a, a] [a, a] [a, c] -> [b, b] [b, c] [c, b] [b, c] , 10.39/2.91 [b, a] [a, b] [b, a] [a, c] ->= [b, c] [c, a] [a, a] [a, c] , 10.39/2.91 [b, a] [a, a] [a, c] [c, c] ->= [b, a] [a, b] [b, c] [c, c] , 10.39/2.91 [b, c] [c, c] [c, b] [b, b] -> [b, c] [c, a] [a, a] [a, b] , 10.39/2.91 [b, c] [c, b] [b, a] [a, b] -> [b, c] [c, a] [a, b] [b, b] , 10.39/2.91 [b, b] [b, b] [b, c] [c, b] -> [b, b] [b, b] [b, a] [a, b] , 10.39/2.91 [b, a] [a, a] [a, a] [a, b] -> [b, b] [b, c] [c, b] [b, b] , 10.39/2.91 [b, a] [a, b] [b, a] [a, b] ->= [b, c] [c, a] [a, a] [a, b] , 10.39/2.91 [b, a] [a, a] [a, c] [c, b] ->= [b, a] [a, b] [b, c] [c, b] , 10.39/2.91 [b, c] [c, c] [c, b] [b, a] -> [b, c] [c, a] [a, a] [a, a] , 10.39/2.91 [b, c] [c, b] [b, a] [a, a] -> [b, c] [c, a] [a, b] [b, a] , 10.39/2.91 [b, b] [b, b] [b, c] [c, a] -> [b, b] [b, b] [b, a] [a, a] , 10.39/2.91 [b, a] [a, a] [a, a] [a, a] -> [b, b] [b, c] [c, b] [b, a] , 10.39/2.91 [b, a] [a, b] [b, a] [a, a] ->= [b, c] [c, a] [a, a] [a, a] , 10.39/2.91 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.39/2.91 [a, c] [c, c] [c, b] [b, c] -> [a, c] [c, a] [a, a] [a, c] , 10.39/2.91 [a, c] [c, b] [b, a] [a, c] -> [a, c] [c, a] [a, b] [b, c] , 10.39/2.91 [a, b] [b, b] [b, c] [c, c] -> [a, b] [b, b] [b, a] [a, c] , 10.39/2.91 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.39/2.91 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.39/2.91 [a, a] [a, a] [a, c] [c, c] ->= [a, a] [a, b] [b, c] [c, c] , 10.39/2.91 [a, c] [c, c] [c, b] [b, b] -> [a, c] [c, a] [a, a] [a, b] , 10.39/2.91 [a, c] [c, b] [b, a] [a, b] -> [a, c] [c, a] [a, b] [b, b] , 10.39/2.91 [a, b] [b, b] [b, c] [c, b] -> [a, b] [b, b] [b, a] [a, b] , 10.39/2.91 [a, a] [a, a] [a, a] [a, b] -> [a, b] [b, c] [c, b] [b, b] , 10.39/2.91 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.39/2.91 [a, a] [a, a] [a, c] [c, b] ->= [a, a] [a, b] [b, c] [c, b] , 10.39/2.91 [a, c] [c, c] [c, b] [b, a] -> [a, c] [c, a] [a, a] [a, a] , 10.39/2.91 [a, c] [c, b] [b, a] [a, a] -> [a, c] [c, a] [a, b] [b, a] , 10.39/2.91 [a, b] [b, b] [b, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] , 10.39/2.91 [a, a] [a, a] [a, a] [a, a] -> [a, b] [b, c] [c, b] [b, a] , 10.39/2.91 [a, a] [a, b] [b, a] [a, a] ->= [a, c] [c, a] [a, a] [a, a] , 10.39/2.91 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.39/2.91 10.39/2.91 10.39/2.91 The system was filtered by the following matrix interpretation 10.39/2.91 of type E_J with J = {1,...,2} and dimension 5: 10.39/2.91 10.39/2.91 [c, c] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 1 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 1 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [c, b] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 1 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [b, c] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [c, a] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [a, a] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [a, c] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [b, a] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [a, b] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [b, b] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 \ / 10.39/2.91 10.39/2.91 Remains to prove termination of the 50-rule system 10.39/2.91 { [c, c] [c, c] [c, b] [b, c] -> [c, c] [c, a] [a, a] [a, c] , 10.39/2.91 [c, b] [b, b] [b, c] [c, c] -> [c, b] [b, b] [b, a] [a, c] , 10.39/2.91 [c, a] [a, a] [a, a] [a, c] -> [c, b] [b, c] [c, b] [b, c] , 10.39/2.91 [c, a] [a, b] [b, a] [a, c] ->= [c, c] [c, a] [a, a] [a, c] , 10.39/2.91 [c, a] [a, a] [a, c] [c, c] ->= [c, a] [a, b] [b, c] [c, c] , 10.39/2.91 [c, c] [c, b] [b, a] [a, b] -> [c, c] [c, a] [a, b] [b, b] , 10.39/2.91 [c, b] [b, b] [b, c] [c, b] -> [c, b] [b, b] [b, a] [a, b] , 10.39/2.91 [c, a] [a, a] [a, a] [a, b] -> [c, b] [b, c] [c, b] [b, b] , 10.39/2.91 [c, a] [a, b] [b, a] [a, b] ->= [c, c] [c, a] [a, a] [a, b] , 10.39/2.91 [c, a] [a, a] [a, c] [c, b] ->= [c, a] [a, b] [b, c] [c, b] , 10.39/2.91 [c, b] [b, b] [b, c] [c, a] -> [c, b] [b, b] [b, a] [a, a] , 10.39/2.91 [c, a] [a, a] [a, a] [a, a] -> [c, b] [b, c] [c, b] [b, a] , 10.39/2.91 [c, a] [a, b] [b, a] [a, a] ->= [c, c] [c, a] [a, a] [a, a] , 10.39/2.91 [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.39/2.91 [b, c] [c, c] [c, b] [b, c] -> [b, c] [c, a] [a, a] [a, c] , 10.39/2.91 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.39/2.91 [b, b] [b, b] [b, c] [c, c] -> [b, b] [b, b] [b, a] [a, c] , 10.39/2.91 [b, a] [a, a] [a, a] [a, c] -> [b, b] [b, c] [c, b] [b, c] , 10.39/2.91 [b, a] [a, b] [b, a] [a, c] ->= [b, c] [c, a] [a, a] [a, c] , 10.39/2.91 [b, a] [a, a] [a, c] [c, c] ->= [b, a] [a, b] [b, c] [c, c] , 10.39/2.91 [b, c] [c, c] [c, b] [b, b] -> [b, c] [c, a] [a, a] [a, b] , 10.39/2.91 [b, c] [c, b] [b, a] [a, b] -> [b, c] [c, a] [a, b] [b, b] , 10.39/2.91 [b, b] [b, b] [b, c] [c, b] -> [b, b] [b, b] [b, a] [a, b] , 10.39/2.91 [b, a] [a, a] [a, a] [a, b] -> [b, b] [b, c] [c, b] [b, b] , 10.39/2.91 [b, a] [a, b] [b, a] [a, b] ->= [b, c] [c, a] [a, a] [a, b] , 10.39/2.91 [b, a] [a, a] [a, c] [c, b] ->= [b, a] [a, b] [b, c] [c, b] , 10.39/2.91 [b, c] [c, c] [c, b] [b, a] -> [b, c] [c, a] [a, a] [a, a] , 10.39/2.91 [b, c] [c, b] [b, a] [a, a] -> [b, c] [c, a] [a, b] [b, a] , 10.39/2.91 [b, b] [b, b] [b, c] [c, a] -> [b, b] [b, b] [b, a] [a, a] , 10.39/2.91 [b, a] [a, a] [a, a] [a, a] -> [b, b] [b, c] [c, b] [b, a] , 10.39/2.91 [b, a] [a, b] [b, a] [a, a] ->= [b, c] [c, a] [a, a] [a, a] , 10.39/2.91 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.39/2.91 [a, c] [c, c] [c, b] [b, c] -> [a, c] [c, a] [a, a] [a, c] , 10.39/2.91 [a, c] [c, b] [b, a] [a, c] -> [a, c] [c, a] [a, b] [b, c] , 10.39/2.91 [a, b] [b, b] [b, c] [c, c] -> [a, b] [b, b] [b, a] [a, c] , 10.39/2.91 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.39/2.91 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.39/2.91 [a, a] [a, a] [a, c] [c, c] ->= [a, a] [a, b] [b, c] [c, c] , 10.39/2.91 [a, c] [c, c] [c, b] [b, b] -> [a, c] [c, a] [a, a] [a, b] , 10.39/2.91 [a, c] [c, b] [b, a] [a, b] -> [a, c] [c, a] [a, b] [b, b] , 10.39/2.91 [a, b] [b, b] [b, c] [c, b] -> [a, b] [b, b] [b, a] [a, b] , 10.39/2.91 [a, a] [a, a] [a, a] [a, b] -> [a, b] [b, c] [c, b] [b, b] , 10.39/2.91 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.39/2.91 [a, a] [a, a] [a, c] [c, b] ->= [a, a] [a, b] [b, c] [c, b] , 10.39/2.91 [a, c] [c, c] [c, b] [b, a] -> [a, c] [c, a] [a, a] [a, a] , 10.39/2.91 [a, c] [c, b] [b, a] [a, a] -> [a, c] [c, a] [a, b] [b, a] , 10.39/2.91 [a, b] [b, b] [b, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] , 10.39/2.91 [a, a] [a, a] [a, a] [a, a] -> [a, b] [b, c] [c, b] [b, a] , 10.39/2.91 [a, a] [a, b] [b, a] [a, a] ->= [a, c] [c, a] [a, a] [a, a] , 10.39/2.91 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.39/2.91 10.39/2.91 10.39/2.91 The system was filtered by the following matrix interpretation 10.39/2.91 of type E_J with J = {1,...,2} and dimension 5: 10.39/2.91 10.39/2.91 [c, c] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 1 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 1 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [c, b] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 1 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [b, c] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 1 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [c, a] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [a, a] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [a, c] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 1 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [b, a] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [a, b] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 [b, b] is interpreted by 10.39/2.91 / \ 10.39/2.91 | 1 0 0 0 0 | 10.39/2.91 | 0 1 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 | 0 0 0 0 0 | 10.39/2.91 \ / 10.39/2.91 10.39/2.91 Remains to prove termination of the 48-rule system 10.39/2.91 { [c, c] [c, c] [c, b] [b, c] -> [c, c] [c, a] [a, a] [a, c] , 10.39/2.91 [c, b] [b, b] [b, c] [c, c] -> [c, b] [b, b] [b, a] [a, c] , 10.39/2.91 [c, a] [a, a] [a, a] [a, c] -> [c, b] [b, c] [c, b] [b, c] , 10.39/2.91 [c, a] [a, b] [b, a] [a, c] ->= [c, c] [c, a] [a, a] [a, c] , 10.39/2.91 [c, a] [a, a] [a, c] [c, c] ->= [c, a] [a, b] [b, c] [c, c] , 10.39/2.91 [c, c] [c, b] [b, a] [a, b] -> [c, c] [c, a] [a, b] [b, b] , 10.39/2.92 [c, b] [b, b] [b, c] [c, b] -> [c, b] [b, b] [b, a] [a, b] , 10.39/2.92 [c, a] [a, a] [a, a] [a, b] -> [c, b] [b, c] [c, b] [b, b] , 10.39/2.92 [c, a] [a, b] [b, a] [a, b] ->= [c, c] [c, a] [a, a] [a, b] , 10.39/2.92 [c, a] [a, a] [a, c] [c, b] ->= [c, a] [a, b] [b, c] [c, b] , 10.39/2.92 [c, b] [b, b] [b, c] [c, a] -> [c, b] [b, b] [b, a] [a, a] , 10.39/2.92 [c, a] [a, a] [a, a] [a, a] -> [c, b] [b, c] [c, b] [b, a] , 10.39/2.92 [c, a] [a, b] [b, a] [a, a] ->= [c, c] [c, a] [a, a] [a, a] , 10.39/2.92 [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.39/2.92 [b, c] [c, c] [c, b] [b, c] -> [b, c] [c, a] [a, a] [a, c] , 10.39/2.92 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.39/2.92 [b, b] [b, b] [b, c] [c, c] -> [b, b] [b, b] [b, a] [a, c] , 10.39/2.92 [b, a] [a, a] [a, a] [a, c] -> [b, b] [b, c] [c, b] [b, c] , 10.39/2.92 [b, a] [a, b] [b, a] [a, c] ->= [b, c] [c, a] [a, a] [a, c] , 10.39/2.92 [b, a] [a, a] [a, c] [c, c] ->= [b, a] [a, b] [b, c] [c, c] , 10.39/2.92 [b, c] [c, c] [c, b] [b, b] -> [b, c] [c, a] [a, a] [a, b] , 10.39/2.92 [b, c] [c, b] [b, a] [a, b] -> [b, c] [c, a] [a, b] [b, b] , 10.39/2.92 [b, b] [b, b] [b, c] [c, b] -> [b, b] [b, b] [b, a] [a, b] , 10.39/2.92 [b, a] [a, a] [a, a] [a, b] -> [b, b] [b, c] [c, b] [b, b] , 10.39/2.92 [b, a] [a, b] [b, a] [a, b] ->= [b, c] [c, a] [a, a] [a, b] , 10.39/2.92 [b, a] [a, a] [a, c] [c, b] ->= [b, a] [a, b] [b, c] [c, b] , 10.39/2.92 [b, c] [c, b] [b, a] [a, a] -> [b, c] [c, a] [a, b] [b, a] , 10.39/2.92 [b, b] [b, b] [b, c] [c, a] -> [b, b] [b, b] [b, a] [a, a] , 10.39/2.92 [b, a] [a, a] [a, a] [a, a] -> [b, b] [b, c] [c, b] [b, a] , 10.39/2.92 [b, a] [a, b] [b, a] [a, a] ->= [b, c] [c, a] [a, a] [a, a] , 10.39/2.92 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.39/2.92 [a, c] [c, c] [c, b] [b, c] -> [a, c] [c, a] [a, a] [a, c] , 10.39/2.92 [a, c] [c, b] [b, a] [a, c] -> [a, c] [c, a] [a, b] [b, c] , 10.39/2.92 [a, b] [b, b] [b, c] [c, c] -> [a, b] [b, b] [b, a] [a, c] , 10.39/2.92 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.39/2.92 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.39/2.92 [a, a] [a, a] [a, c] [c, c] ->= [a, a] [a, b] [b, c] [c, c] , 10.39/2.92 [a, c] [c, c] [c, b] [b, b] -> [a, c] [c, a] [a, a] [a, b] , 10.39/2.92 [a, c] [c, b] [b, a] [a, b] -> [a, c] [c, a] [a, b] [b, b] , 10.39/2.92 [a, b] [b, b] [b, c] [c, b] -> [a, b] [b, b] [b, a] [a, b] , 10.39/2.92 [a, a] [a, a] [a, a] [a, b] -> [a, b] [b, c] [c, b] [b, b] , 10.39/2.92 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.39/2.92 [a, a] [a, a] [a, c] [c, b] ->= [a, a] [a, b] [b, c] [c, b] , 10.39/2.92 [a, c] [c, b] [b, a] [a, a] -> [a, c] [c, a] [a, b] [b, a] , 10.39/2.92 [a, b] [b, b] [b, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] , 10.39/2.92 [a, a] [a, a] [a, a] [a, a] -> [a, b] [b, c] [c, b] [b, a] , 10.39/2.92 [a, a] [a, b] [b, a] [a, a] ->= [a, c] [c, a] [a, a] [a, a] , 10.39/2.92 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.39/2.92 10.39/2.92 10.39/2.92 The system was filtered by the following matrix interpretation 10.39/2.92 of type E_J with J = {1,...,2} and dimension 11: 10.39/2.92 10.39/2.92 [c, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 1 