8.53/2.41 YES 8.53/2.46 8.53/2.46 8.53/2.46 Applying context closure of depth 1 in the following form: System R over Sigma 8.53/2.46 maps to { fold(xly) -> fold(xry) | l -> r in R, x,y in Sigma } over Sigma^2, 8.53/2.46 where fold(a_1,...,a_n) = (a_1,a_2)...(a_{n-1}a_{n}) 8.53/2.46 8.53/2.46 Remains to prove termination of the 36-rule system 8.53/2.46 { [a, a] [a, a] -> [a, a] , 8.53/2.46 [a, a] [a, b] [b, a] -> [a, b] [b, c] [c, a] [a, a] , 8.53/2.46 [a, c] [c, a] -> [a, b] [b, a] , 8.53/2.46 [a, c] [c, c] [c, a] -> [a, a] [a, c] [c, a] , 8.53/2.46 [a, a] [a, b] -> [a, b] , 8.53/2.46 [a, a] [a, b] [b, b] -> [a, b] [b, c] [c, a] [a, b] , 8.53/2.46 [a, c] [c, b] -> [a, b] [b, b] , 8.53/2.46 [a, c] [c, c] [c, b] -> [a, a] [a, c] [c, b] , 8.53/2.46 [a, a] [a, c] -> [a, c] , 8.53/2.46 [a, a] [a, b] [b, c] -> [a, b] [b, c] [c, a] [a, c] , 8.53/2.46 [a, c] [c, c] -> [a, b] [b, c] , 8.53/2.46 [a, c] [c, c] [c, c] -> [a, a] [a, c] [c, c] , 8.53/2.46 [b, a] [a, a] -> [b, a] , 8.53/2.46 [b, a] [a, b] [b, a] -> [b, b] [b, c] [c, a] [a, a] , 8.53/2.46 [b, c] [c, a] -> [b, b] [b, a] , 8.53/2.46 [b, c] [c, c] [c, a] -> [b, a] [a, c] [c, a] , 8.53/2.46 [b, a] [a, b] -> [b, b] , 8.53/2.46 [b, a] [a, b] [b, b] -> [b, b] [b, c] [c, a] [a, b] , 8.53/2.46 [b, c] [c, b] -> [b, b] [b, b] , 8.53/2.46 [b, c] [c, c] [c, b] -> [b, a] [a, c] [c, b] , 8.53/2.46 [b, a] [a, c] -> [b, c] , 8.53/2.46 [b, a] [a, b] [b, c] -> [b, b] [b, c] [c, a] [a, c] , 8.53/2.46 [b, c] [c, c] -> [b, b] [b, c] , 8.53/2.46 [b, c] [c, c] [c, c] -> [b, a] [a, c] [c, c] , 8.53/2.46 [c, a] [a, a] -> [c, a] , 8.53/2.46 [c, a] [a, b] [b, a] -> [c, b] [b, c] [c, a] [a, a] , 8.53/2.46 [c, c] [c, a] -> [c, b] [b, a] , 8.53/2.46 [c, c] [c, c] [c, a] -> [c, a] [a, c] [c, a] , 8.53/2.46 [c, a] [a, b] -> [c, b] , 8.53/2.46 [c, a] [a, b] [b, b] -> [c, b] [b, c] [c, a] [a, b] , 8.53/2.46 [c, c] [c, b] -> [c, b] [b, b] , 8.53/2.46 [c, c] [c, c] [c, b] -> [c, a] [a, c] [c, b] , 8.53/2.46 [c, a] [a, c] -> [c, c] , 8.53/2.46 [c, a] [a, b] [b, c] -> [c, b] [b, c] [c, a] [a, c] , 8.53/2.46 [c, c] [c, c] -> [c, b] [b, c] , 8.53/2.46 [c, c] [c, c] [c, c] -> [c, a] [a, c] [c, c] } 8.53/2.46 8.53/2.46 8.53/2.46 8.53/2.46 The system was filtered by the following matrix interpretation 8.53/2.46 of type E_J with J = {1,...,2} and dimension 2: 8.53/2.46 8.53/2.46 [a, a] is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 1 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 [a, b] is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 1 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 [b, a] is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 [b, c] is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 [c, a] is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 [a, c] is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 1 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 [c, c] is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 1 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 [b, b] is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 [c, b] is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 8.53/2.46 Remains to prove termination of the 20-rule system 8.53/2.46 { [a, a] [a, b] [b, a] -> [a, b] [b, c] [c, a] [a, a] , 8.53/2.46 [a, c] [c, a] -> [a, b] [b, a] , 8.53/2.46 [a, c] [c, c] [c, a] -> [a, a] [a, c] [c, a] , 8.53/2.46 [a, a] [a, b] [b, b] -> [a, b] [b, c] [c, a] [a, b] , 8.53/2.46 [a, c] [c, b] -> [a, b] [b, b] , 8.53/2.46 [a, c] [c, c] [c, b] -> [a, a] [a, c] [c, b] , 8.53/2.46 [a, a] [a, b] [b, c] -> [a, b] [b, c] [c, a] [a, c] , 8.53/2.46 [a, c] [c, c] [c, c] -> [a, a] [a, c] [c, c] , 8.53/2.46 [b, a] [a, b] [b, a] -> [b, b] [b, c] [c, a] [a, a] , 8.53/2.46 [b, c] [c, a] -> [b, b] [b, a] , 8.53/2.46 [b, c] [c, c] [c, a] -> [b, a] [a, c] [c, a] , 8.53/2.46 [b, a] [a, b] [b, b] -> [b, b] [b, c] [c, a] [a, b] , 8.53/2.46 [b, c] [c, b] -> [b, b] [b, b] , 8.53/2.46 [b, c] [c, c] [c, b] -> [b, a] [a, c] [c, b] , 8.53/2.46 [b, a] [a, b] [b, c] -> [b, b] [b, c] [c, a] [a, c] , 8.53/2.46 [b, c] [c, c] [c, c] -> [b, a] [a, c] [c, c] , 8.53/2.46 [c, a] [a, b] [b, a] -> [c, b] [b, c] [c, a] [a, a] , 8.53/2.46 [c, a] [a, b] [b, b] -> [c, b] [b, c] [c, a] [a, b] , 8.53/2.46 [c, a] [a, c] -> [c, c] , 8.53/2.46 [c, a] [a, b] [b, c] -> [c, b] [b, c] [c, a] [a, c] } 8.53/2.46 8.53/2.46 8.53/2.46 The system was reversed. 8.53/2.46 8.53/2.46 Remains to prove termination of the 20-rule system 8.53/2.46 { [b, a] [a, b] [a, a] -> [a, a] [c, a] [b, c] [a, b] , 8.53/2.46 [c, a] [a, c] -> [b, a] [a, b] , 8.53/2.46 [c, a] [c, c] [a, c] -> [c, a] [a, c] [a, a] , 8.53/2.46 [b, b] [a, b] [a, a] -> [a, b] [c, a] [b, c] [a, b] , 8.53/2.46 [c, b] [a, c] -> [b, b] [a, b] , 8.53/2.46 [c, b] [c, c] [a, c] -> [c, b] [a, c] [a, a] , 8.53/2.46 [b, c] [a, b] [a, a] -> [a, c] [c, a] [b, c] [a, b] , 8.53/2.46 [c, c] [c, c] [a, c] -> [c, c] [a, c] [a, a] , 8.53/2.46 [b, a] [a, b] [b, a] -> [a, a] [c, a] [b, c] [b, b] , 8.53/2.46 [c, a] [b, c] -> [b, a] [b, b] , 8.53/2.46 [c, a] [c, c] [b, c] -> [c, a] [a, c] [b, a] , 8.53/2.46 [b, b] [a, b] [b, a] -> [a, b] [c, a] [b, c] [b, b] , 8.53/2.46 [c, b] [b, c] -> [b, b] [b, b] , 8.53/2.46 [c, b] [c, c] [b, c] -> [c, b] [a, c] [b, a] , 8.53/2.46 [b, c] [a, b] [b, a] -> [a, c] [c, a] [b, c] [b, b] , 8.53/2.46 [c, c] [c, c] [b, c] -> [c, c] [a, c] [b, a] , 8.53/2.46 [b, a] [a, b] [c, a] -> [a, a] [c, a] [b, c] [c, b] , 8.53/2.46 [b, b] [a, b] [c, a] -> [a, b] [c, a] [b, c] [c, b] , 8.53/2.46 [a, c] [c, a] -> [c, c] , 8.53/2.46 [b, c] [a, b] [c, a] -> [a, c] [c, a] [b, c] [c, b] } 8.53/2.46 8.53/2.46 8.53/2.46 The dependency pairs transformation was applied. 8.53/2.46 8.53/2.46 Remains to prove termination of the 69-rule system 8.53/2.46 { ([b, a],true) ([a, b],false) ([a, a],false) -> ([c, a],true) ([b, c],false) ([a, b],false) , 8.53/2.46 ([b, a],true) ([a, b],false) ([a, a],false) -> ([b, c],true) ([a, b],false) , 8.53/2.46 ([c, a],true) ([a, c],false) -> ([b, a],true) ([a, b],false) , 8.53/2.46 ([c, a],true) ([c, c],false) ([a, c],false) -> ([c, a],true) ([a, c],false) ([a, a],false) , 8.53/2.46 ([c, a],true) ([c, c],false) ([a, c],false) -> ([a, c],true) ([a, a],false) , 8.53/2.46 ([b, b],true) ([a, b],false) ([a, a],false) -> ([c, a],true) ([b, c],false) ([a, b],false) , 8.53/2.46 ([b, b],true) ([a, b],false) ([a, a],false) -> ([b, c],true) ([a, b],false) , 8.53/2.46 ([c, b],true) ([a, c],false) -> ([b, b],true) ([a, b],false) , 8.53/2.46 ([c, b],true) ([c, c],false) ([a, c],false) -> ([c, b],true) ([a, c],false) ([a, a],false) , 8.53/2.46 ([c, b],true) ([c, c],false) ([a, c],false) -> ([a, c],true) ([a, a],false) , 8.53/2.46 ([b, c],true) ([a, b],false) ([a, a],false) -> ([a, c],true) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([b, c],true) ([a, b],false) ([a, a],false) -> ([c, a],true) ([b, c],false) ([a, b],false) , 8.53/2.46 ([b, c],true) ([a, b],false) ([a, a],false) -> ([b, c],true) ([a, b],false) , 8.53/2.46 ([c, c],true) ([c, c],false) ([a, c],false) -> ([c, c],true) ([a, c],false) ([a, a],false) , 8.53/2.46 ([c, c],true) ([c, c],false) ([a, c],false) -> ([a, c],true) ([a, a],false) , 8.53/2.46 ([b, a],true) ([a, b],false) ([b, a],false) -> ([c, a],true) ([b, c],false) ([b, b],false) , 