10.27/2.87 YES 10.41/2.92 10.41/2.92 10.41/2.92 Applying context closure of depth 1 in the following form: System R over Sigma 10.41/2.92 maps to { fold(xly) -> fold(xry) | l -> r in R, x,y in Sigma } over Sigma^2, 10.41/2.92 where fold(a_1,...,a_n) = (a_1,a_2)...(a_{n-1}a_{n}) 10.41/2.92 10.41/2.92 Remains to prove termination of the 4-rule system 10.41/2.92 { [a, a] [a, b] [b, a] [a, b] [b, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] -> [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, b] [b, a] [a, b] [b, a] [a, b] [b, a] , 10.41/2.92 [a, a] [a, b] [b, a] [a, b] [b, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, b] -> [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, b] [b, a] [a, b] [b, a] [a, b] [b, b] , 10.41/2.92 [b, a] [a, b] [b, a] [a, b] [b, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] -> [b, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, b] [b, a] [a, b] [b, a] [a, b] [b, a] , 10.41/2.92 [b, a] [a, b] [b, a] [a, b] [b, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, b] -> [b, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, b] [b, a] [a, b] [b, a] [a, b] [b, b] } 10.41/2.92 10.41/2.92 10.41/2.92 10.41/2.92 The system was filtered by the following matrix interpretation 10.41/2.92 of type E_J with J = {1,...,2} and dimension 13: 10.41/2.92 10.41/2.92 [a, a] is interpreted by 10.41/2.92 / \ 10.41/2.92 | 1 0 1 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 1 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 1 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 1 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 1 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 1 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 1 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 1 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 \ / 10.41/2.92 [a, b] is interpreted by 10.41/2.92 / \ 10.41/2.92 | 1 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 1 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 1 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 1 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 1 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 \ / 10.41/2.92 [b, a] is interpreted by 10.41/2.92 / \ 10.41/2.92 | 1 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 1 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 1 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 1 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 \ / 10.41/2.92 [b, b] is interpreted by 10.41/2.92 / \ 10.41/2.92 | 1 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 1 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 \ / 10.41/2.92 10.41/2.92 Remains to prove termination of the 3-rule system 10.41/2.92 { [a, a] [a, b] [b, a] [a, b] [b, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] -> [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, b] [b, a] [a, b] [b, a] [a, b] [b, a] , 10.41/2.92 [b, a] [a, b] [b, a] [a, b] [b, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] -> [b, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, b] [b, a] [a, b] [b, a] [a, b] [b, a] , 10.41/2.92 [b, a] [a, b] [b, a] [a, b] [b, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, b] -> [b, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, b] [b, a] [a, b] [b, a] [a, b] [b, b] } 10.41/2.92 10.41/2.92 10.41/2.92 The system was reversed. 10.41/2.92 10.41/2.92 Remains to prove termination of the 3-rule system 10.41/2.92 { [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [b, a] [a, b] [b, a] [a, b] [a, a] -> [b, a] [a, b] [b, a] [a, b] [b, a] [a, b] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] , 10.41/2.92 [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [b, a] [a, b] [b, a] [a, b] [b, a] -> [b, a] [a, b] [b, a] [a, b] [b, a] [a, b] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [b, a] , 10.41/2.92 [a, b] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [b, a] [a, b] [b, a] [a, b] [b, a] -> [b, b] [a, b] [b, a] [a, b] [b, a] [a, b] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [b, a] } 10.41/2.92 10.41/2.92 10.41/2.92 The dependency pairs transformation was applied. 10.41/2.92 10.41/2.92 Remains to prove termination of the 34-rule system 10.41/2.92 { ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) -> ([a, b],true) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) -> ([a, b],true) ([b, a],false) ([a, b],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) -> ([a, b],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) -> ([a, a],true) ([a, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) -> ([a, a],true) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, b],true) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, b],true) ([b, a],false) ([a, b],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, b],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([b, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, a],true) ([a, a],false) ([b, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, a],true) ([b, a],false) , 