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 1 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [c, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [c, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 1 0 0 | 10.39/2.92 | 0 0 0 0 0 1 1 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 1 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 1 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 1 0 0 0 1 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 1 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 10.39/2.92 Remains to prove termination of the 47-rule system 10.39/2.92 { [c, b] [b, b] [b, c] [c, c] -> [c, b] [b, b] [b, a] [a, c] , 10.39/2.92 [c, a] [a, a] [a, a] [a, c] -> [c, b] [b, c] [c, b] [b, c] , 10.39/2.92 [c, a] [a, b] [b, a] [a, c] ->= [c, c] [c, a] [a, a] [a, c] , 10.39/2.92 [c, a] [a, a] [a, c] [c, c] ->= [c, a] [a, b] [b, c] [c, c] , 10.39/2.92 [c, c] [c, b] [b, a] [a, b] -> [c, c] [c, a] [a, b] [b, b] , 10.39/2.92 [c, b] [b, b] [b, c] [c, b] -> [c, b] [b, b] [b, a] [a, b] , 10.39/2.92 [c, a] [a, a] [a, a] [a, b] -> [c, b] [b, c] [c, b] [b, b] , 10.39/2.92 [c, a] [a, b] [b, a] [a, b] ->= [c, c] [c, a] [a, a] [a, b] , 10.39/2.92 [c, a] [a, a] [a, c] [c, b] ->= [c, a] [a, b] [b, c] [c, b] , 10.39/2.92 [c, b] [b, b] [b, c] [c, a] -> [c, b] [b, b] [b, a] [a, a] , 10.39/2.92 [c, a] [a, a] [a, a] [a, a] -> [c, b] [b, c] [c, b] [b, a] , 10.39/2.92 [c, a] [a, b] [b, a] [a, a] ->= [c, c] [c, a] [a, a] [a, a] , 10.39/2.92 [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.39/2.92 [b, c] [c, c] [c, b] [b, c] -> [b, c] [c, a] [a, a] [a, c] , 10.39/2.92 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.39/2.92 [b, b] [b, b] [b, c] [c, c] -> [b, b] [b, b] [b, a] [a, c] , 10.39/2.92 [b, a] [a, a] [a, a] [a, c] -> [b, b] [b, c] [c, b] [b, c] , 10.39/2.92 [b, a] [a, b] [b, a] [a, c] ->= [b, c] [c, a] [a, a] [a, c] , 10.39/2.92 [b, a] [a, a] [a, c] [c, c] ->= [b, a] [a, b] [b, c] [c, c] , 10.39/2.92 [b, c] [c, c] [c, b] [b, b] -> [b, c] [c, a] [a, a] [a, b] , 10.39/2.92 [b, c] [c, b] [b, a] [a, b] -> [b, c] [c, a] [a, b] [b, b] , 10.39/2.92 [b, b] [b, b] [b, c] [c, b] -> [b, b] [b, b] [b, a] [a, b] , 10.39/2.92 [b, a] [a, a] [a, a] [a, b] -> [b, b] [b, c] [c, b] [b, b] , 10.39/2.92 [b, a] [a, b] [b, a] [a, b] ->= [b, c] [c, a] [a, a] [a, b] , 10.39/2.92 [b, a] [a, a] [a, c] [c, b] ->= [b, a] [a, b] [b, c] [c, b] , 10.39/2.92 [b, c] [c, b] [b, a] [a, a] -> [b, c] [c, a] [a, b] [b, a] , 10.39/2.92 [b, b] [b, b] [b, c] [c, a] -> [b, b] [b, b] [b, a] [a, a] , 10.39/2.92 [b, a] [a, a] [a, a] [a, a] -> [b, b] [b, c] [c, b] [b, a] , 10.39/2.92 [b, a] [a, b] [b, a] [a, a] ->= [b, c] [c, a] [a, a] [a, a] , 10.39/2.92 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.39/2.92 [a, c] [c, c] [c, b] [b, c] -> [a, c] [c, a] [a, a] [a, c] , 10.39/2.92 [a, c] [c, b] [b, a] [a, c] -> [a, c] [c, a] [a, b] [b, c] , 10.39/2.92 [a, b] [b, b] [b, c] [c, c] -> [a, b] [b, b] [b, a] [a, c] , 10.39/2.92 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.39/2.92 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.39/2.92 [a, a] [a, a] [a, c] [c, c] ->= [a, a] [a, b] [b, c] [c, c] , 10.39/2.92 [a, c] [c, c] [c, b] [b, b] -> [a, c] [c, a] [a, a] [a, b] , 10.39/2.92 [a, c] [c, b] [b, a] [a, b] -> [a, c] [c, a] [a, b] [b, b] , 10.39/2.92 [a, b] [b, b] [b, c] [c, b] -> [a, b] [b, b] [b, a] [a, b] , 10.39/2.92 [a, a] [a, a] [a, a] [a, b] -> [a, b] [b, c] [c, b] [b, b] , 10.39/2.92 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.39/2.92 [a, a] [a, a] [a, c] [c, b] ->= [a, a] [a, b] [b, c] [c, b] , 10.39/2.92 [a, c] [c, b] [b, a] [a, a] -> [a, c] [c, a] [a, b] [b, a] , 10.39/2.92 [a, b] [b, b] [b, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] , 10.39/2.92 [a, a] [a, a] [a, a] [a, a] -> [a, b] [b, c] [c, b] [b, a] , 10.39/2.92 [a, a] [a, b] [b, a] [a, a] ->= [a, c] [c, a] [a, a] [a, a] , 10.39/2.92 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.39/2.92 10.39/2.92 10.39/2.92 The system was filtered by the following matrix interpretation 10.39/2.92 of type E_J with J = {1,...,2} and dimension 5: 10.39/2.92 10.39/2.92 [c, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 1 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [c, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 | 0 0 0 1 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [c, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 1 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 10.39/2.92 Remains to prove termination of the 46-rule system 10.39/2.92 { [c, b] [b, b] [b, c] [c, c] -> [c, b] [b, b] [b, a] [a, c] , 10.39/2.92 [c, a] [a, a] [a, a] [a, c] -> [c, b] [b, c] [c, b] [b, c] , 10.39/2.92 [c, a] [a, b] [b, a] [a, c] ->= [c, c] [c, a] [a, a] [a, c] , 10.39/2.92 [c, a] [a, a] [a, c] [c, c] ->= [c, a] [a, b] [b, c] [c, c] , 10.39/2.92 [c, b] [b, b] [b, c] [c, b] -> [c, b] [b, b] [b, a] [a, b] , 10.39/2.92 [c, a] [a, a] [a, a] [a, b] -> [c, b] [b, c] [c, b] [b, b] , 10.39/2.92 [c, a] [a, b] [b, a] [a, b] ->= [c, c] [c, a] [a, a] [a, b] , 10.39/2.92 [c, a] [a, a] [a, c] [c, b] ->= [c, a] [a, b] [b, c] [c, b] , 10.39/2.92 [c, b] [b, b] [b, c] [c, a] -> [c, b] [b, b] [b, a] [a, a] , 10.39/2.92 [c, a] [a, a] [a, a] [a, a] -> [c, b] [b, c] [c, b] [b, a] , 10.39/2.92 [c, a] [a, b] [b, a] [a, a] ->= [c, c] [c, a] [a, a] [a, a] , 10.39/2.92 [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.39/2.92 [b, c] [c, c] [c, b] [b, c] -> [b, c] [c, a] [a, a] [a, c] , 10.39/2.92 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.39/2.92 [b, b] [b, b] [b, c] [c, c] -> [b, b] [b, b] [b, a] [a, c] , 10.39/2.92 [b, a] [a, a] [a, a] [a, c] -> [b, b] [b, c] [c, b] [b, c] , 10.39/2.92 [b, a] [a, b] [b, a] [a, c] ->= [b, c] [c, a] [a, a] [a, c] , 10.39/2.92 [b, a] [a, a] [a, c] [c, c] ->= [b, a] [a, b] [b, c] [c, c] , 10.39/2.92 [b, c] [c, c] [c, b] [b, b] -> [b, c] [c, a] [a, a] [a, b] , 10.39/2.92 [b, c] [c, b] [b, a] [a, b] -> [b, c] [c, a] [a, b] [b, b] , 10.39/2.92 [b, b] [b, b] [b, c] [c, b] -> [b, b] [b, b] [b, a] [a, b] , 10.39/2.92 [b, a] [a, a] [a, a] [a, b] -> [b, b] [b, c] [c, b] [b, b] , 10.39/2.92 [b, a] [a, b] [b, a] [a, b] ->= [b, c] [c, a] [a, a] [a, b] , 10.39/2.92 [b, a] [a, a] [a, c] [c, b] ->= [b, a] [a, b] [b, c] [c, b] , 10.39/2.92 [b, c] [c, b] [b, a] [a, a] -> [b, c] [c, a] [a, b] [b, a] , 10.39/2.92 [b, b] [b, b] [b, c] [c, a] -> [b, b] [b, b] [b, a] [a, a] , 10.39/2.92 [b, a] [a, a] [a, a] [a, a] -> [b, b] [b, c] [c, b] [b, a] , 10.39/2.92 [b, a] [a, b] [b, a] [a, a] ->= [b, c] [c, a] [a, a] [a, a] , 10.39/2.92 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.39/2.92 [a, c] [c, c] [c, b] [b, c] -> [a, c] [c, a] [a, a] [a, c] , 10.39/2.92 [a, c] [c, b] [b, a] [a, c] -> [a, c] [c, a] [a, b] [b, c] , 10.39/2.92 [a, b] [b, b] [b, c] [c, c] -> [a, b] [b, b] [b, a] [a, c] , 10.39/2.92 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.39/2.92 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.39/2.92 [a, a] [a, a] [a, c] [c, c] ->= [a, a] [a, b] [b, c] [c, c] , 10.39/2.92 [a, c] [c, c] [c, b] [b, b] -> [a, c] [c, a] [a, a] [a, b] , 10.39/2.92 [a, c] [c, b] [b, a] [a, b] -> [a, c] [c, a] [a, b] [b, b] , 10.39/2.92 [a, b] [b, b] [b, c] [c, b] -> [a, b] [b, b] [b, a] [a, b] , 10.39/2.92 [a, a] [a, a] [a, a] [a, b] -> [a, b] [b, c] [c, b] [b, b] , 10.39/2.92 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.39/2.92 [a, a] [a, a] [a, c] [c, b] ->= [a, a] [a, b] [b, c] [c, b] , 10.39/2.92 [a, c] [c, b] [b, a] [a, a] -> [a, c] [c, a] [a, b] [b, a] , 10.39/2.92 [a, b] [b, b] [b, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] , 10.39/2.92 [a, a] [a, a] [a, a] [a, a] -> [a, b] [b, c] [c, b] [b, a] , 10.39/2.92 [a, a] [a, b] [b, a] [a, a] ->= [a, c] [c, a] [a, a] [a, a] , 10.39/2.92 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.39/2.92 10.39/2.92 10.39/2.92 The system was filtered by the following matrix interpretation 10.39/2.92 of type E_J with J = {1,...,2} and dimension 5: 10.39/2.92 10.39/2.92 [c, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 1 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 | 0 0 0 1 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [c, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 1 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 1 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [c, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 1 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 \ / 10.39/2.92 10.39/2.92 Remains to prove termination of the 44-rule system 10.39/2.92 { [c, b] [b, b] [b, c] [c, c] -> [c, b] [b, b] [b, a] [a, c] , 10.39/2.92 [c, a] [a, a] [a, a] [a, c] -> [c, b] [b, c] [c, b] [b, c] , 10.39/2.92 [c, a] [a, b] [b, a] [a, c] ->= [c, c] [c, a] [a, a] [a, c] , 10.39/2.92 [c, a] [a, a] [a, c] [c, c] ->= [c, a] [a, b] [b, c] [c, c] , 10.39/2.92 [c, b] [b, b] [b, c] [c, b] -> [c, b] [b, b] [b, a] [a, b] , 10.39/2.92 [c, a] [a, a] [a, a] [a, b] -> [c, b] [b, c] [c, b] [b, b] , 10.39/2.92 [c, a] [a, b] [b, a] [a, b] ->= [c, c] [c, a] [a, a] [a, b] , 10.39/2.92 [c, a] [a, a] [a, c] [c, b] ->= [c, a] [a, b] [b, c] [c, b] , 10.39/2.92 [c, b] [b, b] [b, c] [c, a] -> [c, b] [b, b] [b, a] [a, a] , 10.39/2.92 [c, a] [a, a] [a, a] [a, a] -> [c, b] [b, c] [c, b] [b, a] , 10.39/2.92 [c, a] [a, b] [b, a] [a, a] ->= [c, c] [c, a] [a, a] [a, a] , 10.39/2.92 [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.39/2.92 [b, c] [c, c] [c, b] [b, c] -> [b, c] [c, a] [a, a] [a, c] , 10.39/2.92 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.39/2.92 [b, b] [b, b] [b, c] [c, c] -> [b, b] [b, b] [b, a] [a, c] , 10.39/2.92 [b, a] [a, a] [a, a] [a, c] -> [b, b] [b, c] [c, b] [b, c] , 10.39/2.92 [b, a] [a, b] [b, a] [a, c] ->= [b, c] [c, a] [a, a] [a, c] , 10.39/2.92 [b, a] [a, a] [a, c] [c, c] ->= [b, a] [a, b] [b, c] [c, c] , 10.39/2.92 [b, c] [c, b] [b, a] [a, b] -> [b, c] [c, a] [a, b] [b, b] , 10.39/2.92 [b, b] [b, b] [b, c] [c, b] -> [b, b] [b, b] [b, a] [a, b] , 10.39/2.92 [b, a] [a, a] [a, a] [a, b] -> [b, b] [b, c] [c, b] [b, b] , 10.39/2.92 [b, a] [a, b] [b, a] [a, b] ->= [b, c] [c, a] [a, a] [a, b] , 10.39/2.92 [b, a] [a, a] [a, c] [c, b] ->= [b, a] [a, b] [b, c] [c, b] , 10.39/2.92 [b, c] [c, b] [b, a] [a, a] -> [b, c] [c, a] [a, b] [b, a] , 10.39/2.92 [b, b] [b, b] [b, c] [c, a] -> [b, b] [b, b] [b, a] [a, a] , 10.39/2.92 [b, a] [a, a] [a, a] [a, a] -> [b, b] [b, c] [c, b] [b, a] , 10.39/2.92 [b, a] [a, b] [b, a] [a, a] ->= [b, c] [c, a] [a, a] [a, a] , 10.39/2.92 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.39/2.92 [a, c] [c, c] [c, b] [b, c] -> [a, c] [c, a] [a, a] [a, c] , 10.39/2.92 [a, c] [c, b] [b, a] [a, c] -> [a, c] [c, a] [a, b] [b, c] , 10.39/2.92 [a, b] [b, b] [b, c] [c, c] -> [a, b] [b, b] [b, a] [a, c] , 10.39/2.92 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.39/2.92 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.39/2.92 [a, a] [a, a] [a, c] [c, c] ->= [a, a] [a, b] [b, c] [c, c] , 10.39/2.92 [a, c] [c, b] [b, a] [a, b] -> [a, c] [c, a] [a, b] [b, b] , 10.39/2.92 [a, b] [b, b] [b, c] [c, b] -> [a, b] [b, b] [b, a] [a, b] , 10.39/2.92 [a, a] [a, a] [a, a] [a, b] -> [a, b] [b, c] [c, b] [b, b] , 10.39/2.92 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.39/2.92 [a, a] [a, a] [a, c] [c, b] ->= [a, a] [a, b] [b, c] [c, b] , 10.39/2.92 [a, c] [c, b] [b, a] [a, a] -> [a, c] [c, a] [a, b] [b, a] , 10.39/2.92 [a, b] [b, b] [b, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] , 10.39/2.92 [a, a] [a, a] [a, a] [a, a] -> [a, b] [b, c] [c, b] [b, a] , 10.39/2.92 [a, a] [a, b] [b, a] [a, a] ->= [a, c] [c, a] [a, a] [a, a] , 10.39/2.92 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.39/2.92 10.39/2.92 10.39/2.92 The system was filtered by the