8.53/2.46 ([b, a],true) ([a, b],false) ([b, a],false) -> ([b, c],true) ([b, b],false) , 8.53/2.46 ([b, a],true) ([a, b],false) ([b, a],false) -> ([b, b],true) , 8.53/2.46 ([c, a],true) ([b, c],false) -> ([b, a],true) ([b, b],false) , 8.53/2.46 ([c, a],true) ([b, c],false) -> ([b, b],true) , 8.53/2.46 ([c, a],true) ([c, c],false) ([b, c],false) -> ([c, a],true) ([a, c],false) ([b, a],false) , 8.53/2.46 ([c, a],true) ([c, c],false) ([b, c],false) -> ([a, c],true) ([b, a],false) , 8.53/2.46 ([c, a],true) ([c, c],false) ([b, c],false) -> ([b, a],true) , 8.53/2.46 ([b, b],true) ([a, b],false) ([b, a],false) -> ([c, a],true) ([b, c],false) ([b, b],false) , 8.53/2.46 ([b, b],true) ([a, b],false) ([b, a],false) -> ([b, c],true) ([b, b],false) , 8.53/2.46 ([b, b],true) ([a, b],false) ([b, a],false) -> ([b, b],true) , 8.53/2.46 ([c, b],true) ([b, c],false) -> ([b, b],true) ([b, b],false) , 8.53/2.46 ([c, b],true) ([b, c],false) -> ([b, b],true) , 8.53/2.46 ([c, b],true) ([c, c],false) ([b, c],false) -> ([c, b],true) ([a, c],false) ([b, a],false) , 8.53/2.46 ([c, b],true) ([c, c],false) ([b, c],false) -> ([a, c],true) ([b, a],false) , 8.53/2.46 ([c, b],true) ([c, c],false) ([b, c],false) -> ([b, a],true) , 8.53/2.46 ([b, c],true) ([a, b],false) ([b, a],false) -> ([a, c],true) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([b, c],true) ([a, b],false) ([b, a],false) -> ([c, a],true) ([b, c],false) ([b, b],false) , 8.53/2.46 ([b, c],true) ([a, b],false) ([b, a],false) -> ([b, c],true) ([b, b],false) , 8.53/2.46 ([b, c],true) ([a, b],false) ([b, a],false) -> ([b, b],true) , 8.53/2.46 ([c, c],true) ([c, c],false) ([b, c],false) -> ([c, c],true) ([a, c],false) ([b, a],false) , 8.53/2.46 ([c, c],true) ([c, c],false) ([b, c],false) -> ([a, c],true) ([b, a],false) , 8.53/2.46 ([c, c],true) ([c, c],false) ([b, c],false) -> ([b, a],true) , 8.53/2.46 ([b, a],true) ([a, b],false) ([c, a],false) -> ([c, a],true) ([b, c],false) ([c, b],false) , 8.53/2.46 ([b, a],true) ([a, b],false) ([c, a],false) -> ([b, c],true) ([c, b],false) , 8.53/2.46 ([b, a],true) ([a, b],false) ([c, a],false) -> ([c, b],true) , 8.53/2.46 ([b, b],true) ([a, b],false) ([c, a],false) -> ([c, a],true) ([b, c],false) ([c, b],false) , 8.53/2.46 ([b, b],true) ([a, b],false) ([c, a],false) -> ([b, c],true) ([c, b],false) , 8.53/2.46 ([b, b],true) ([a, b],false) ([c, a],false) -> ([c, b],true) , 8.53/2.46 ([a, c],true) ([c, a],false) -> ([c, c],true) , 8.53/2.46 ([b, c],true) ([a, b],false) ([c, a],false) -> ([a, c],true) ([c, a],false) ([b, c],false) ([c, b],false) , 8.53/2.46 ([b, c],true) ([a, b],false) ([c, a],false) -> ([c, a],true) ([b, c],false) ([c, b],false) , 8.53/2.46 ([b, c],true) ([a, b],false) ([c, a],false) -> ([b, c],true) ([c, b],false) , 8.53/2.46 ([b, c],true) ([a, b],false) ([c, a],false) -> ([c, b],true) , 8.53/2.46 ([b, a],false) ([a, b],false) ([a, a],false) ->= ([a, a],false) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, a],false) ([a, c],false) ->= ([b, a],false) ([a, b],false) , 8.53/2.46 ([c, a],false) ([c, c],false) ([a, c],false) ->= ([c, a],false) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, b],false) ([a, b],false) ([a, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, b],false) ([a, c],false) ->= ([b, b],false) ([a, b],false) , 8.53/2.46 ([c, b],false) ([c, c],false) ([a, c],false) ->= ([c, b],false) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, c],false) ([a, b],false) ([a, a],false) ->= ([a, c],false) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, c],false) ([c, c],false) ([a, c],false) ->= ([c, c],false) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, a],false) ([a, b],false) ([b, a],false) ->= ([a, a],false) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, a],false) ([b, c],false) ->= ([b, a],false) ([b, b],false) , 