10.41/2.92 ([a, b],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, b],true) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) , 10.41/2.92 ([a, b],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, b],true) ([b, a],false) ([a, b],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) , 10.41/2.92 ([a, b],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, b],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) , 10.41/2.92 ([a, b],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) , 10.41/2.92 ([a, b],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) , 10.41/2.92 ([a, b],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) , 10.41/2.92 ([a, b],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) , 10.41/2.92 ([a, b],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([b, a],false) , 10.41/2.92 ([a, b],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, a],true) ([a, a],false) ([b, a],false) , 10.41/2.92 ([a, b],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, a],true) ([b, a],false) , 10.41/2.92 ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) ->= ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) , 10.41/2.92 ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) ->= ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) , 10.41/2.92 ([a, b],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) ->= ([b, b],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) } 10.41/2.92 10.41/2.92 10.41/2.92 10.41/2.92 10.41/2.92 The system was filtered by the following matrix interpretation 10.41/2.92 of type E_J with J = {1,...,2} and dimension 13: 10.41/2.92 10.41/2.92 ([a, a],true) is interpreted by 10.41/2.92 / \ 10.41/2.92 | 1 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 1 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 \ / 10.41/2.92 ([a, a],false) is interpreted by 10.41/2.92 / \ 10.41/2.92 | 1 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 1 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 1 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 1 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 1 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 1 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 1 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 1 0 0 0 0 | 10.41/2.92 | 0 0 1 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 1 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 1 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 \ / 10.41/2.92 ([b, a],false) is interpreted by 10.41/2.92 / \ 10.41/2.92 | 1 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 1 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 1 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 1 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 1 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 \ / 10.41/2.92 ([a, b],false) is interpreted by 10.41/2.92 / \ 10.41/2.92 | 1 0 1 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 1 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 1 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 1 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 \ / 10.41/2.92 ([a, b],true) is interpreted by 10.41/2.92 / \ 10.41/2.92 | 1 0 1 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 1 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 \ / 10.41/2.92 ([b, b],false) is interpreted by 10.41/2.92 / \ 10.41/2.92 | 1 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 1 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 \ / 10.41/2.92 10.41/2.92 Remains to prove termination of the 23-rule system 10.41/2.92 { ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) -> ([a, b],true) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) -> ([a, b],true) ([b, a],false) ([a, b],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) -> ([a, b],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) -> ([a, a],true) ([a, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) -> ([a, a],true) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, b],true) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, b],true) ([b, a],false) ([a, b],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, b],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([b, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, a],true) ([a, a],false) ([b, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, a],true) ([b, a],false) , 10.41/2.92 ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) ->= ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) , 10.41/2.92 ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) ->= ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) } 10.41/2.92 10.41/2.92 10.41/2.92 The system was filtered by the following matrix