0.00/0.51 YES 0.00/0.54 0.00/0.54 0.00/0.54 The system was inverted. 0.00/0.54 0.00/0.54 Remains to prove termination of the 7-rule system 0.00/0.54 { c a a -> a c a , 0.00/0.54 a c c -> a c b , 0.00/0.54 a b b -> a a b , 0.00/0.54 a c c ->= c a b , 0.00/0.54 a a b ->= c a b , 0.00/0.54 a b b ->= a b c , 0.00/0.54 a a a ->= c b a } 0.00/0.54 0.00/0.54 0.00/0.54 0.00/0.54 0.00/0.54 The system was filtered by the following matrix interpretation 0.00/0.54 of type E_J with J = {1,...,2} and dimension 4: 0.00/0.54 0.00/0.54 a is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 1 0 | 0.00/0.54 | 0 1 0 0 | 0.00/0.54 | 0 0 0 0 | 0.00/0.54 | 0 0 0 0 | 0.00/0.54 \ / 0.00/0.54 c is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 0 0 | 0.00/0.54 | 0 1 0 0 | 0.00/0.54 | 0 0 0 1 | 0.00/0.54 | 0 0 0 0 | 0.00/0.54 \ / 0.00/0.54 b is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 0 0 | 0.00/0.54 | 0 1 0 0 | 0.00/0.54 | 0 0 0 0 | 0.00/0.54 | 0 1 0 0 | 0.00/0.54 \ / 0.00/0.54 0.00/0.54 Remains to prove termination of the 6-rule system 0.00/0.54 { a c a -> c a a , 0.00/0.54 a a b -> a b b , 0.00/0.54 c a b ->= a c c , 0.00/0.54 c a b ->= a a b , 0.00/0.54 a b c ->= a b b , 0.00/0.54 c b a ->= a a a } 0.00/0.54 0.00/0.54 0.00/0.54 Applying context closure of depth 1 in the following form: System R over Sigma 0.00/0.54 maps to { fold(xly) -> fold(xry) | l -> r in R, x,y in Sigma } over Sigma^2, 0.00/0.54 where fold(a_1,...,a_n) = (a_1,a_2)...(a_{n-1}a_{n}) 0.00/0.54 0.00/0.54 Remains to prove termination of the 54-rule system 0.00/0.54 { [a, a] [a, c] [c, a] [a, a] -> [a, c] [c, a] [a, a] [a, a] , 0.00/0.54 [a, a] [a, a] [a, b] [b, a] -> [a, a] [a, b] [b, b] [b, a] , 0.00/0.54 [a, c] [c, a] [a, b] [b, a] ->= [a, a] [a, c] [c, c] [c, a] , 0.00/0.54 [a, c] [c, a] [a, b] [b, a] ->= [a, a] [a, a] [a, b] [b, a] , 0.00/0.54 [a, a] [a, b] [b, c] [c, a] ->= [a, a] [a, b] [b, b] [b, a] , 0.00/0.54 [a, c] [c, b] [b, a] [a, a] ->= [a, a] [a, a] [a, a] [a, a] , 0.00/0.54 [a, a] [a, c] [c, a] [a, c] -> [a, c] [c, a] [a, a] [a, c] , 0.00/0.54 [a, a] [a, a] [a, b] [b, c] -> [a, a] [a, b] [b, b] [b, c] , 0.00/0.54 [a, c] [c, a] [a, b] [b, c] ->= [a, a] [a, c] [c, c] [c, c] , 0.00/0.54 [a, c] [c, a] [a, b] [b, c] ->= [a, a] [a, a] [a, b] [b, c] , 0.00/0.54 [a, a] [a, b] [b, c] [c, c] ->= [a, a] [a, b] [b, b] [b, c] , 0.00/0.54 [a, c] [c, b] [b, a] [a, c] ->= [a, a] [a, a] [a, a] [a, c] , 0.00/0.54 [a, a] [a, c] [c, a] [a, b] -> [a, c] [c, a] [a, a] [a, b] , 0.00/0.54 [a, a] [a, a] [a, b] [b, b] -> [a, a] [a, b] [b, b] [b, b] , 0.00/0.54 [a, c] [c, a] [a, b] [b, b] ->= [a, a] [a, c] [c, c] [c, b] , 0.00/0.54 [a, c] [c, a] [a, b] [b, b] ->= [a, a] [a, a] [a, b] [b, b] , 0.00/0.54 [a, a] [a, b] [b, c] [c, b] ->= [a, a] [a, b] [b, b] [b, b] , 0.00/0.54 [a, c] [c, b] [b, a] [a, b] ->= [a, a] [a, a] [a, a] [a, b] , 0.00/0.54 [c, a] [a, c] [c, a] [a, a] -> [c, c] [c, a] [a, a] [a, a] , 0.00/0.54 [c, a] [a, a] [a, b] [b, a] -> [c, a] [a, b] [b, b] [b, a] , 