following matrix interpretation 10.39/2.92 of type E_J with J = {1,...,2} and dimension 2: 10.39/2.92 10.39/2.92 [c, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 1 | 10.39/2.92 | 0 1 | 10.39/2.92 \ / 10.39/2.92 [c, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 2 | 10.39/2.92 | 0 1 | 10.39/2.92 \ / 10.39/2.92 [b, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 | 10.39/2.92 | 0 1 | 10.39/2.92 \ / 10.39/2.92 [c, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 2 | 10.39/2.92 | 0 1 | 10.39/2.92 \ / 10.39/2.92 [a, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 1 | 10.39/2.92 | 0 1 | 10.39/2.92 \ / 10.39/2.92 [a, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 | 10.39/2.92 | 0 1 | 10.39/2.92 \ / 10.39/2.92 [b, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 1 | 10.39/2.92 | 0 1 | 10.39/2.92 \ / 10.39/2.92 [a, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 1 | 10.39/2.92 | 0 1 | 10.39/2.92 \ / 10.39/2.92 [b, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 | 10.39/2.92 | 0 1 | 10.39/2.92 \ / 10.39/2.92 10.39/2.92 Remains to prove termination of the 37-rule system 10.39/2.92 { [c, b] [b, b] [b, c] [c, c] -> [c, b] [b, b] [b, a] [a, c] , 10.39/2.92 [c, a] [a, a] [a, a] [a, c] -> [c, b] [b, c] [c, b] [b, c] , 10.39/2.92 [c, a] [a, b] [b, a] [a, c] ->= [c, c] [c, a] [a, a] [a, c] , 10.39/2.92 [c, a] [a, a] [a, c] [c, c] ->= [c, a] [a, b] [b, c] [c, c] , 10.39/2.92 [c, b] [b, b] [b, c] [c, b] -> [c, b] [b, b] [b, a] [a, b] , 10.39/2.92 [c, a] [a, b] [b, a] [a, b] ->= [c, c] [c, a] [a, a] [a, b] , 10.39/2.92 [c, a] [a, a] [a, c] [c, b] ->= [c, a] [a, b] [b, c] [c, b] , 10.39/2.92 [c, b] [b, b] [b, c] [c, a] -> [c, b] [b, b] [b, a] [a, a] , 10.39/2.92 [c, a] [a, a] [a, a] [a, a] -> [c, b] [b, c] [c, b] [b, a] , 10.39/2.92 [c, a] [a, b] [b, a] [a, a] ->= [c, c] [c, a] [a, a] [a, a] , 10.39/2.92 [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.39/2.92 [b, c] [c, c] [c, b] [b, c] -> [b, c] [c, a] [a, a] [a, c] , 10.39/2.92 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.39/2.92 [b, b] [b, b] [b, c] [c, c] -> [b, b] [b, b] [b, a] [a, c] , 10.39/2.92 [b, a] [a, b] [b, a] [a, c] ->= [b, c] [c, a] [a, a] [a, c] , 10.39/2.92 [b, a] [a, a] [a, c] [c, c] ->= [b, a] [a, b] [b, c] [c, c] , 10.39/2.92 [b, b] [b, b] [b, c] [c, b] -> [b, b] [b, b] [b, a] [a, b] , 10.39/2.92 [b, a] [a, b] [b, a] [a, b] ->= [b, c] [c, a] [a, a] [a, b] , 10.39/2.92 [b, a] [a, a] [a, c] [c, b] ->= [b, a] [a, b] [b, c] [c, b] , 10.39/2.92 [b, c] [c, b] [b, a] [a, a] -> [b, c] [c, a] [a, b] [b, a] , 10.39/2.92 [b, b] [b, b] [b, c] [c, a] -> [b, b] [b, b] [b, a] [a, a] , 10.39/2.92 [b, a] [a, b] [b, a] [a, a] ->= [b, c] [c, a] [a, a] [a, a] , 10.39/2.92 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.39/2.92 [a, c] [c, c] [c, b] [b, c] -> [a, c] [c, a] [a, a] [a, c] , 10.39/2.92 [a, c] [c, b] [b, a] [a, c] -> [a, c] [c, a] [a, b] [b, c] , 10.39/2.92 [a, b] [b, b] [b, c] [c, c] -> [a, b] [b, b] [b, a] [a, c] , 10.39/2.92 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.39/2.92 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.39/2.92 [a, a] [a, a] [a, c] [c, c] ->= [a, a] [a, b] [b, c] [c, c] , 10.39/2.92 [a, b] [b, b] [b, c] [c, b] -> [a, b] [b, b] [b, a] [a, b] , 10.39/2.92 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.39/2.92 [a, a] [a, a] [a, c] [c, b] ->= [a, a] [a, b] [b, c] [c, b] , 10.39/2.92 [a, c] [c, b] [b, a] [a, a] -> [a, c] [c, a] [a, b] [b, a] , 10.39/2.92 [a, b] [b, b] [b, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] , 10.39/2.92 [a, a] [a, a] [a, a] [a, a] -> [a, b] [b, c] [c, b] [b, a] , 10.39/2.92 [a, a] [a, b] [b, a] [a, a] ->= [a, c] [c, a] [a, a] [a, a] , 10.39/2.92 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.39/2.92 10.39/2.92 10.39/2.92 The system was filtered by the following matrix interpretation 10.39/2.92 of type E_J with J = {1,...,2} and dimension 11: 10.39/2.92 10.39/2.92 [c, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [c, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 1 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 1 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [c, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 1 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 1 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 1 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 1 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 1 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 1 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 1 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 1 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 10.39/2.92 Remains to prove termination of the 36-rule system 10.39/2.92 { [c, b] [b, b] [b, c] [c, c] -> [c, b] [b, b] [b, a] [a, c] , 10.39/2.92 [c, a] [a, a] [a, a] [a, c] -> [c, b] [b, c] [c, b] [b, c] , 10.39/2.92 [c, a] [a, b] [b, a] [a, c] ->= [c, c] [c, a] [a, a] [a, c] , 10.39/2.92 [c, a] [a, a] [a, c] [c, c] ->= [c, a] [a, b] [b, c] [c, c] , 10.39/2.92 [c, a] [a, b] [b, a] [a, b] ->= [c, c] [c, a] [a, a] [a, b] , 10.39/2.92 [c, a] [a, a] [a, c] [c, b] ->= [c, a] [a, b] [b, c] [c, b] , 10.39/2.92 [c, b] [b, b] [b, c] [c, a] -> [c, b] [b, b] [b, a] [a, a] , 10.39/2.92 [c, a] [a, a] [a, a] [a, a] -> [c, b] [b, c] [c, b] [b, a] , 10.39/2.92 [c, a] [a, b] [b, a] [a, a] ->= [c, c] [c, a] [a, a] [a, a] , 10.39/2.92 [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.39/2.92 [b, c] [c, c] [c, b] [b, c] -> [b, c] [c, a] [a, a] [a, c] , 10.39/2.92 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.39/2.92 [b, b] [b, b] [b, c] [c, c] -> [b, b] [b, b] [b, a] [a, c] , 10.39/2.92 [b, a] [a, b] [b, a] [a, c] ->= [b, c] [c, a] [a, a] [a, c] , 10.39/2.92 [b, a] [a, a] [a, c] [c, c] ->= [b, a] [a, b] [b, c] [c, c] , 10.39/2.92 [b, b] [b, b] [b, c] [c, b] -> [b, b] [b, b] [b, a] [a, b] , 10.39/2.92 [b, a] [a, b] [b, a] [a, b] ->= [b, c] [c, a] [a, a] [a, b] , 10.39/2.92 [b, a] [a, a] [a, c] [c, b] ->= [b, a] [a, b] [b, c] [c, b] , 10.39/2.92 [b, c] [c, b] [b, a] [a, a] -> [b, c] [c, a] [a, b] [b, a] , 10.39/2.92 [b, b] [b, b] [b, c] [c, a] -> [b, b] [b, b] [b, a] [a, a] , 10.39/2.92 [b, a] [a, b] [b, a] [a, a] ->= [b, c] [c, a] [a, a] [a, a] , 10.39/2.92 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.39/2.92 [a, c] [c, c] [c, b] [b, c] -> [a, c] [c, a] [a, a] [a, c] , 10.39/2.92 [a, c] [c, b] [b, a] [a, c] -> [a, c] [c, a] [a, b] [b, c] , 10.39/2.92 [a, b] [b, b] [b, c] [c, c] -> [a, b] [b, b] [b, a] [a, c] , 10.39/2.92 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.39/2.92 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.39/2.92 [a, a] [a, a] [a, c] [c, c] ->= [a, a] [a, b] [b, c] [c, c] , 10.39/2.92 [a, b] [b, b] [b, c] [c, b] -> [a, b] [b, b] [b, a] [a, b] , 10.39/2.92 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.39/2.92 [a, a] [a, a] [a, c] [c, b] ->= [a, a] [a, b] [b, c] [c, b] , 10.39/2.92 [a, c] [c, b] [b, a] [a, a] -> [a, c] [c, a] [a, b] [b, a] , 10.39/2.92 [a, b] [b, b] [b, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] , 10.39/2.92 [a, a] [a, a] [a, a] [a, a] -> [a, b] [b, c] [c, b] [b, a] , 10.39/2.92 [a, a] [a, b] [b, a] [a, a] ->= [a, c] [c, a] [a, a] [a, a] , 10.39/2.92 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.39/2.92 10.39/2.92 10.39/2.92 The system was filtered by the following matrix interpretation 10.39/2.92 of type E_J with J = {1,...,2} and dimension 11: 10.39/2.92 10.39/2.92 [c, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [c, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 1 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [c, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 1 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 1 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 1 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 1 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 1 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 1 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 1 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 1 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 1 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 10.39/2.92 Remains to prove termination of the 35-rule system 10.39/2.92 { [c, b] [b, b] [b, c] [c, c] -> [c, b] [b, b] [b, a] [a, c] , 10.39/2.92 [c, a] [a, a] [a, a] [a, c] -> [c, b] [b, c] [c, b] [b, c] , 10.39/2.92 [c, a] [a, b] [b, a] [a, c] ->= [c, c] [c, a] [a, a] [a, c] , 10.39/2.92 [c, a] [a, a] [a, c] [c, c] ->= [c, a] [a, b] [b, c] [c, c] , 10.39/2.92 [c, a] [a, b] [b, a] [a, b] ->= [c, c] [c, a] [a, a] [a, b] , 10.39/2.92 [c, a] [a, a] [a, c] [c, b] ->= [c, a] [a, b] [b, c] [c, b] , 10.39/2.92 [c, b] [b, b] [b, c] [c, a] -> [c, b] [b, b] [b, a] [a, a] , 10.39/2.92 [c, a] [a, a] [a, a] [a, a] -> [c, b] [b, c] [c, b] [b, a] , 10.39/2.92 [c, a] [a, b] [b, a] [a, a] ->= [c, c] [c, a] [a, a] [a, a] , 10.39/2.92 [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.39/2.92 [b, c] [c, c] [c, b] [b, c] -> [b, c] [c, a] [a, a] [a, c] , 10.39/2.92 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.39/2.92 [b, b] [b, b] [b, c] [c, c] -> [b, b] [b, b] [b, a] [a, c] , 10.39/2.92 [b, a] [a, b] [b, a] [a, c] ->= [b, c] [c, a] [a, a] [a, c] , 10.39/2.92 [b, a] [a, a] [a, c] [c, c] ->= [b, a] [a, b] [b, c] [c, c] , 10.39/2.92 [b, a] [a, b] [b, a] [a, b] ->= [b, c] [c, a] [a, a] [a, b] , 10.39/2.92 [b, a] [a, a] [a, c] [c, b] ->= [b, a] [a, b] [b, c] [c, b] , 10.39/2.92 [b, c] [c, b] [b, a] [a, a] -> [b, c] [c, a] [a, b] [b, a] , 10.39/2.92 [b, b] [b, b] [b, c] [c, a] -> [b, b] [b, b] [b, a] [a, a] , 10.39/2.92 [b, a] [a, b] [b, a] [a, a] ->= [b, c] [c, a] [a, a] [a, a] , 10.39/2.92 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.39/2.92 [a, c] [c, c] [c, b] [b, c] -> [a, c] [c, a] [a, a] [a, c] , 10.39/2.92 [a, c] [c, b] [b, a] [a, c] -> [a, c] [c, a] [a, b] [b, c] , 10.39/2.92 [a, b] [b, b] [b, c] [c, c] -> [a, b] [b, b] [b, a] [a, c] , 10.39/2.92 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.39/2.92 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.39/2.92 [a, a] [a, a] [a, c] [c, c] ->= [a, a] [a, b] [b, c] [c, c] , 10.39/2.92 [a, b] [b, b] [b, c] [c, b] -> [a, b] [b, b] [b, a] [a, b] , 10.39/2.92 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.39/2.92 [a, a] [a, a] [a, c] [c, b] ->= [a, a] [a, b] [b, c] [c, b] , 10.39/2.92 [a, c] [c, b] [b, a] [a, a] -> [a, c] [c, a] [a, b] [b, a] , 10.39/2.92 [a, b] [b, b] [b, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] , 10.39/2.92 [a, a] [a, a] [a, a] [a, a] -> [a, b] [b, c] [c, b] [b, a] , 10.39/2.92 [a, a] [a, b] [b, a] [a, a] ->= [a, c] [c, a] [a, a] [a, a] , 10.39/2.92 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.39/2.92 10.39/2.92 10.39/2.92 The system was filtered by the following matrix interpretation 10.39/2.92 of type E_J with J = {1,...,2} and dimension 11: 10.39/2.92 10.39/2.92 [c, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [c, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 1 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 1 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [c, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 1 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 1 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 1 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 1 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 1 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 1 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 1 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 1 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 1 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 10.39/2.92 