interpretation 10.41/2.92 of type E_J with J = {1,...,2} and dimension 2: 10.41/2.92 10.41/2.92 ([a, a],true) is interpreted by 10.41/2.92 / \ 10.41/2.92 | 1 1 | 10.41/2.92 | 0 1 | 10.41/2.92 \ / 10.41/2.92 ([a, a],false) is interpreted by 10.41/2.92 / \ 10.41/2.92 | 1 0 | 10.41/2.92 | 0 1 | 10.41/2.92 \ / 10.41/2.92 ([b, a],false) is interpreted by 10.41/2.92 / \ 10.41/2.92 | 1 0 | 10.41/2.92 | 0 1 | 10.41/2.92 \ / 10.41/2.92 ([a, b],false) is interpreted by 10.41/2.92 / \ 10.41/2.92 | 1 0 | 10.41/2.92 | 0 1 | 10.41/2.92 \ / 10.41/2.92 ([a, b],true) is interpreted by 10.41/2.92 / \ 10.41/2.92 | 1 0 | 10.41/2.92 | 0 1 | 10.41/2.92 \ / 10.41/2.92 ([b, b],false) is interpreted by 10.41/2.92 / \ 10.41/2.92 | 1 0 | 10.41/2.92 | 0 1 | 10.41/2.92 \ / 10.41/2.92 10.41/2.92 Remains to prove termination of the 17-rule system 10.41/2.92 { ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) -> ([a, a],true) ([a, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) -> ([a, a],true) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([b, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, a],true) ([a, a],false) ([b, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, a],true) ([b, a],false) , 10.41/2.92 ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) ->= ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) , 10.41/2.92 ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) ->= ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) } 10.41/2.92 10.41/2.92 10.41/2.92 The system was filtered by the following matrix interpretation 10.41/2.92 of type E_J with J = {1,...,2} and dimension 2: 10.41/2.92 10.41/2.92 ([a, a],true) is interpreted by 10.41/2.92 / \ 10.41/2.92 | 1 0 | 10.41/2.92 | 0 1 | 10.41/2.92 \ / 10.41/2.92 ([a, a],false) is interpreted by 10.41/2.92 / \ 10.41/2.92 | 1 1 | 10.41/2.92 | 0 1 | 10.41/2.92 \ / 10.41/2.92 ([b, a],false) is interpreted by 10.41/2.92 / \ 10.41/2.92 | 1 0 | 10.41/2.92 | 0 1 | 10.41/2.92 \ / 10.41/2.92 ([a, b],false) is interpreted by 10.41/2.92 / \ 10.41/2.92 | 1 0 | 10.41/2.92 | 0 1 | 10.41/2.92 \ / 10.41/2.92 ([a, b],true) is interpreted by 10.41/2.92 / \ 10.41/2.92 | 1 0 | 10.41/2.92 | 0 1 | 10.41/2.92 \ / 10.41/2.92 ([b, b],false) is interpreted by 10.41/2.92 / \ 10.41/2.92 | 1 0 | 10.41/2.92 | 0 1 | 10.41/2.92 \ / 10.41/2.92 10.41/2.92 Remains to prove termination of the 4-rule system 10.41/2.92 { ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) , 10.41/2.92 ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) , 10.41/2.92 ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) ->= ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) , 10.41/2.92 ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) ->= ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ([b, a],false) } 10.41/2.92 10.41/2.92 10.41/2.92 The system was filtered by the following matrix interpretation 10.41/2.92 of type E_J with J = {1,...,2} and dimension 13: 10.41/2.92 10.41/2.92 ([a, a],true) is interpreted by 10.41/2.92 / \ 10.41/2.92 | 1 0 1 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 1 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 \ / 10.41/2.92 ([a, a],false) is interpreted by 10.41/2.92 / \ 10.41/2.92 | 2 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 1 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 1 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 1 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 1 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 1 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 1 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 1 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 1 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 \ / 10.41/2.92 ([b, a],false) is interpreted by 10.41/2.92 / \ 10.41/2.92 | 1 1 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 1 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 1 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 1 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 \ / 10.41/2.92 ([a, b],false) is interpreted by 10.41/2.92 / \ 10.41/2.92 | 1 0 0 0 0 0 0 0 1 0 0 0 0 | 10.41/2.92 | 0 1 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 1 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 1 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 \ / 10.41/2.92 ([a, b],true) is interpreted by 10.41/2.92 / \ 10.41/2.92 | 1 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 1 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 \ / 10.41/2.92 ([b, b],false) is interpreted by 10.41/2.92 / \ 10.41/2.92 | 1 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 1 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 | 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10.41/2.92 \ / 10.41/2.92 10.41/2.92 Remains to prove termination of the 0-rule system 10.41/2.92 { } 10.41/2.92 10.41/2.92 10.41/2.92 The system is trivially terminating. 10.59/2.95 EOF