0.00/0.54 [c, c] [c, a] [a, b] [b, a] ->= [c, a] [a, c] [c, c] [c, a] , 0.00/0.54 [c, c] [c, a] [a, b] [b, a] ->= [c, a] [a, a] [a, b] [b, a] , 0.00/0.54 [c, a] [a, b] [b, c] [c, a] ->= [c, a] [a, b] [b, b] [b, a] , 0.00/0.54 [c, c] [c, b] [b, a] [a, a] ->= [c, a] [a, a] [a, a] [a, a] , 0.00/0.54 [c, a] [a, c] [c, a] [a, c] -> [c, c] [c, a] [a, a] [a, c] , 0.00/0.54 [c, a] [a, a] [a, b] [b, c] -> [c, a] [a, b] [b, b] [b, c] , 0.00/0.54 [c, c] [c, a] [a, b] [b, c] ->= [c, a] [a, c] [c, c] [c, c] , 0.00/0.54 [c, c] [c, a] [a, b] [b, c] ->= [c, a] [a, a] [a, b] [b, c] , 0.00/0.54 [c, a] [a, b] [b, c] [c, c] ->= [c, a] [a, b] [b, b] [b, c] , 0.00/0.54 [c, c] [c, b] [b, a] [a, c] ->= [c, a] [a, a] [a, a] [a, c] , 0.00/0.54 [c, a] [a, c] [c, a] [a, b] -> [c, c] [c, a] [a, a] [a, b] , 0.00/0.54 [c, a] [a, a] [a, b] [b, b] -> [c, a] [a, b] [b, b] [b, b] , 0.00/0.54 [c, c] [c, a] [a, b] [b, b] ->= [c, a] [a, c] [c, c] [c, b] , 0.00/0.54 [c, c] [c, a] [a, b] [b, b] ->= [c, a] [a, a] [a, b] [b, b] , 0.00/0.54 [c, a] [a, b] [b, c] [c, b] ->= [c, a] [a, b] [b, b] [b, b] , 0.00/0.54 [c, c] [c, b] [b, a] [a, b] ->= [c, a] [a, a] [a, a] [a, b] , 0.00/0.54 [b, a] [a, c] [c, a] [a, a] -> [b, c] [c, a] [a, a] [a, a] , 0.00/0.54 [b, a] [a, a] [a, b] [b, a] -> [b, a] [a, b] [b, b] [b, a] , 0.00/0.54 [b, c] [c, a] [a, b] [b, a] ->= [b, a] [a, c] [c, c] [c, a] , 0.00/0.54 [b, c] [c, a] [a, b] [b, a] ->= [b, a] [a, a] [a, b] [b, a] , 0.00/0.54 [b, a] [a, b] [b, c] [c, a] ->= [b, a] [a, b] [b, b] [b, a] , 0.00/0.54 [b, c] [c, b] [b, a] [a, a] ->= [b, a] [a, a] [a, a] [a, a] , 0.00/0.54 [b, a] [a, c] [c, a] [a, c] -> [b, c] [c, a] [a, a] [a, c] , 0.00/0.54 [b, a] [a, a] [a, b] [b, c] -> [b, a] [a, b] [b, b] [b, c] , 0.00/0.54 [b, c] [c, a] [a, b] [b, c] ->= [b, a] [a, c] [c, c] [c, c] , 0.00/0.54 [b, c] [c, a] [a, b] [b, c] ->= [b, a] [a, a] [a, b] [b, c] , 0.00/0.54 [b, a] [a, b] [b, c] [c, c] ->= [b, a] [a, b] [b, b] [b, c] , 0.00/0.54 [b, c] [c, b] [b, a] [a, c] ->= [b, a] [a, a] [a, a] [a, c] , 0.00/0.54 [b, a] [a, c] [c, a] [a, b] -> [b, c] [c, a] [a, a] [a, b] , 0.00/0.54 [b, a] [a, a] [a, b] [b, b] -> [b, a] [a, b] [b, b] [b, b] , 0.00/0.54 [b, c] [c, a] [a, b] [b, b] ->= [b, a] [a, c] [c, c] [c, b] , 0.00/0.54 [b, c] [c, a] [a, b] [b, b] ->= [b, a] [a, a] [a, b] [b, b] , 0.00/0.54 [b, a] [a, b] [b, c] [c, b] ->= [b, a] [a, b] [b, b] [b, b] , 0.00/0.54 [b, c] [c, b] [b, a] [a, b] ->= [b, a] [a, a] [a, a] [a, b] } 0.00/0.54 0.00/0.54 0.00/0.54 0.00/0.54 The system was filtered by the following matrix interpretation 0.00/0.54 of type E_J with J = {1,...,2} and dimension 2: 0.00/0.54 0.00/0.54 [a, a] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [a, c] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [c, a] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [a, b] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 1 