Remains to prove termination of the 34-rule system 10.39/2.92 { [c, b] [b, b] [b, c] [c, c] -> [c, b] [b, b] [b, a] [a, c] , 10.39/2.92 [c, a] [a, a] [a, a] [a, c] -> [c, b] [b, c] [c, b] [b, c] , 10.39/2.92 [c, a] [a, b] [b, a] [a, c] ->= [c, c] [c, a] [a, a] [a, c] , 10.39/2.92 [c, a] [a, a] [a, c] [c, c] ->= [c, a] [a, b] [b, c] [c, c] , 10.39/2.92 [c, a] [a, b] [b, a] [a, b] ->= [c, c] [c, a] [a, a] [a, b] , 10.39/2.92 [c, a] [a, a] [a, c] [c, b] ->= [c, a] [a, b] [b, c] [c, b] , 10.39/2.92 [c, b] [b, b] [b, c] [c, a] -> [c, b] [b, b] [b, a] [a, a] , 10.39/2.92 [c, a] [a, a] [a, a] [a, a] -> [c, b] [b, c] [c, b] [b, a] , 10.39/2.92 [c, a] [a, b] [b, a] [a, a] ->= [c, c] [c, a] [a, a] [a, a] , 10.39/2.92 [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.39/2.92 [b, c] [c, c] [c, b] [b, c] -> [b, c] [c, a] [a, a] [a, c] , 10.39/2.92 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.39/2.92 [b, b] [b, b] [b, c] [c, c] -> [b, b] [b, b] [b, a] [a, c] , 10.39/2.92 [b, a] [a, b] [b, a] [a, c] ->= [b, c] [c, a] [a, a] [a, c] , 10.39/2.92 [b, a] [a, a] [a, c] [c, c] ->= [b, a] [a, b] [b, c] [c, c] , 10.39/2.92 [b, a] [a, b] [b, a] [a, b] ->= [b, c] [c, a] [a, a] [a, b] , 10.39/2.92 [b, a] [a, a] [a, c] [c, b] ->= [b, a] [a, b] [b, c] [c, b] , 10.39/2.92 [b, c] [c, b] [b, a] [a, a] -> [b, c] [c, a] [a, b] [b, a] , 10.39/2.92 [b, b] [b, b] [b, c] [c, a] -> [b, b] [b, b] [b, a] [a, a] , 10.39/2.92 [b, a] [a, b] [b, a] [a, a] ->= [b, c] [c, a] [a, a] [a, a] , 10.39/2.92 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.39/2.92 [a, c] [c, c] [c, b] [b, c] -> [a, c] [c, a] [a, a] [a, c] , 10.39/2.92 [a, c] [c, b] [b, a] [a, c] -> [a, c] [c, a] [a, b] [b, c] , 10.39/2.92 [a, b] [b, b] [b, c] [c, c] -> [a, b] [b, b] [b, a] [a, c] , 10.39/2.92 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.39/2.92 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.39/2.92 [a, a] [a, a] [a, c] [c, c] ->= [a, a] [a, b] [b, c] [c, c] , 10.39/2.92 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.39/2.92 [a, a] [a, a] [a, c] [c, b] ->= [a, a] [a, b] [b, c] [c, b] , 10.39/2.92 [a, c] [c, b] [b, a] [a, a] -> [a, c] [c, a] [a, b] [b, a] , 10.39/2.92 [a, b] [b, b] [b, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] , 10.39/2.92 [a, a] [a, a] [a, a] [a, a] -> [a, b] [b, c] [c, b] [b, a] , 10.39/2.92 [a, a] [a, b] [b, a] [a, a] ->= [a, c] [c, a] [a, a] [a, a] , 10.39/2.92 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.39/2.92 10.39/2.92 10.39/2.92 The system was filtered by the following matrix interpretation 10.39/2.92 of type E_J with J = {1,...,2} and dimension 8: 10.39/2.92 10.39/2.92 [c, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [c, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 1 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 1 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [c, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 1 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 1 | 10.39/2.92 \ / 10.39/2.92 [a, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 1 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 1 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 1 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 10.39/2.92 Remains to prove termination of the 33-rule system 10.39/2.92 { [c, a] [a, a] [a, a] [a, c] -> [c, b] [b, c] [c, b] [b, c] , 10.39/2.92 [c, a] [a, b] [b, a] [a, c] ->= [c, c] [c, a] [a, a] [a, c] , 10.39/2.92 [c, a] [a, a] [a, c] [c, c] ->= [c, a] [a, b] [b, c] [c, c] , 10.39/2.92 [c, a] [a, b] [b, a] [a, b] ->= [c, c] [c, a] [a, a] [a, b] , 10.39/2.92 [c, a] [a, a] [a, c] [c, b] ->= [c, a] [a, b] [b, c] [c, b] , 10.39/2.92 [c, b] [b, b] [b, c] [c, a] -> [c, b] [b, b] [b, a] [a, a] , 10.39/2.92 [c, a] [a, a] [a, a] [a, a] -> [c, b] [b, c] [c, b] [b, a] , 10.39/2.92 [c, a] [a, b] [b, a] [a, a] ->= [c, c] [c, a] [a, a] [a, a] , 10.39/2.92 [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.39/2.92 [b, c] [c, c] [c, b] [b, c] -> [b, c] [c, a] [a, a] [a, c] , 10.39/2.92 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.39/2.92 [b, b] [b, b] [b, c] [c, c] -> [b, b] [b, b] [b, a] [a, c] , 10.39/2.92 [b, a] [a, b] [b, a] [a, c] ->= [b, c] [c, a] [a, a] [a, c] , 10.39/2.92 [b, a] [a, a] [a, c] [c, c] ->= [b, a] [a, b] [b, c] [c, c] , 10.39/2.92 [b, a] [a, b] [b, a] [a, b] ->= [b, c] [c, a] [a, a] [a, b] , 10.39/2.92 [b, a] [a, a] [a, c] [c, b] ->= [b, a] [a, b] [b, c] [c, b] , 10.39/2.92 [b, c] [c, b] [b, a] [a, a] -> [b, c] [c, a] [a, b] [b, a] , 10.39/2.92 [b, b] [b, b] [b, c] [c, a] -> [b, b] [b, b] [b, a] [a, a] , 10.39/2.92 [b, a] [a, b] [b, a] [a, a] ->= [b, c] [c, a] [a, a] [a, a] , 10.39/2.92 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.39/2.92 [a, c] [c, c] [c, b] [b, c] -> [a, c] [c, a] [a, a] [a, c] , 10.39/2.92 [a, c] [c, b] [b, a] [a, c] -> [a, c] [c, a] [a, b] [b, c] , 10.39/2.92 [a, b] [b, b] [b, c] [c, c] -> [a, b] [b, b] [b, a] [a, c] , 10.39/2.92 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.39/2.92 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.39/2.92 [a, a] [a, a] [a, c] [c, c] ->= [a, a] [a, b] [b, c] [c, c] , 10.39/2.92 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.39/2.92 [a, a] [a, a] [a, c] [c, b] ->= [a, a] [a, b] [b, c] [c, b] , 10.39/2.92 [a, c] [c, b] [b, a] [a, a] -> [a, c] [c, a] [a, b] [b, a] , 10.39/2.92 [a, b] [b, b] [b, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] , 10.39/2.92 [a, a] [a, a] [a, a] [a, a] -> [a, b] [b, c] [c, b] [b, a] , 10.39/2.92 [a, a] [a, b] [b, a] [a, a] ->= [a, c] [c, a] [a, a] [a, a] , 10.39/2.92 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.39/2.92 10.39/2.92 10.39/2.92 The system was filtered by the following matrix interpretation 10.39/2.92 of type E_J with J = {1,...,2} and dimension 8: 10.39/2.92 10.39/2.92 [c, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [c, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 1 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [c, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 1 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 1 | 10.39/2.92 \ / 10.39/2.92 [a, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 1 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 1 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 1 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 1 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 10.39/2.92 Remains to prove termination of the 32-rule system 10.39/2.92 { [c, a] [a, a] [a, a] [a, c] -> [c, b] [b, c] [c, b] [b, c] , 10.39/2.92 [c, a] [a, b] [b, a] [a, c] ->= [c, c] [c, a] [a, a] [a, c] , 10.39/2.92 [c, a] [a, a] [a, c] [c, c] ->= [c, a] [a, b] [b, c] [c, c] , 10.39/2.92 [c, a] [a, b] [b, a] [a, b] ->= [c, c] [c, a] [a, a] [a, b] , 10.39/2.92 [c, a] [a, a] [a, c] [c, b] ->= [c, a] [a, b] [b, c] [c, b] , 10.39/2.92 [c, b] [b, b] [b, c] [c, a] -> [c, b] [b, b] [b, a] [a, a] , 10.39/2.92 [c, a] [a, a] [a, a] [a, a] -> [c, b] [b, c] [c, b] [b, a] , 10.39/2.92 [c, a] [a, b] [b, a] [a, a] ->= [c, c] [c, a] [a, a] [a, a] , 10.39/2.92 [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.39/2.92 [b, c] [c, c] [c, b] [b, c] -> [b, c] [c, a] [a, a] [a, c] , 10.39/2.92 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.39/2.92 [b, a] [a, b] [b, a] [a, c] ->= [b, c] [c, a] [a, a] [a, c] , 10.39/2.92 [b, a] [a, a] [a, c] [c, c] ->= [b, a] [a, b] [b, c] [c, c] , 10.39/2.92 [b, a] [a, b] [b, a] [a, b] ->= [b, c] [c, a] [a, a] [a, b] , 10.39/2.92 [b, a] [a, a] [a, c] [c, b] ->= [b, a] [a, b] [b, c] [c, b] , 10.39/2.92 [b, c] [c, b] [b, a] [a, a] -> [b, c] [c, a] [a, b] [b, a] , 10.39/2.92 [b, b] [b, b] [b, c] [c, a] -> [b, b] [b, b] [b, a] [a, a] , 10.39/2.92 [b, a] [a, b] [b, a] [a, a] ->= [b, c] [c, a] [a, a] [a, a] , 10.39/2.92 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.39/2.92 [a, c] [c, c] [c, b] [b, c] -> [a, c] [c, a] [a, a] [a, c] , 10.39/2.92 [a, c] [c, b] [b, a] [a, c] -> [a, c] [c, a] [a, b] [b, c] , 10.39/2.92 [a, b] [b, b] [b, c] [c, c] -> [a, b] [b, b] [b, a] [a, c] , 10.39/2.92 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.39/2.92 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.39/2.92 [a, a] [a, a] [a, c] [c, c] ->= [a, a] [a, b] [b, c] [c, c] , 10.39/2.92 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.39/2.92 [a, a] [a, a] [a, c] [c, b] ->= [a, a] [a, b] [b, c] [c, b] , 10.39/2.92 [a, c] [c, b] [b, a] [a, a] -> [a, c] [c, a] [a, b] [b, a] , 10.39/2.92 [a, b] [b, b] [b, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] , 10.39/2.92 [a, a] [a, a] [a, a] [a, a] -> [a, b] [b, c] [c, b] [b, a] , 10.39/2.92 [a, a] [a, b] [b, a] [a, a] ->= [a, c] [c, a] [a, a] [a, a] , 10.39/2.92 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.39/2.92 10.39/2.92 10.39/2.92 The system was filtered by the following matrix interpretation 10.39/2.92 of type E_J with J = {1,...,2} and dimension 8: 10.39/2.92 10.39/2.92 [c, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [c, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 1 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [c, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 1 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 1 | 10.39/2.92 \ / 10.39/2.92 [a, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 1 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 1 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 1 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 1 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 10.39/2.92 Remains to prove termination of the 31-rule system 10.39/2.92 { [c, a] [a, a] [a, a] [a, c] -> [c, b] [b, c] [c, b] [b, c] , 10.39/2.92 [c, a] [a, b] [b, a] [a, c] ->= [c, c] [c, a] [a, a] [a, c] , 10.39/2.92 [c, a] [a, a] [a, c] [c, c] ->= [c, a] [a, b] [b, c] [c, c] , 10.39/2.92 [c, a] [a, b] [b, a] [a, b] ->= [c, c] [c, a] [a, a] [a, b] , 10.39/2.92 [c, a] [a, a] [a, c] [c, b] ->= [c, a] [a, b] [b, c] [c, b] , 10.39/2.92 [c, b] [b, b] [b, c] [c, a] -> [c, b] [b, b] [b, a] [a, a] , 10.39/2.92 [c, a] [a, a] [a, a] [a, a] -> [c, b] [b, c] [c, b] [b, a] , 10.39/2.92 [c, a] [a, b] [b, a] [a, a] ->= [c, c] [c, a] [a, a] [a, a] , 10.39/2.92 [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.39/2.92 [b, c] [c, c] [c, b] [b, c] -> [b, c] [c, a] [a, a] [a, c] , 10.39/2.92 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.39/2.92 [b, a] [a, b] [b, a] [a, c] ->= [b, c] [c, a] [a, a] [a, c] , 10.39/2.92 [b, a] [a, a] [a, c] [c, c] ->= [b, a] [a, b] [b, c] [c, c] , 10.39/2.92 [b, a] [a, b] [b, a] [a, b] ->= [b, c] [c, a] [a, a] [a, b] , 10.39/2.92 [b, a] [a, a] [a, c] [c, b] ->= [b, a] [a, b] [b, c] [c, b] , 10.39/2.92 [b, c] [c, b] [b, a] [a, a] -> [b, c] [c, a] [a, b] [b, a] , 10.39/2.92 [b, b] [b, b] [b, c] [c, a] -> [b, b] [b, b] [b, a] [a, a] , 10.39/2.92 [b, a] [a, b] [b, a] [a, a] ->= [b, c] [c, a] [a, a] [a, a] , 10.39/2.92 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.39/2.92 [a, c] [c, c] [c, b] [b, c] -> [a, c] [c, a] [a, a] [a, c] , 10.39/2.92 [a, c] [c, b] [b, a] [a, c] -> [a, c] [c, a] [a, b] [b, c] , 10.39/2.92 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.39/2.92 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.39/2.92 [a, a] [a, a] [a, c] [c, c] ->= [a, a] [a, b] [b, c] [c, c] , 10.39/2.92 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.39/2.92 [a, a] [a, a] [a, c] [c, b] ->= [a, a] [a, b] [b, c] [c, b] , 10.39/2.92 [a, c] [c, b] [b, a] [a, a] -> [a, c] [c, a] [a, b] [b, a] , 10.39/2.92 [a, b] [b, b] [b, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] , 10.39/2.92 [a, a] [a, a] [a, a] [a, a] -> [a, b] [b, c] [c, b] [b, a] , 10.39/2.92 [a, a] [a, b] [b, a] [a, a] ->= [a, c] [c, a] [a, a] [a, a] , 