0.00/0.30 YES 0.00/0.30 0.00/0.30 0.00/0.30 Applying context closure of depth 1 in the following form: System R over Sigma 0.00/0.30 maps to { fold(xly) -> fold(xry) | l -> r in R, x,y in Sigma } over Sigma^2, 0.00/0.30 where fold(a_1,...,a_n) = (a_1,a_2)...(a_{n-1}a_{n}) 0.00/0.30 0.00/0.30 Remains to prove termination of the 8-rule system 0.00/0.30 { [a, a] [a, b] [b, b] [b, b] [b, a] [a, a] -> [a, a] , 0.00/0.30 [a, a] ->= [a, a] [a, b] [b, a] [a, a] , 0.00/0.30 [a, a] [a, b] [b, b] [b, b] [b, a] [a, b] -> [a, b] , 0.00/0.30 [a, b] ->= [a, a] [a, b] [b, a] [a, b] , 0.00/0.30 [b, a] [a, b] [b, b] [b, b] [b, a] [a, a] -> [b, a] , 0.00/0.30 [b, a] ->= [b, a] [a, b] [b, a] [a, a] , 0.00/0.30 [b, a] [a, b] [b, b] [b, b] [b, a] [a, b] -> [b, b] , 0.00/0.30 [b, b] ->= [b, a] [a, b] [b, a] [a, b] } 0.00/0.30 0.00/0.30 0.00/0.30 0.00/0.30 The system was filtered by the following matrix interpretation 0.00/0.30 of type E_J with J = {1,...,2} and dimension 2: 0.00/0.30 0.00/0.30 [a, a] is interpreted by 0.00/0.30 / \ 0.00/0.30 | 1 0 | 0.00/0.30 | 0 1 | 0.00/0.30 \ / 0.00/0.30 [a, b] is interpreted by 0.00/0.30 / \ 0.00/0.30 | 1 0 | 0.00/0.30 | 0 1 | 0.00/0.30 \ / 0.00/0.30 [b, b] is interpreted by 0.00/0.30 / \ 0.00/0.30 | 1 1 | 0.00/0.30 | 0 1 | 0.00/0.30 \ / 0.00/0.30 [b, a] is interpreted by 0.00/0.30 / \ 0.00/0.30 | 1 0 | 0.00/0.30 | 0 1 | 0.00/0.30 \ / 0.00/0.30 0.00/0.30 Remains to prove termination of the 3-rule system 0.00/0.30 { [a, a] ->= [a, a] [a, b] [b, a] [a, a] , 0.00/0.30 [a, b] ->= [a, a] [a, b] [b, a] [a, b] , 0.00/0.30 [b, a] ->= [b, a] [a, b] [b, a] [a, a] } 0.00/0.30 0.00/0.30 0.00/0.30 The system is trivially terminating. 0.00/0.33 EOF