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [b, a] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [b, b] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [c, c] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [b, c] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [c, b] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 0.00/0.54 Remains to prove termination of the 45-rule system 0.00/0.54 { [a, a] [a, c] [c, a] [a, a] -> [a, c] [c, a] [a, a] [a, a] , 0.00/0.54 [a, a] [a, a] [a, b] [b, a] -> [a, a] [a, b] [b, b] [b, a] , 0.00/0.54 [a, c] [c, a] [a, b] [b, a] ->= [a, a] [a, a] [a, b] [b, a] , 0.00/0.54 [a, a] [a, b] [b, c] [c, a] ->= [a, a] [a, b] [b, b] [b, a] , 0.00/0.54 [a, c] [c, b] [b, a] [a, a] ->= [a, a] [a, a] [a, a] [a, a] , 0.00/0.54 [a, a] [a, c] [c, a] [a, c] -> [a, c] [c, a] [a, a] [a, c] , 0.00/0.54 [a, a] [a, a] [a, b] [b, c] -> [a, a] [a, b] [b, b] [b, c] , 0.00/0.54 [a, c] [c, a] [a, b] [b, c] ->= [a, a] [a, a] [a, b] [b, c] , 0.00/0.54 [a, a] [a, b] [b, c] [c, c] ->= [a, a] [a, b] [b, b] [b, c] , 0.00/0.54 [a, c] [c, b] [b, a] [a, c] ->= [a, a] [a, a] [a, a] [a, c] , 0.00/0.54 [a, a] [a, c] [c, a] [a, b] -> [a, c] [c, a] [a, a] [a, b] , 0.00/0.54 [a, a] [a, a] [a, b] [b, b] -> [a, a] [a, b] [b, b] [b, b] , 0.00/0.54 [a, c] [c, a] [a, b] [b, b] ->= [a, a] [a, a] [a, b] [b, b] , 0.00/0.54 [a, a] [a, b] [b, c] [c, b] ->= [a, a] [a, b] [b, b] [b, b] , 0.00/0.54 [a, c] [c, b] [b, a] [a, b] ->= [a, a] [a, a] [a, a] [a, b] , 0.00/0.54 [c, a] [a, c] [c, a] [a, a] -> [c, c] [c, a] [a, a] [a, a] , 0.00/0.54 [c, a] [a, a] [a, b] [b, a] -> [c, a] [a, b] [b, b] [b, a] , 0.00/0.54 [c, c] [c, a] [a, b] [b, a] ->= [c, a] [a, a] [a, b] [b, a] , 0.00/0.54 [c, a] [a, b] [b, c] [c, a] ->= [c, a] [a, b] [b, b] [b, a] , 0.00/0.54 [c, c] [c, b] [b, a] [a, a] ->= [c, a] [a, a] [a, a] [a, a] , 0.00/0.54 [c, a] [a, c] [c, a] [a, c] -> [c, c] [c, a] [a, a] [a, c] , 0.00/0.54 [c, a] [a, a] [a, b] [b, c] -> [c, a] [a, b] [b, b] [b, c] , 0.00/0.54 [c, c] [c, a] [a, b] [b, c] ->= [c, a] [a, a] [a, b] [b, c] , 0.00/0.54 [c, a] [a, b] [b, c] [c, c] ->= [c, a] [a, b] [b, b] [b, c] , 0.00/0.54 [c, c] [c, b] [b, a] [a, c] ->= [c, a] [a, a] [a, a] [a, c] , 0.00/0.54 [c, a] [a, c] [c, a] [a, b] -> [c, c] [c, a] [a, a] [a, b] , 0.00/0.54 [c, a] [a, a] [a, b] [b, b] -> [c, a] [a, b] [b, b] [b, b] , 0.00/0.54 [c, c] [c, a] [a, b] [b, b] ->= [c, a] [a, a] [a, b] [b, b] , 0.00/0.54 [c, a] [a, b] [b, c] [c, b] ->= [c, a] [a, b] [b, b] [b, b] , 0.00/0.54 [c, c] [c, b] [b, a] [a, b] ->= [c, a] [a, a] [a, a] [a, b] , 0.00/0.54 [b, a] [a, c] [c, a] [a, a] -> [b, c] [c, a] [a, a] [a, a] , 0.00/0.54 [b, a] [a, a] [a, b] [b, a] -> [b, a] [a, b] [b, b] [b, a] , 0.00/0.54 [b, c] [c, a] [a, b] [b, a] ->= [b, a] [a, a] [a, b] [b, a] , 0.00/0.54 [b, a] [a, b] [b, c] [c, a] ->= [b, a] [a, b] [b, b] [b, a] , 0.00/0.54 [b, c] [c, b] [b, a] [a, a] ->= [b, a] [a, a] [a, a] [a, a] , 0.00/0.54 [b, a] [a, c] [c, a] [a, c] -> [b, c] [c, a] [a, a] [a, c] , 0.00/0.54 [b, a] [a, a] [a, b] [b, c] -> [b, a] [a, b] [b, b] [b, c] , 0.00/0.54 [b, c] [c, a] [a, b] [b, c] ->= [b, a] [a, a] [a, b] [b, c] , 0.00/0.54 [b, a] [a, b] [b, c] [c, c] ->= [b, a] [a, b] [b, b] [b, c] , 0.00/0.54 [b, c] [c, b] [b, a] [a, c] ->= [b, a] [a, a] [a, a] [a, c] , 0.00/0.54 [b, a] [a, c] [c, a] [a, b] -> [b, c] [c, a] [a, a] [a, b] , 0.00/0.54 [b, a] [a, a] [a, b] [b, b] -> [b, a] [a, b] [b, b] [b, b] , 0.00/0.54 [b, c] [c, a] [a, b] [b, b] ->= [b, a] [a, a] [a, b] [b, b] , 0.00/0.54 [b, a] [a, b] [b, c] [c, b] ->= [b, a] [a, b] [b, b] [b, b] , 0.00/0.54 [b, c] [c, b] [b, a] [a, b] ->= [b, a] [a, a] [a, a] [a, b] } 0.00/0.54 0.00/0.54 0.00/0.54 The system was filtered by the following matrix interpretation 0.00/0.54 of type E_J with J = {1,...,2} and dimension 2: 0.00/0.54 0.00/0.54 [a, a] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [a, c] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 1 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [c, a] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [a, b] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [b, a] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [b, b] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [c, c] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [b, c] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [c, b] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 0.00/0.54 Remains to prove termination of the 33-rule system 0.00/0.54 { [a, a] [a, c] [c, a] [a, a] -> [a, c] [c, a] [a, a] [a, a] , 0.00/0.54 [a, a] [a, a] [a, b] [b, a] -> [a, a] [a, b] [b, b] [b, a] , 0.00/0.54 [a, a] [a, b] [b, c] [c, a] ->= [a, a] [a, b] [b, b] [b, a] , 0.00/0.54 [a, a] [a, c] [c, a] [a, c] -> [a, c] [c, a] [a, a] [a, c] , 0.00/0.54 [a, a] [a, a] [a, b] [b, c] -> [a, a] [a, b] [b, b] [b, c] , 0.00/0.54 [a, a] [a, b] [b, c] [c, c] ->= [a, a] [a, b] [b, b] [b, c] , 0.00/0.54 [a, a] [a, c] [c, a] [a, b] -> [a, c] [c, a] [a, a] [a, b] , 0.00/0.54 [a, a] [a, a] [a, b] [b, b] -> [a, a] [a, b] [b, b] [b, b] , 0.00/0.54 [a, a] [a, b] [b, c] [c, b] ->= [a, a] [a, b] [b, b] [b, b] , 0.00/0.54 [c, a] [a, a] [a, b] [b, a] -> [c, a] [a, b] [b, b] [b, a] , 0.00/0.54 [c, c] [c, a] [a, b] [b, a] ->= [c, a] [a, a] [a, b] [b, a] , 0.00/0.54 [c, a] [a, b] [b, c] [c, a] ->= [c, a] [a, b] [b, b] [b, a] , 0.00/0.54 [c, c] [c, b] [b, a] [a, a] ->= [c, a] [a, a] [a, a] [a, a] , 0.00/0.54 [c, a] [a, a] [a, b] [b, c] -> [c, a] [a, b] [b, b] [b, c] , 0.00/0.54 [c, c] [c, a] [a, b] [b, c] ->= [c, a] [a, a] [a, b] [b, c] , 0.00/0.54 [c, a] [a, b] [b, c] [c, c] ->= [c, a] [a, b] [b, b] [b, c] , 0.00/0.54 [c, c] [c, b] [b, a] [a, c] ->= [c, a] [a, a] [a, a] [a, c] , 0.00/0.54 [c, a] [a, a] [a, b] [b, b] -> [c, a] [a, b] [b, b] [b, b] , 0.00/0.54 [c, c] [c, a] [a, b] [b, b] ->= [c, a] [a, a] [a, b] [b, b] , 0.00/0.54 [c, a] [a, b] [b, c] [c, b] ->= [c, a] [a, b] [b, b] [b, b] , 0.00/0.54 [c, c] [c, b] [b, a] [a, b] ->= [c, a] [a, a] [a, a] [a, b] , 0.00/0.54 [b, a] [a, a] [a, b] [b, a] -> [b, a] [a, b] [b, b] [b, a] , 0.00/0.54 [b, c] [c, a] [a, b] [b, a] ->= [b, a] [a, a] [a, b] [b, a] , 0.00/0.54 [b, a] [a, b] [b, c] [c, a] ->= [b, a] [a, b] [b, b] [b, a] , 0.00/0.54 [b, c] [c, b] [b, a] [a, a] ->= [b, a] [a, a] [a, a] [a, a] , 0.00/0.54 [b, a] [a, a] [a, b] [b, c] -> [b, a] [a, b] [b, b] [b, c] , 0.00/0.54 [b, c] [c, a] [a, b] [b, c] ->= [b, a] [a, a] [a, b] [b, c] , 0.00/0.54 [b, a] [a, b] [b, c] [c, c] ->= [b, a] [a, b] [b, b] [b, c] , 0.00/0.54 [b, c] [c, b] [b, a] [a, c] ->= [b, a] [a, a] [a, a] [a, c] , 0.00/0.54 [b, a] [a, a] [a, b] [b, b] -> [b, a] [a, b] [b, b] [b, b] , 0.00/0.54 [b, c] [c, a] [a, b] [b, b] ->= [b, a] [a, a] [a, b] [b, b] , 0.00/0.54 [b, a] [a, b] [b, c] [c, b] ->= [b, a] [a, b] [b, b] [b, b] , 0.00/0.54 [b, c] [c, b] [b, a] [a, b] ->= [b, a] [a, a] [a, a] [a, b] } 0.00/0.54 0.00/0.54 0.00/0.54 The system was filtered by the following matrix interpretation 0.00/0.54 of type E_J with J = {1,...,2} and dimension 2: 0.00/0.54 0.00/0.54 [a, a] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [a, c] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [c, a] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [a, b] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [b, a] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [b, b] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [c, c] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 1 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [b, c] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [c, b] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 0.00/0.54 Remains to prove termination of the 24-rule system 0.00/0.54 { [a, a] [a, c] [c, a] [a, a] -> [a, c] [c, a] [a, a] [a, a] , 0.00/0.54 [a, a] [a, a] [a, b] [b, a] -> [a, a] [a, b] [b, b] [b, a] , 0.00/0.54 [a, a] [a, b] [b, c] [c, a] ->= [a, a] [a, b] [b, b] [b, a] , 0.00/0.54 [a, a] [a, c] [c, a] [a, c] -> [a, c] [c, a] [a, a] [a, c] , 0.00/0.54 [a, a] [a, a] [a, b] [b, c] -> [a, a] [a, b] [b, b] [b, c] , 0.00/0.54 [a, a] [a, c] [c, a] [a, b] -> [a, c] [c, a] [a, a] [a, b] , 0.00/0.54 [a, a] [a, a] [a, b] [b, b] -> [a, a] [a, b] [b, b] [b, b] , 0.00/0.54 [a, a] [a, b] [b, c] [c, b] ->= [a, a] [a, b] [b, b] [b, b] , 0.00/0.54 [c, a] [a, a] [a, b] [b, a] -> [c, a] [a, b] [b, b] [b, a] , 0.00/0.54 [c, a] [a, b] [b, c] [c, a] ->= [c, a] [a, b] [b, b] [b, a] , 0.00/0.54 [c, a] [a, a] [a, b] [b, c] -> [c, a] [a, b] [b, b] [b, c] , 0.00/0.54 [c, a] [a, a] [a, b] [b, b] -> [c, a] [a, b] [b, b] [b, b] , 0.00/0.54 [c, a] [a, b] [b, c] [c, b] ->= [c, a] [a, b] [b, b] [b, b] , 0.00/0.54 [b, a] [a, a] [a, b] [b, a] -> [b, a] [a, b] [b, b] [b, a] , 0.00/0.54 [b, c] [c, a] [a, b] [b, a] ->= [b, a] [a, a] [a, b] [b, a] , 0.00/0.54 [b, a] [a, b] [b, c] [c, a] ->= [b, a] [a, b] [b, b] [b, a] , 0.00/0.54 [b, c] [c, b] [b, a] [a, a] ->= [b, a] [a, a] [a, a] [a, a] , 0.00/0.54 [b, a] [a, a] [a, b] [b, c] -> [b, a] [a, b] [b, b] [b, c] , 0.00/0.54 [b, c] [c, a] [a, b] [b, c] ->= [b, a] [a, a] [a, b] [b, c] , 0.00/0.54 [b, c] [c, b] [b, a] [a, c] ->= [b, a] [a, a] [a, a] [a, c] , 0.00/0.54 [b, a] [a, a] [a, b] [b, b] -> [b, a] [a, b] [b, b] [b, b] , 0.00/0.54 [b, c] [c, a] [a, b] [b, b] ->= [b, a] [a, a] [a, b] [b, b] , 0.00/0.54 [b, a] [a, b] [b, c] [c, b] ->= [b, a] [a, b] [b, b] [b, b] , 0.00/0.54 [b, c] [c, b] [b, a] [a, b] ->= [b, a] [a, a] [a, a] [a, b] } 0.00/0.54 0.00/0.54 0.00/0.54 The system was filtered by the following matrix interpretation 0.00/0.54 of type E_J with J = {1,...,2} and dimension 2: 0.00/0.54 0.00/0.54 [a, a] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [a, c] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [c, a] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 1 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [a, b] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [b, a] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [b, b] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [c, c] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [b, c] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [c, b] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 0.00/0.54 Remains to prove termination of the 18-rule system 0.00/0.54 { [a, a] [a, c] [c, a] [a, a] -> [a, c] [c, a] [a, a] [a, a] , 0.00/0.54 [a, a] [a, a] [a, b] [b, a] -> [a, a] [a, b] [b, b] [b, a] , 0.00/0.54 [a, a] [a, c] [c, a] [a, c] -> [a, c] [c, a] [a, a] [a, c] , 0.00/0.54 [a, a] [a, a] [a, b] [b, c] -> [a, a] [a, b] [b, b] [b, c] , 0.00/0.54 [a, a] [a, c] [c, a] [a, b] -> [a, c] [c, a] [a, a] [a, b] , 0.00/0.54 [a, a] [a, a] [a, b] [b, b] -> [a, a] [a, b] [b, b] [b, b] , 0.00/0.54 [a, a] [a, b] [b, c] [c, b] ->= [a, a] [a, b] [b, b] [b, b] , 0.00/0.54 [c, a] [a, a] [a, b] [b, a] -> [c, a] [a, b] [b, b] [b, a] , 0.00/0.54 [c, a] [a, a] [a, b] [b, c] -> [c, a] [a, b] [b, b] [b, c] , 0.00/0.54 [c, a] [a, a] [a, b] [b, b] -> [c, a] [a, b] [b, b] [b, b] , 0.00/0.54 [c, a] [a, b] [b, c] [c, b] ->= [c, a] [a, b] [b, b] [b, b] , 0.00/0.54 [b, a] [a, a] [a, b] [b, a] -> [b, a] [a, b] [b, b] [b, a] , 0.00/0.54 [b, c] [c, b] [b, a] [a, a] ->= [b, a] [a, a] [a, a] [a, a] , 0.00/0.54 [b, a] [a, a] [a, b] [b, c] -> [b, a] [a, b] [b, b] [b, c] , 0.00/0.54 [b, c] [c, b] [b, a] [a, c] ->= [b, a] [a, a] [a, a] [a, c] , 0.00/0.54 [b, a] [a, a] [a, b] [b, b] -> [b, a] [a, b] [b, b] [b, b] , 0.00/0.54 [b, a] [a, b] [b, c] [c, b] ->= [b, a] [a, b] [b, b] [b, b] , 0.00/0.54 [b, c] [c, b] [b, a] [a, b] ->= [b, a] [a, a] [a, a] [a, b] } 0.00/0.54 0.00/0.54 0.00/0.54 The system was filtered by the following matrix interpretation 0.00/0.54 of type E_J with J = {1,...,2} and dimension 2: 0.00/0.54 0.00/0.54 [a, a] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [a, c] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [c, a] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [a, b] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [b, a] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [b, b] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [c, c] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [b, c] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 