10.39/2.92 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.39/2.92 10.39/2.92 10.39/2.92 The system was filtered by the following matrix interpretation 10.39/2.92 of type E_J with J = {1,...,2} and dimension 11: 10.39/2.92 10.39/2.92 [c, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [c, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 1 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 1 1 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [c, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 1 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 1 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 1 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 1 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 1 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 1 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 1 1 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 1 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 10.39/2.92 Remains to prove termination of the 29-rule system 10.39/2.92 { [c, a] [a, a] [a, a] [a, c] -> [c, b] [b, c] [c, b] [b, c] , 10.39/2.92 [c, a] [a, b] [b, a] [a, c] ->= [c, c] [c, a] [a, a] [a, c] , 10.39/2.92 [c, a] [a, a] [a, c] [c, c] ->= [c, a] [a, b] [b, c] [c, c] , 10.39/2.92 [c, a] [a, b] [b, a] [a, b] ->= [c, c] [c, a] [a, a] [a, b] , 10.39/2.92 [c, a] [a, a] [a, c] [c, b] ->= [c, a] [a, b] [b, c] [c, b] , 10.39/2.92 [c, b] [b, b] [b, c] [c, a] -> [c, b] [b, b] [b, a] [a, a] , 10.39/2.92 [c, a] [a, a] [a, a] [a, a] -> [c, b] [b, c] [c, b] [b, a] , 10.39/2.92 [c, a] [a, b] [b, a] [a, a] ->= [c, c] [c, a] [a, a] [a, a] , 10.39/2.92 [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.39/2.92 [b, c] [c, c] [c, b] [b, c] -> [b, c] [c, a] [a, a] [a, c] , 10.39/2.92 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.39/2.92 [b, a] [a, b] [b, a] [a, c] ->= [b, c] [c, a] [a, a] [a, c] , 10.39/2.92 [b, a] [a, a] [a, c] [c, c] ->= [b, a] [a, b] [b, c] [c, c] , 10.39/2.92 [b, a] [a, b] [b, a] [a, b] ->= [b, c] [c, a] [a, a] [a, b] , 10.39/2.92 [b, a] [a, a] [a, c] [c, b] ->= [b, a] [a, b] [b, c] [c, b] , 10.39/2.92 [b, c] [c, b] [b, a] [a, a] -> [b, c] [c, a] [a, b] [b, a] , 10.39/2.92 [b, b] [b, b] [b, c] [c, a] -> [b, b] [b, b] [b, a] [a, a] , 10.39/2.92 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.39/2.92 [a, c] [c, c] [c, b] [b, c] -> [a, c] [c, a] [a, a] [a, c] , 10.39/2.92 [a, c] [c, b] [b, a] [a, c] -> [a, c] [c, a] [a, b] [b, c] , 10.39/2.92 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.39/2.92 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.39/2.92 [a, a] [a, a] [a, c] [c, c] ->= [a, a] [a, b] [b, c] [c, c] , 10.39/2.92 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.39/2.92 [a, a] [a, a] [a, c] [c, b] ->= [a, a] [a, b] [b, c] [c, b] , 10.39/2.92 [a, c] [c, b] [b, a] [a, a] -> [a, c] [c, a] [a, b] [b, a] , 10.39/2.92 [a, b] [b, b] [b, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] , 10.39/2.92 [a, a] [a, a] [a, a] [a, a] -> [a, b] [b, c] [c, b] [b, a] , 10.39/2.92 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.39/2.92 10.39/2.92 10.39/2.92 The system was filtered by the following matrix interpretation 10.39/2.92 of type E_J with J = {1,...,2} and dimension 11: 10.39/2.92 10.39/2.92 [c, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [c, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 1 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 1 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [c, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 1 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 1 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 1 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 1 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 1 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 1 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 1 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 1 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 1 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 10.39/2.92 Remains to prove termination of the 28-rule system 10.39/2.92 { [c, a] [a, a] [a, a] [a, c] -> [c, b] [b, c] [c, b] [b, c] , 10.39/2.92 [c, a] [a, b] [b, a] [a, c] ->= [c, c] [c, a] [a, a] [a, c] , 10.39/2.92 [c, a] [a, a] [a, c] [c, c] ->= [c, a] [a, b] [b, c] [c, c] , 10.39/2.92 [c, a] [a, b] [b, a] [a, b] ->= [c, c] [c, a] [a, a] [a, b] , 10.39/2.92 [c, a] [a, a] [a, c] [c, b] ->= [c, a] [a, b] [b, c] [c, b] , 10.39/2.92 [c, b] [b, b] [b, c] [c, a] -> [c, b] [b, b] [b, a] [a, a] , 10.39/2.92 [c, a] [a, a] [a, a] [a, a] -> [c, b] [b, c] [c, b] [b, a] , 10.39/2.92 [c, a] [a, b] [b, a] [a, a] ->= [c, c] [c, a] [a, a] [a, a] , 10.39/2.92 [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.39/2.92 [b, c] [c, c] [c, b] [b, c] -> [b, c] [c, a] [a, a] [a, c] , 10.39/2.92 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.39/2.92 [b, a] [a, b] [b, a] [a, c] ->= [b, c] [c, a] [a, a] [a, c] , 10.39/2.92 [b, a] [a, a] [a, c] [c, c] ->= [b, a] [a, b] [b, c] [c, c] , 10.39/2.92 [b, a] [a, b] [b, a] [a, b] ->= [b, c] [c, a] [a, a] [a, b] , 10.39/2.92 [b, a] [a, a] [a, c] [c, b] ->= [b, a] [a, b] [b, c] [c, b] , 10.39/2.92 [b, c] [c, b] [b, a] [a, a] -> [b, c] [c, a] [a, b] [b, a] , 10.39/2.92 [b, b] [b, b] [b, c] [c, a] -> [b, b] [b, b] [b, a] [a, a] , 10.39/2.92 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.39/2.92 [a, c] [c, c] [c, b] [b, c] -> [a, c] [c, a] [a, a] [a, c] , 10.39/2.92 [a, c] [c, b] [b, a] [a, c] -> [a, c] [c, a] [a, b] [b, c] , 10.39/2.92 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.39/2.92 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.39/2.92 [a, a] [a, a] [a, c] [c, c] ->= [a, a] [a, b] [b, c] [c, c] , 10.39/2.92 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.39/2.92 [a, a] [a, a] [a, c] [c, b] ->= [a, a] [a, b] [b, c] [c, b] , 10.39/2.92 [a, c] [c, b] [b, a] [a, a] -> [a, c] [c, a] [a, b] [b, a] , 10.39/2.92 [a, b] [b, b] [b, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] , 10.39/2.92 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.39/2.92 10.39/2.92 10.39/2.92 The system was filtered by the following matrix interpretation 10.39/2.92 of type E_J with J = {1,...,2} and dimension 11: 10.39/2.92 10.39/2.92 [c, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [c, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 1 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 1 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [c, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 1 0 0 0 0 0 1 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 1 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 1 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 1 | 10.39/2.92 | 0 0 0 0 0 0 0 1 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 1 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 1 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 1 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 0 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 10.39/2.92 Remains to prove termination of the 27-rule system 10.39/2.92 { [c, a] [a, a] [a, a] [a, c] -> [c, b] [b, c] [c, b] [b, c] , 10.39/2.92 [c, a] [a, b] [b, a] [a, c] ->= [c, c] [c, a] [a, a] [a, c] , 10.39/2.92 [c, a] [a, a] [a, c] [c, c] ->= [c, a] [a, b] [b, c] [c, c] , 10.39/2.92 [c, a] [a, b] [b, a] [a, b] ->= [c, c] [c, a] [a, a] [a, b] , 10.39/2.92 [c, a] [a, a] [a, c] [c, b] ->= [c, a] [a, b] [b, c] [c, b] , 10.39/2.92 [c, b] [b, b] [b, c] [c, a] -> [c, b] [b, b] [b, a] [a, a] , 10.39/2.92 [c, a] [a, a] [a, a] [a, a] -> [c, b] [b, c] [c, b] [b, a] , 10.39/2.92 [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.39/2.92 [b, c] [c, c] [c, b] [b, c] -> [b, c] [c, a] [a, a] [a, c] , 10.39/2.92 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.39/2.92 [b, a] [a, b] [b, a] [a, c] ->= [b, c] [c, a] [a, a] [a, c] , 10.39/2.92 [b, a] [a, a] [a, c] [c, c] ->= [b, a] [a, b] [b, c] [c, c] , 10.39/2.92 [b, a] [a, b] [b, a] [a, b] ->= [b, c] [c, a] [a, a] [a, b] , 10.39/2.92 [b, a] [a, a] [a, c] [c, b] ->= [b, a] [a, b] [b, c] [c, b] , 10.39/2.92 [b, c] [c, b] [b, a] [a, a] -> [b, c] [c, a] [a, b] [b, a] , 10.39/2.92 [b, b] [b, b] [b, c] [c, a] -> [b, b] [b, b] [b, a] [a, a] , 10.39/2.92 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.39/2.92 [a, c] [c, c] [c, b] [b, c] -> [a, c] [c, a] [a, a] [a, c] , 10.39/2.92 [a, c] [c, b] [b, a] [a, c] -> [a, c] [c, a] [a, b] [b, c] , 10.39/2.92 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.39/2.92 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.39/2.92 [a, a] [a, a] [a, c] [c, c] ->= [a, a] [a, b] [b, c] [c, c] , 10.39/2.92 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.39/2.92 [a, a] [a, a] [a, c] [c, b] ->= [a, a] [a, b] [b, c] [c, b] , 10.39/2.92 [a, c] [c, b] [b, a] [a, a] -> [a, c] [c, a] [a, b] [b, a] , 10.39/2.92 [a, b] [b, b] [b, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] , 10.39/2.92 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.39/2.92 10.39/2.92 10.39/2.92 The system was filtered by the following matrix interpretation 10.39/2.92 of type E_J with J = {1,...,2} and dimension 5: 10.39/2.92 10.39/2.92 [c, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [c, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [c, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 1 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 | 0 0 0 1 0 | 10.39/2.92 | 0 0 0 0 1 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 10.39/2.92 Remains to prove termination of the 26-rule system 10.39/2.92 { [c, a] [a, a] [a, a] [a, c] -> [c, b] [b, c] [c, b] [b, c] , 10.39/2.92 [c, a] [a, b] [b, a] [a, c] ->= [c, c] [c, a] [a, a] [a, c] , 10.39/2.92 [c, a] [a, a] [a, c] [c, c] ->= [c, a] [a, b] [b, c] [c, c] , 10.39/2.92 [c, a] [a, b] [b, a] [a, b] ->= [c, c] [c, a] [a, a] [a, b] , 10.39/2.92 [c, a] [a, a] [a, c] [c, b] ->= [c, a] [a, b] [b, c] [c, b] , 10.39/2.92 [c, b] [b, b] [b, c] [c, a] -> [c, b] [b, b] [b, a] [a, a] , 10.39/2.92 [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.39/2.92 [b, c] [c, c] [c, b] [b, c] -> [b, c] [c, a] [a, a] [a, c] , 10.39/2.92 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.39/2.92 [b, a] [a, b] [b, a] [a, c] ->= [b, c] [c, a] [a, a] [a, c] , 10.39/2.92 [b, a] [a, a] [a, c] [c, c] ->= [b, a] [a, b] [b, c] [c, c] , 10.39/2.92 [b, a] [a, b] [b, a] [a, b] ->= [b, c] [c, a] [a, a] [a, b] , 10.39/2.92 [b, a] [a, a] [a, c] [c, b] ->= [b, a] [a, b] [b, c] [c, b] , 10.39/2.92 [b, c] [c, b] [b, a] [a, a] -> [b, c] [c, a] [a, b] [b, a] , 10.39/2.92 [b, b] [b, b] [b, c] [c, a] -> [b, b] [b, b] [b, a] [a, a] , 10.39/2.92 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.39/2.92 [a, c] [c, c] [c, b] [b, c] -> [a, c] [c, a] [a, a] [a, c] , 10.39/2.92 [a, c] [c, b] [b, a] [a, c] -> [a, c] [c, a] [a, b] [b, c] , 10.39/2.92 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.39/2.92 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.39/2.92 [a, a] [a, a] [a, c] [c, c] ->= [a, a] [a, b] [b, c] [c, c] , 10.39/2.92 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.39/2.92 [a, a] [a, a] [a, c] [c, b] ->= [a, a] [a, b] [b, c] [c, b] , 10.39/2.92 [a, c] [c, b] [b, a] [a, a] -> [a, c] [c, a] [a, b] [b, a] , 10.39/2.92 [a, b] [b, b] [b, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] , 10.39/2.92 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.39/2.92 10.39/2.92 10.39/2.92 The system was filtered by the following matrix interpretation 10.39/2.92 of type E_J with J = {1,...,2} and dimension 5: 10.39/2.92 10.39/2.92 [c, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [c, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [c, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 