1 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [c, b] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 0.00/0.54 Remains to prove termination of the 12-rule system 0.00/0.54 { [a, a] [a, c] [c, a] [a, a] -> [a, c] [c, a] [a, a] [a, a] , 0.00/0.54 [a, a] [a, a] [a, b] [b, a] -> [a, a] [a, b] [b, b] [b, a] , 0.00/0.54 [a, a] [a, c] [c, a] [a, c] -> [a, c] [c, a] [a, a] [a, c] , 0.00/0.54 [a, a] [a, a] [a, b] [b, c] -> [a, a] [a, b] [b, b] [b, c] , 0.00/0.54 [a, a] [a, c] [c, a] [a, b] -> [a, c] [c, a] [a, a] [a, b] , 0.00/0.54 [a, a] [a, a] [a, b] [b, b] -> [a, a] [a, b] [b, b] [b, b] , 0.00/0.54 [c, a] [a, a] [a, b] [b, a] -> [c, a] [a, b] [b, b] [b, a] , 0.00/0.54 [c, a] [a, a] [a, b] [b, c] -> [c, a] [a, b] [b, b] [b, c] , 0.00/0.54 [c, a] [a, a] [a, b] [b, b] -> [c, a] [a, b] [b, b] [b, b] , 0.00/0.54 [b, a] [a, a] [a, b] [b, a] -> [b, a] [a, b] [b, b] [b, a] , 0.00/0.54 [b, a] [a, a] [a, b] [b, c] -> [b, a] [a, b] [b, b] [b, c] , 0.00/0.54 [b, a] [a, a] [a, b] [b, b] -> [b, a] [a, b] [b, b] [b, b] } 0.00/0.54 0.00/0.54 0.00/0.54 The system was filtered by the following matrix interpretation 0.00/0.54 of type E_J with J = {1,...,2} and dimension 2: 0.00/0.54 0.00/0.54 [a, a] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 1 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [a, c] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [c, a] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [a, b] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [b, a] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [b, b] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [c, c] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [b, c] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 [c, b] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 | 0.00/0.54 | 0 1 | 0.00/0.54 \ / 0.00/0.54 0.00/0.54 Remains to prove termination of the 3-rule system 0.00/0.54 { [a, a] [a, c] [c, a] [a, a] -> [a, c] [c, a] [a, a] [a, a] , 0.00/0.54 [a, a] [a, c] [c, a] [a, c] -> [a, c] [c, a] [a, a] [a, c] , 0.00/0.54 [a, a] [a, c] [c, a] [a, b] -> [a, c] [c, a] [a, a] [a, b] } 0.00/0.54 0.00/0.54 0.00/0.54 The system was filtered by the following matrix interpretation 0.00/0.54 of type E_J with J = {1,...,2} and dimension 5: 0.00/0.54 0.00/0.54 [a, a] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 1 0 0 | 0.00/0.54 | 0 1 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 \ / 0.00/0.54 [a, c] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 0 0 0 | 0.00/0.54 | 0 1 0 0 0 | 0.00/0.54 | 0 0 0 1 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 \ / 0.00/0.54 [c, a] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 1 0 0 | 0.00/0.54 | 0 1 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 | 0 0 0 0 1 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 \ / 0.00/0.54 [a, b] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 