1 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 | 0 0 0 1 0 | 10.39/2.92 | 0 0 0 0 1 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, c] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, a] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [a, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 [b, b] is interpreted by 10.39/2.92 / \ 10.39/2.92 | 1 0 0 0 0 | 10.39/2.92 | 0 1 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 | 0 0 0 0 0 | 10.39/2.92 \ / 10.39/2.92 10.39/2.92 Remains to prove termination of the 25-rule system 10.39/2.92 { [c, a] [a, b] [b, a] [a, c] ->= [c, c] [c, a] [a, a] [a, c] , 10.39/2.93 [c, a] [a, a] [a, c] [c, c] ->= [c, a] [a, b] [b, c] [c, c] , 10.39/2.93 [c, a] [a, b] [b, a] [a, b] ->= [c, c] [c, a] [a, a] [a, b] , 10.39/2.93 [c, a] [a, a] [a, c] [c, b] ->= [c, a] [a, b] [b, c] [c, b] , 10.39/2.93 [c, b] [b, b] [b, c] [c, a] -> [c, b] [b, b] [b, a] [a, a] , 10.39/2.93 [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.39/2.93 [b, c] [c, c] [c, b] [b, c] -> [b, c] [c, a] [a, a] [a, c] , 10.39/2.93 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.39/2.93 [b, a] [a, b] [b, a] [a, c] ->= [b, c] [c, a] [a, a] [a, c] , 10.39/2.93 [b, a] [a, a] [a, c] [c, c] ->= [b, a] [a, b] [b, c] [c, c] , 10.39/2.93 [b, a] [a, b] [b, a] [a, b] ->= [b, c] [c, a] [a, a] [a, b] , 10.39/2.93 [b, a] [a, a] [a, c] [c, b] ->= [b, a] [a, b] [b, c] [c, b] , 10.39/2.93 [b, c] [c, b] [b, a] [a, a] -> [b, c] [c, a] [a, b] [b, a] , 10.39/2.93 [b, b] [b, b] [b, c] [c, a] -> [b, b] [b, b] [b, a] [a, a] , 10.39/2.93 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.39/2.93 [a, c] [c, c] [c, b] [b, c] -> [a, c] [c, a] [a, a] [a, c] , 10.39/2.93 [a, c] [c, b] [b, a] [a, c] -> [a, c] [c, a] [a, b] [b, c] , 10.39/2.93 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.39/2.93 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.39/2.93 [a, a] [a, a] [a, c] [c, c] ->= [a, a] [a, b] [b, c] [c, c] , 10.39/2.93 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.39/2.93 [a, a] [a, a] [a, c] [c, b] ->= [a, a] [a, b] [b, c] [c, b] , 10.39/2.93 [a, c] [c, b] [b, a] [a, a] -> [a, c] [c, a] [a, b] [b, a] , 10.39/2.93 [a, b] [b, b] [b, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] , 10.39/2.93 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.39/2.93 10.39/2.93 10.39/2.93 The system was filtered by the following matrix interpretation 10.39/2.93 of type E_J with J = {1,...,2} and dimension 5: 10.39/2.93 10.39/2.93 [c, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [c, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 1 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 1 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [c, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 1 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 1 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 10.39/2.93 Remains to prove termination of the 23-rule system 10.39/2.93 { [c, a] [a, b] [b, a] [a, c] ->= [c, c] [c, a] [a, a] [a, c] , 10.39/2.93 [c, a] [a, a] [a, c] [c, c] ->= [c, a] [a, b] [b, c] [c, c] , 10.39/2.93 [c, a] [a, b] [b, a] [a, b] ->= [c, c] [c, a] [a, a] [a, b] , 10.39/2.93 [c, a] [a, a] [a, c] [c, b] ->= [c, a] [a, b] [b, c] [c, b] , 10.39/2.93 [c, b] [b, b] [b, c] [c, a] -> [c, b] [b, b] [b, a] [a, a] , 10.39/2.93 [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.39/2.93 [b, c] [c, c] [c, b] [b, c] -> [b, c] [c, a] [a, a] [a, c] , 10.39/2.93 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.39/2.93 [b, a] [a, b] [b, a] [a, c] ->= [b, c] [c, a] [a, a] [a, c] , 10.39/2.93 [b, a] [a, a] [a, c] [c, c] ->= [b, a] [a, b] [b, c] [c, c] , 10.39/2.93 [b, a] [a, b] [b, a] [a, b] ->= [b, c] [c, a] [a, a] [a, b] , 10.39/2.93 [b, a] [a, a] [a, c] [c, b] ->= [b, a] [a, b] [b, c] [c, b] , 10.39/2.93 [b, b] [b, b] [b, c] [c, a] -> [b, b] [b, b] [b, a] [a, a] , 10.39/2.93 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.39/2.93 [a, c] [c, c] [c, b] [b, c] -> [a, c] [c, a] [a, a] [a, c] , 10.39/2.93 [a, c] [c, b] [b, a] [a, c] -> [a, c] [c, a] [a, b] [b, c] , 10.39/2.93 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.39/2.93 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.39/2.93 [a, a] [a, a] [a, c] [c, c] ->= [a, a] [a, b] [b, c] [c, c] , 10.39/2.93 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.39/2.93 [a, a] [a, a] [a, c] [c, b] ->= [a, a] [a, b] [b, c] [c, b] , 10.39/2.93 [a, b] [b, b] [b, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] , 10.39/2.93 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.39/2.93 10.39/2.93 10.39/2.93 The system was filtered by the following matrix interpretation 10.39/2.93 of type E_J with J = {1,...,2} and dimension 5: 10.39/2.93 10.39/2.93 [c, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [c, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [c, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 1 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 1 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 1 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 10.39/2.93 Remains to prove termination of the 22-rule system 10.39/2.93 { [c, a] [a, a] [a, c] [c, c] ->= [c, a] [a, b] [b, c] [c, c] , 10.39/2.93 [c, a] [a, b] [b, a] [a, b] ->= [c, c] [c, a] [a, a] [a, b] , 10.39/2.93 [c, a] [a, a] [a, c] [c, b] ->= [c, a] [a, b] [b, c] [c, b] , 10.39/2.93 [c, b] [b, b] [b, c] [c, a] -> [c, b] [b, b] [b, a] [a, a] , 10.39/2.93 [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.39/2.93 [b, c] [c, c] [c, b] [b, c] -> [b, c] [c, a] [a, a] [a, c] , 10.39/2.93 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.39/2.93 [b, a] [a, b] [b, a] [a, c] ->= [b, c] [c, a] [a, a] [a, c] , 10.39/2.93 [b, a] [a, a] [a, c] [c, c] ->= [b, a] [a, b] [b, c] [c, c] , 10.39/2.93 [b, a] [a, b] [b, a] [a, b] ->= [b, c] [c, a] [a, a] [a, b] , 10.39/2.93 [b, a] [a, a] [a, c] [c, b] ->= [b, a] [a, b] [b, c] [c, b] , 10.39/2.93 [b, b] [b, b] [b, c] [c, a] -> [b, b] [b, b] [b, a] [a, a] , 10.39/2.93 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.39/2.93 [a, c] [c, c] [c, b] [b, c] -> [a, c] [c, a] [a, a] [a, c] , 10.39/2.93 [a, c] [c, b] [b, a] [a, c] -> [a, c] [c, a] [a, b] [b, c] , 10.39/2.93 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.39/2.93 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.39/2.93 [a, a] [a, a] [a, c] [c, c] ->= [a, a] [a, b] [b, c] [c, c] , 10.39/2.93 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.39/2.93 [a, a] [a, a] [a, c] [c, b] ->= [a, a] [a, b] [b, c] [c, b] , 10.39/2.93 [a, b] [b, b] [b, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] , 10.39/2.93 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.39/2.93 10.39/2.93 10.39/2.93 The system was filtered by the following matrix interpretation 10.39/2.93 of type E_J with J = {1,...,2} and dimension 5: 10.39/2.93 10.39/2.93 [c, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [c, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [c, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 1 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 1 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 1 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 10.39/2.93 Remains to prove termination of the 21-rule system 10.39/2.93 { [c, a] [a, a] [a, c] [c, c] ->= [c, a] [a, b] [b, c] [c, c] , 10.39/2.93 [c, a] [a, b] [b, a] [a, b] ->= [c, c] [c, a] [a, a] [a, b] , 10.39/2.93 [c, a] [a, a] [a, c] [c, b] ->= [c, a] [a, b] [b, c] [c, b] , 10.39/2.93 [c, b] [b, b] [b, c] [c, a] -> [c, b] [b, b] [b, a] [a, a] , 10.39/2.93 [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.39/2.93 [b, c] [c, c] [c, b] [b, c] -> [b, c] [c, a] [a, a] [a, c] , 10.39/2.93 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.39/2.93 [b, a] [a, a] [a, c] [c, c] ->= [b, a] [a, b] [b, c] [c, c] , 10.39/2.93 [b, a] [a, b] [b, a] [a, b] ->= [b, c] [c, a] [a, a] [a, b] , 10.39/2.93 [b, a] [a, a] [a, c] [c, b] ->= [b, a] [a, b] [b, c] [c, b] , 10.39/2.93 [b, b] [b, b] [b, c] [c, a] -> [b, b] [b, b] [b, a] [a, a] , 10.39/2.93 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.39/2.93 [a, c] [c, c] [c, b] [b, c] -> [a, c] [c, a] [a, a] [a, c] , 10.39/2.93 [a, c] [c, b] [b, a] [a, c] -> [a, c] [c, a] [a, b] [b, c] , 10.39/2.93 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.39/2.93 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.39/2.93 [a, a] [a, a] [a, c] [c, c] ->= [a, a] [a, b] [b, c] [c, c] , 10.39/2.93 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.39/2.93 [a, a] [a, a] [a, c] [c, b] ->= [a, a] [a, b] [b, c] [c, b] , 10.39/2.93 [a, b] [b, b] [b, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] , 10.39/2.93 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.39/2.93 10.39/2.93 10.39/2.93 The system was filtered by the following matrix interpretation 10.39/2.93 of type E_J with J = {1,...,2} and dimension 5: 10.39/2.93 10.39/2.93 [c, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [c, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [c, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 1 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 1 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 1 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 1 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 10.39/2.93 Remains to prove termination of the 20-rule system 10.39/2.93 { [c, a] [a, a] [a, c] [c, c] ->= [c, a] [a, b] [b, c] [c, c] , 10.39/2.93 [c, a] [a, b] [b, a] [a, b] ->= [c, c] [c, a] [a, a] [a, b] , 10.39/2.93 [c, a] [a, a] [a, c] [c, b] ->= [c, a] [a, b] [b, c] [c, b] , 10.39/2.93 [c, b] [b, b] [b, c] [c, a] -> [c, b] [b, b] [b, a] [a, a] , 10.39/2.93 [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.39/2.93 [b, c] [c, c] [c, b] [b, c] -> [b, c] [c, a] [a, a] [a, c] , 10.39/2.93 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.39/2.93 [b, a] [a, a] [a, c] [c, c] ->= [b, a] [a, b] [b, c] [c, c] , 10.39/2.93 [b, a] [a, b] [b, a] [a, b] ->= [b, c] [c, a] [a, a] [a, b] , 10.39/2.93 [b, b] [b, b] [b, c] [c, a] -> [b, b] [b, b] [b, a] [a, a] , 10.39/2.93 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.39/2.93 [a, c] [c, c] [c, b] [b, c] -> [a, c] [c, a] [a, a] [a, c] , 10.39/2.93 [a, c] [c, b] [b, a] [a, c] -> [a, c] [c, a] [a, b] [b, c] , 10.39/2.93 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.39/2.93 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.39/2.93 [a, a] [a, a] [a, c] [c, c] ->= [a, a] [a, b] [b, c] [c, c] , 10.39/2.93 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.39/2.93 [a, a] [a, a] [a, c] [c, b] ->= [a, a] [a, b] [b, c] [c, b] , 10.39/2.93 [a, b] [b, b] [b, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] , 10.39/2.93 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.39/2.93 10.39/2.93 10.39/2.93 The system was filtered by the following matrix interpretation 10.39/2.93 of type E_J with J = {1,...,2} and dimension 5: 10.39/2.93 10.39/2.93 [c, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [c, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [c, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 1 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 1 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 1 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 10.39/2.93 Remains to prove termination of the 19-rule system 10.39/2.93 { [c, a] [a, a] [a, c] [c, c] ->= [c, a] [a, b] [b, c] [c, c] , 10.39/2.93 [c, a] [a, a] [a, c] [c, b] ->= [c, a] [a, b] [b, c] [c, b] , 10.39/2.93 [c, b] [b, b] [b, c] [c, a] -> [c, b] [b, b] [b, a] [a, a] , 10.39/2.93 [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.39/2.93 [b, c] [c, c] [c, b] [b, c] -> [b, c] [c, a] [a, a] [a, c] , 