0 0 0 | 0.00/0.54 | 0 1 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 | 0 1 0 0 0 | 0.00/0.54 \ / 0.00/0.54 [b, a] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 0 0 0 | 0.00/0.54 | 0 1 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 \ / 0.00/0.54 [b, b] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 0 0 0 | 0.00/0.54 | 0 1 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 \ / 0.00/0.54 [c, c] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 0 0 0 | 0.00/0.54 | 0 1 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 \ / 0.00/0.54 [b, c] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 0 0 0 | 0.00/0.54 | 0 1 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 \ / 0.00/0.54 [c, b] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 0 0 0 | 0.00/0.54 | 0 1 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 \ / 0.00/0.54 0.00/0.54 Remains to prove termination of the 2-rule system 0.00/0.54 { [a, a] [a, c] [c, a] [a, a] -> [a, c] [c, a] [a, a] [a, a] , 0.00/0.54 [a, a] [a, c] [c, a] [a, c] -> [a, c] [c, a] [a, a] [a, c] } 0.00/0.54 0.00/0.54 0.00/0.54 The system was filtered by the following matrix interpretation 0.00/0.54 of type E_J with J = {1,...,2} and dimension 5: 0.00/0.54 0.00/0.54 [a, a] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 1 0 0 | 0.00/0.54 | 0 1 0 0 0 | 0.00/0.54 | 0 0 1 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 | 0 1 0 0 0 | 0.00/0.54 \ / 0.00/0.54 [a, c] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 0 0 0 | 0.00/0.54 | 0 1 0 0 0 | 0.00/0.54 | 0 0 0 1 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 | 0 1 0 0 0 | 0.00/0.54 \ / 0.00/0.54 [c, a] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 0 0 0 | 0.00/0.54 | 0 1 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 | 0 0 1 0 1 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 \ / 0.00/0.54 [a, b] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 0 0 0 | 0.00/0.54 | 0 1 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 \ / 0.00/0.54 [b, a] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 0 0 0 | 0.00/0.54 | 0 1 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 \ / 0.00/0.54 [b, b] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 0 0 0 | 0.00/0.54 | 0 1 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 \ / 0.00/0.54 [c, c] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 0 0 0 | 0.00/0.54 | 0 1 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 \ / 0.00/0.54 [b, c] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 0 0 0 | 0.00/0.54 | 0 1 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 \ / 0.00/0.54 [c, b] is interpreted by 0.00/0.54 / \ 0.00/0.54 | 1 0 0 0 0 | 0.00/0.54 | 0 1 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 | 0 0 0 0 0 | 0.00/0.54 \ / 0.00/0.54 0.00/0.54 Remains to prove termination of the 0-rule system 0.00/0.54 { } 0.00/0.54 0.00/0.54 0.00/0.54 The system is trivially terminating. 1.44/0.58 EOF