10.39/2.93 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.39/2.93 [b, a] [a, a] [a, c] [c, c] ->= [b, a] [a, b] [b, c] [c, c] , 10.39/2.93 [b, a] [a, b] [b, a] [a, b] ->= [b, c] [c, a] [a, a] [a, b] , 10.39/2.93 [b, b] [b, b] [b, c] [c, a] -> [b, b] [b, b] [b, a] [a, a] , 10.39/2.93 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.39/2.93 [a, c] [c, c] [c, b] [b, c] -> [a, c] [c, a] [a, a] [a, c] , 10.39/2.93 [a, c] [c, b] [b, a] [a, c] -> [a, c] [c, a] [a, b] [b, c] , 10.39/2.93 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.39/2.93 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.39/2.93 [a, a] [a, a] [a, c] [c, c] ->= [a, a] [a, b] [b, c] [c, c] , 10.39/2.93 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.39/2.93 [a, a] [a, a] [a, c] [c, b] ->= [a, a] [a, b] [b, c] [c, b] , 10.39/2.93 [a, b] [b, b] [b, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] , 10.39/2.93 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.39/2.93 10.39/2.93 10.39/2.93 The system was filtered by the following matrix interpretation 10.39/2.93 of type E_J with J = {1,...,2} and dimension 2: 10.39/2.93 10.39/2.93 [c, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 1 | 10.39/2.93 | 0 1 | 10.39/2.93 \ / 10.39/2.93 [c, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 | 10.39/2.93 | 0 1 | 10.39/2.93 \ / 10.39/2.93 [b, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 | 10.39/2.93 | 0 1 | 10.39/2.93 \ / 10.39/2.93 [c, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 | 10.39/2.93 | 0 1 | 10.39/2.93 \ / 10.39/2.93 [a, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 | 10.39/2.93 | 0 1 | 10.39/2.93 \ / 10.39/2.93 [a, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 | 10.39/2.93 | 0 1 | 10.39/2.93 \ / 10.39/2.93 [b, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 | 10.39/2.93 | 0 1 | 10.39/2.93 \ / 10.39/2.93 [a, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 | 10.39/2.93 | 0 1 | 10.39/2.93 \ / 10.39/2.93 [b, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 | 10.39/2.93 | 0 1 | 10.39/2.93 \ / 10.39/2.93 10.39/2.93 Remains to prove termination of the 17-rule system 10.39/2.93 { [c, a] [a, a] [a, c] [c, c] ->= [c, a] [a, b] [b, c] [c, c] , 10.39/2.93 [c, a] [a, a] [a, c] [c, b] ->= [c, a] [a, b] [b, c] [c, b] , 10.39/2.93 [c, b] [b, b] [b, c] [c, a] -> [c, b] [b, b] [b, a] [a, a] , 10.39/2.93 [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.39/2.93 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.39/2.93 [b, a] [a, a] [a, c] [c, c] ->= [b, a] [a, b] [b, c] [c, c] , 10.39/2.93 [b, a] [a, b] [b, a] [a, b] ->= [b, c] [c, a] [a, a] [a, b] , 10.39/2.93 [b, b] [b, b] [b, c] [c, a] -> [b, b] [b, b] [b, a] [a, a] , 10.39/2.93 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.39/2.93 [a, c] [c, b] [b, a] [a, c] -> [a, c] [c, a] [a, b] [b, c] , 10.39/2.93 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.39/2.93 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.39/2.93 [a, a] [a, a] [a, c] [c, c] ->= [a, a] [a, b] [b, c] [c, c] , 10.39/2.93 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.39/2.93 [a, a] [a, a] [a, c] [c, b] ->= [a, a] [a, b] [b, c] [c, b] , 10.39/2.93 [a, b] [b, b] [b, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] , 10.39/2.93 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.39/2.93 10.39/2.93 10.39/2.93 The system was filtered by the following matrix interpretation 10.39/2.93 of type E_J with J = {1,...,2} and dimension 5: 10.39/2.93 10.39/2.93 [c, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [c, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [c, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 1 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 1 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 1 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 1 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 10.39/2.93 Remains to prove termination of the 16-rule system 10.39/2.93 { [c, a] [a, a] [a, c] [c, b] ->= [c, a] [a, b] [b, c] [c, b] , 10.39/2.93 [c, b] [b, b] [b, c] [c, a] -> [c, b] [b, b] [b, a] [a, a] , 10.39/2.93 [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.39/2.93 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.39/2.93 [b, a] [a, a] [a, c] [c, c] ->= [b, a] [a, b] [b, c] [c, c] , 10.39/2.93 [b, a] [a, b] [b, a] [a, b] ->= [b, c] [c, a] [a, a] [a, b] , 10.39/2.93 [b, b] [b, b] [b, c] [c, a] -> [b, b] [b, b] [b, a] [a, a] , 10.39/2.93 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.39/2.93 [a, c] [c, b] [b, a] [a, c] -> [a, c] [c, a] [a, b] [b, c] , 10.39/2.93 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.39/2.93 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.39/2.93 [a, a] [a, a] [a, c] [c, c] ->= [a, a] [a, b] [b, c] [c, c] , 10.39/2.93 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.39/2.93 [a, a] [a, a] [a, c] [c, b] ->= [a, a] [a, b] [b, c] [c, b] , 10.39/2.93 [a, b] [b, b] [b, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] , 10.39/2.93 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.39/2.93 10.39/2.93 10.39/2.93 The system was filtered by the following matrix interpretation 10.39/2.93 of type E_J with J = {1,...,2} and dimension 5: 10.39/2.93 10.39/2.93 [c, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [c, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [c, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 1 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 1 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 1 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 1 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 10.39/2.93 Remains to prove termination of the 15-rule system 10.39/2.93 { [c, b] [b, b] [b, c] [c, a] -> [c, b] [b, b] [b, a] [a, a] , 10.39/2.93 [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.39/2.93 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.39/2.93 [b, a] [a, a] [a, c] [c, c] ->= [b, a] [a, b] [b, c] [c, c] , 10.39/2.93 [b, a] [a, b] [b, a] [a, b] ->= [b, c] [c, a] [a, a] [a, b] , 10.39/2.93 [b, b] [b, b] [b, c] [c, a] -> [b, b] [b, b] [b, a] [a, a] , 10.39/2.93 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.39/2.93 [a, c] [c, b] [b, a] [a, c] -> [a, c] [c, a] [a, b] [b, c] , 10.39/2.93 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.39/2.93 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.39/2.93 [a, a] [a, a] [a, c] [c, c] ->= [a, a] [a, b] [b, c] [c, c] , 10.39/2.93 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.39/2.93 [a, a] [a, a] [a, c] [c, b] ->= [a, a] [a, b] [b, c] [c, b] , 10.39/2.93 [a, b] [b, b] [b, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] , 10.39/2.93 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.39/2.93 10.39/2.93 10.39/2.93 The system was filtered by the following matrix interpretation 10.39/2.93 of type E_J with J = {1,...,2} and dimension 5: 10.39/2.93 10.39/2.93 [c, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [c, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 1 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [c, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 1 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 1 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 10.39/2.93 Remains to prove termination of the 14-rule system 10.39/2.93 { [c, b] [b, b] [b, c] [c, a] -> [c, b] [b, b] [b, a] [a, a] , 10.39/2.93 [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.39/2.93 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.39/2.93 [b, a] [a, a] [a, c] [c, c] ->= [b, a] [a, b] [b, c] [c, c] , 10.39/2.93 [b, a] [a, b] [b, a] [a, b] ->= [b, c] [c, a] [a, a] [a, b] , 10.39/2.93 [b, b] [b, b] [b, c] [c, a] -> [b, b] [b, b] [b, a] [a, a] , 10.39/2.93 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.39/2.93 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.39/2.93 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.39/2.93 [a, a] [a, a] [a, c] [c, c] ->= [a, a] [a, b] [b, c] [c, c] , 10.39/2.93 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.39/2.93 [a, a] [a, a] [a, c] [c, b] ->= [a, a] [a, b] [b, c] [c, b] , 10.39/2.93 [a, b] [b, b] [b, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] , 10.39/2.93 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.39/2.93 10.39/2.93 10.39/2.93 The system was filtered by the following matrix interpretation 10.39/2.93 of type E_J with J = {1,...,2} and dimension 5: 10.39/2.93 10.39/2.93 [c, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [c, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [c, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 1 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 1 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 1 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 10.39/2.93 Remains to prove termination of the 13-rule system 10.39/2.93 { [c, b] [b, b] [b, c] [c, a] -> [c, b] [b, b] [b, a] [a, a] , 10.39/2.93 [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.39/2.93 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.39/2.93 [b, a] [a, a] [a, c] [c, c] ->= [b, a] [a, b] [b, c] [c, c] , 10.39/2.93 [b, b] [b, b] [b, c] [c, a] -> [b, b] [b, b] [b, a] [a, a] , 10.39/2.93 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.39/2.93 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.39/2.93 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.39/2.93 [a, a] [a, a] [a, c] [c, c] ->= [a, a] [a, b] [b, c] [c, c] , 10.39/2.93 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.39/2.93 [a, a] [a, a] [a, c] [c, b] ->= [a, a] [a, b] [b, c] [c, b] , 10.39/2.93 [a, b] [b, b] [b, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] , 10.39/2.93 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.39/2.93 10.39/2.93 10.39/2.93 The system was filtered by the following matrix interpretation 10.39/2.93 of type E_J with J = {1,...,2} and dimension 5: 10.39/2.93 10.39/2.93 [c, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [c, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 1 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 1 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [c, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 1 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 10.39/2.93 Remains to prove termination of the 12-rule system 10.39/2.93 { [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.39/2.93 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.39/2.93 [b, a] [a, a] [a, c] [c, c] ->= [b, a] [a, b] [b, c] [c, c] , 10.39/2.93 [b, b] [b, b] [b, c] [c, a] -> [b, b] [b, b] [b, a] [a, a] , 10.39/2.93 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.39/2.93 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.39/2.93 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.39/2.93 [a, a] [a, a] [a, c] [c, c] ->= [a, a] [a, b] [b, c] [c, c] , 10.39/2.93 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.39/2.93 [a, a] [a, a] [a, c] [c, b] ->= [a, a] [a, b] [b, c] [c, b] , 10.39/2.93 [a, b] [b, b] [b, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] , 10.39/2.93 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.39/2.93 10.39/2.93 10.39/2.93 The system was filtered by the following matrix interpretation 10.39/2.93 of type E_J with J = {1,...,2} and dimension 5: 10.39/2.93 10.39/2.93 [c, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [c, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 1 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [c, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 1 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 1 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 10.39/2.93 Remains to prove termination of the 11-rule system 10.39/2.93 { [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.39/2.93 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.39/2.93 [b, a] [a, a] [a, c] [c, c] ->= [b, a] [a, b] [b, c] [c, c] , 10.39/2.93 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.39/2.93 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.39/2.93 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.39/2.93 [a, a] [a, a] [a, c] [c, c] ->= [a, a] [a, b] [b, c] [c, c] , 10.39/2.93 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.39/2.93 [a, a] [a, a] [a, c] [c, b] ->= [a, a] [a, b] [b, c] [c, b] , 10.39/2.93 [a, b] [b, b] [b, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] , 10.39/2.93 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.39/2.93 10.39/2.93 10.39/2.93 The system was filtered by the following matrix interpretation 10.39/2.93 of type E_J with J = {1,...,2} and dimension 5: 10.39/2.93 10.39/2.93 [c, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [c, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [c, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 1 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 1 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 1 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 1 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 10.39/2.93 Remains to prove termination of the 10-rule system 10.39/2.93 { [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.39/2.93 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.39/2.93 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.39/2.93 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.39/2.93 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.39/2.93 [a, a] [a, a] [a, c] [c, c] ->= [a, a] [a, b] [b, c] [c, c] , 10.39/2.93 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.39/2.93 [a, a] [a, a] [a, c] [c, b] ->= [a, a] [a, b] [b, c] [c, b] , 10.39/2.93 [a, b] [b, b] [b, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] , 10.39/2.93 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.39/2.93 10.39/2.93 10.39/2.93 The system was filtered by the following matrix interpretation 10.39/2.93 of type E_J with J = {1,...,2} and dimension 8: 10.39/2.93 10.39/2.93 [c, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [c, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 1 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [c, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 | 0 0 1 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 1 0 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 1 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, c] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 1 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, a] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 0 0 0 | 10.39/2.93 | 0 1 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [a, b] is interpreted by 10.39/2.93 / \ 10.39/2.93 | 1 0 0 0 0 1 0 0 | 10.39/2.93 | 0 1 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 | 0 0 0 0 0 0 0 0 | 10.39/2.93 \ / 10.39/2.93 [b, b] is interpreted by 10.39/2.93 / \ 10.65/2.93 | 1 0 0 0 0 0 0 0 | 10.65/2.93 | 0 1 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 1 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 \ / 10.65/2.93 10.65/2.93 Remains to prove termination of the 9-rule system 10.65/2.93 { [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.65/2.93 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.65/2.93 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.65/2.93 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.65/2.93 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.65/2.93 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.65/2.93 [a, a] [a, a] [a, c] [c, b] ->= [a, a] [a, b] [b, c] [c, b] , 10.65/2.93 [a, b] [b, b] [b, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] , 10.65/2.93 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.65/2.93 10.65/2.93 10.65/2.93 The system was filtered by the following matrix interpretation 10.65/2.93 of type E_J with J = {1,...,2} and dimension 8: 10.65/2.93 10.65/2.93 [c, c] is interpreted by 10.65/2.93 / \ 10.65/2.93 | 1 0 0 0 0 0 0 0 | 10.65/2.93 | 0 1 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 \ / 10.65/2.93 [c, b] is interpreted by 10.65/2.93 / \ 10.65/2.93 | 1 0 0 0 0 0 0 0 | 10.65/2.93 | 0 1 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 1 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 \ / 10.65/2.93 [b, c] is interpreted by 10.65/2.93 / \ 10.65/2.93 | 1 0 0 0 0 0 0 0 | 10.65/2.93 | 0 1 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 1 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 \ / 10.65/2.93 [c, a] is interpreted by 10.65/2.93 / \ 10.65/2.93 | 1 0 0 0 0 0 0 0 | 10.65/2.93 | 0 1 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 1 0 0 0 0 0 | 10.65/2.93 \ / 10.65/2.93 [a, a] is interpreted by 10.65/2.93 / \ 10.65/2.93 | 1 0 1 0 0 0 0 0 | 10.65/2.93 | 0 1 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 1 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 \ / 10.65/2.93 [a, c] is interpreted by 10.65/2.93 / \ 10.65/2.93 | 1 0 0 0 0 0 0 0 | 10.65/2.93 | 0 1 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 1 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 \ / 10.65/2.93 [b, a] is interpreted by 10.65/2.93 / \ 10.65/2.93 | 1 0 0 0 0 0 0 0 | 10.65/2.93 | 0 1 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 \ / 10.65/2.93 [a, b] is interpreted by 10.65/2.93 / \ 10.65/2.93 | 1 0 0 0 0 1 0 0 | 10.65/2.93 | 0 1 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 \ / 10.65/2.93 [b, b] is interpreted by 10.65/2.93 / \ 10.65/2.93 | 1 0 0 0 0 0 0 0 | 10.65/2.93 | 0 1 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 1 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 0 0 0 | 10.65/2.93 \ / 10.65/2.93 10.65/2.93 Remains to prove termination of the 8-rule system 10.65/2.93 { [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.65/2.93 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.65/2.93 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.65/2.93 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.65/2.93 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.65/2.93 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.65/2.93 [a, b] [b, b] [b, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] , 10.65/2.93 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.65/2.93 10.65/2.93 10.65/2.93 The system was filtered by the following matrix interpretation 10.65/2.93 of type E_J with J = {1,...,2} and dimension 5: 10.65/2.93 10.65/2.93 [c, c] is interpreted by 10.65/2.93 / \ 10.65/2.93 | 1 0 0 0 0 | 10.65/2.93 | 0 1 0 0 0 | 10.65/2.93 | 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 | 10.65/2.93 \ / 10.65/2.93 [c, b] is interpreted by 10.65/2.93 / \ 10.65/2.93 | 1 0 0 0 0 | 10.65/2.93 | 0 1 0 0 0 | 10.65/2.93 | 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 | 10.65/2.93 | 0 1 0 0 0 | 10.65/2.93 \ / 10.65/2.93 [b, c] is interpreted by 10.65/2.93 / \ 10.65/2.93 | 1 0 0 0 0 | 10.65/2.93 | 0 1 0 0 0 | 10.65/2.93 | 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 1 | 10.65/2.93 | 0 0 0 0 0 | 10.65/2.93 \ / 10.65/2.93 [c, a] is interpreted by 10.65/2.93 / \ 10.65/2.93 | 1 0 0 0 0 | 10.65/2.93 | 0 1 0 0 0 | 10.65/2.93 | 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 | 10.65/2.93 | 0 1 0 0 0 | 10.65/2.93 \ / 10.65/2.93 [a, a] is interpreted by 10.65/2.93 / \ 10.65/2.93 | 1 0 0 0 0 | 10.65/2.93 | 0 1 0 0 0 | 10.65/2.93 | 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 | 10.65/2.93 \ / 10.65/2.93 [a, c] is interpreted by 10.65/2.93 / \ 10.65/2.93 | 1 0 0 0 0 | 10.65/2.93 | 0 1 0 0 0 | 10.65/2.93 | 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 | 10.65/2.93 \ / 10.65/2.93 [b, a] is interpreted by 10.65/2.93 / \ 10.65/2.93 | 1 0 0 0 0 | 10.65/2.93 | 0 1 0 0 0 | 10.65/2.93 | 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 | 10.65/2.93 \ / 10.65/2.93 [a, b] is interpreted by 10.65/2.93 / \ 10.65/2.93 | 1 0 1 0 0 | 10.65/2.93 | 0 1 0 0 0 | 10.65/2.93 | 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 | 10.65/2.93 \ / 10.65/2.93 [b, b] is interpreted by 10.65/2.93 / \ 10.65/2.93 | 1 0 0 0 0 | 10.65/2.93 | 0 1 0 0 0 | 10.65/2.93 | 0 0 0 1 0 | 10.65/2.93 | 0 0 0 0 0 | 10.65/2.93 | 0 0 0 0 0 | 10.65/2.93 \ / 10.65/2.93 10.65/2.93 Remains to prove termination of the 7-rule system 10.65/2.93 { [c, a] [a, a] [a, c] [c, a] ->= [c, a] [a, b] [b, c] [c, a] , 10.65/2.93 [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.65/2.93 [b, a] [a, a] [a, c] [c, a] ->= [b, a] [a, b] [b, c] [c, a] , 10.65/2.93 [a, a] [a, a] [a, a] [a, c] -> [a, b] [b, c] [c, b] [b, c] , 10.65/2.93 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.65/2.93 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] , 10.65/2.93 [a, a] [a, a] [a, c] [c, a] ->= [a, a] [a, b] [b, c] [c, a] } 10.65/2.93 10.65/2.93 10.65/2.93 The system was filtered by the following matrix interpretation 10.65/2.93 of type E_J with J = {1,...,2} and dimension 2: 10.65/2.93 10.65/2.93 [c, c] is interpreted by 10.65/2.93 / \ 10.65/2.93 | 1 0 | 10.65/2.93 | 0 1 | 10.65/2.93 \ / 10.65/2.93 [c, b] is interpreted by 10.65/2.93 / \ 10.65/2.93 | 1 0 | 10.65/2.93 | 0 1 | 10.65/2.93 \ / 10.65/2.93 [b, c] is interpreted by 10.65/2.93 / \ 10.65/2.93 | 1 0 | 10.65/2.93 | 0 1 | 10.65/2.93 \ / 10.65/2.93 [c, a] is interpreted by 10.65/2.93 / \ 10.65/2.93 | 1 0 | 10.65/2.93 | 0 1 | 10.65/2.93 \ / 10.65/2.93 [a, a] is interpreted by 10.65/2.93 / \ 10.65/2.93 | 1 1 | 10.65/2.93 | 0 1 | 10.65/2.93 \ / 10.65/2.93 [a, c] is interpreted by 10.65/2.93 / \ 10.65/2.93 | 1 0 | 10.65/2.93 | 0 1 | 10.65/2.93 \ / 10.65/2.93 [b, a] is interpreted by 10.65/2.93 / \ 10.65/2.93 | 1 0 | 10.65/2.93 | 0 1 | 10.65/2.93 \ / 10.65/2.93 [a, b] is interpreted by 10.65/2.93 / \ 10.65/2.93 | 1 0 | 10.65/2.93 | 0 1 | 10.65/2.93 \ / 10.65/2.93 [b, b] is interpreted by 10.65/2.93 / \ 10.65/2.93 | 1 0 | 10.65/2.93 | 0 1 | 10.65/2.93 \ / 10.65/2.93 10.65/2.93 Remains to prove termination of the 3-rule system 10.65/2.93 { [b, c] [c, b] [b, a] [a, c] -> [b, c] [c, a] [a, b] [b, c] , 10.65/2.93 [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.65/2.93 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] } 10.65/2.93 10.65/2.93 10.65/2.93 The system was filtered by the following matrix interpretation 10.65/2.93 of type E_J with J = {1,...,2} and dimension 2: 10.65/2.93 10.65/2.93 [c, c] is interpreted by 10.65/2.93 / \ 10.65/2.93 | 1 0 | 10.65/2.93 | 0 1 | 10.65/2.93 \ / 10.65/2.93 [c, b] is interpreted by 10.65/2.93 / \ 10.65/2.93 | 1 1 | 10.65/2.93 | 0 1 | 10.65/2.93 \ / 10.65/2.93 [b, c] is interpreted by 10.65/2.93 / \ 10.65/2.93 | 1 0 | 10.65/2.93 | 0 1 | 10.65/2.93 \ / 10.65/2.93 [c, a] is interpreted by 10.65/2.93 / \ 10.65/2.93 | 1 0 | 10.65/2.93 | 0 1 | 10.65/2.93 \ / 10.65/2.93 [a, a] is interpreted by 10.65/2.93 / \ 10.65/2.93 | 1 0 | 10.65/2.93 | 0 1 | 10.65/2.93 \ / 10.65/2.93 [a, c] is interpreted by 10.65/2.93 / \ 10.65/2.93 | 1 0 | 10.65/2.93 | 0 1 | 10.65/2.93 \ / 10.65/2.93 [b, a] is interpreted by 10.65/2.93 / \ 10.65/2.93 | 1 0 | 10.65/2.93 | 0 1 | 10.65/2.93 \ / 10.65/2.93 [a, b] is interpreted by 10.65/2.93 / \ 10.65/2.93 | 1 0 | 10.65/2.93 | 0 1 | 10.65/2.93 \ / 10.65/2.93 [b, b] is interpreted by 10.65/2.93 / \ 10.65/2.93 | 1 0 | 10.65/2.93 | 0 1 | 10.65/2.93 \ / 10.65/2.93 10.65/2.93 Remains to prove termination of the 2-rule system 10.65/2.93 { [a, a] [a, b] [b, a] [a, c] ->= [a, c] [c, a] [a, a] [a, c] , 10.65/2.93 [a, a] [a, b] [b, a] [a, b] ->= [a, c] [c, a] [a, a] [a, b] } 10.65/2.93 10.65/2.93 10.65/2.93 The system is trivially terminating. 10.65/2.96 EOF