8.53/2.46 ([c, a],false) ([c, c],false) ([b, c],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, b],false) ([a, b],false) ([b, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, b],false) ([b, c],false) ->= ([b, b],false) ([b, b],false) , 8.53/2.46 ([c, b],false) ([c, c],false) ([b, c],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, c],false) ([a, b],false) ([b, a],false) ->= ([a, c],false) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, c],false) ([c, c],false) ([b, c],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, a],false) ([a, b],false) ([c, a],false) ->= ([a, a],false) ([c, a],false) ([b, c],false) ([c, b],false) , 8.53/2.46 ([b, b],false) ([a, b],false) ([c, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([c, b],false) , 8.53/2.46 ([a, c],false) ([c, a],false) ->= ([c, c],false) , 8.53/2.46 ([b, c],false) ([a, b],false) ([c, a],false) ->= ([a, c],false) ([c, a],false) ([b, c],false) ([c, b],false) } 8.53/2.46 8.53/2.46 8.53/2.46 8.53/2.46 8.53/2.46 The system was filtered by the following matrix interpretation 8.53/2.46 of type E_J with J = {1,...,2} and dimension 2: 8.53/2.46 8.53/2.46 ([b, a],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([a, b],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([a, a],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 1 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([c, a],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([b, c],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([b, c],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([a, c],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([c, c],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 1 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([a, c],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([b, b],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([c, b],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([c, a],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 1 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([c, c],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([b, a],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 1 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([b, b],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([c, b],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 8.53/2.46 Remains to prove termination of the 41-rule system 8.53/2.46 { ([c, a],true) ([a, c],false) -> ([b, a],true) ([a, b],false) , 8.53/2.46 ([c, a],true) ([c, c],false) ([a, c],false) -> ([c, a],true) ([a, c],false) ([a, a],false) , 8.53/2.46 ([c, a],true) ([c, c],false) ([a, c],false) -> ([a, c],true) ([a, a],false) , 8.53/2.46 ([c, b],true) ([a, c],false) -> ([b, b],true) ([a, b],false) , 8.53/2.46 ([c, b],true) ([c, c],false) ([a, c],false) -> ([c, b],true) ([a, c],false) ([a, a],false) , 8.53/2.46 ([c, b],true) ([c, c],false) ([a, c],false) -> ([a, c],true) ([a, a],false) , 8.53/2.46 ([b, c],true) ([a, b],false) ([a, a],false) -> ([a, c],true) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, c],true) ([c, c],false) ([a, c],false) -> ([c, c],true) ([a, c],false) ([a, a],false) , 8.53/2.46 ([c, c],true) ([c, c],false) ([a, c],false) -> ([a, c],true) ([a, a],false) , 8.53/2.46 ([c, a],true) ([b, c],false) -> ([b, a],true) ([b, b],false) , 8.53/2.46 ([c, a],true) ([b, c],false) -> ([b, b],true) , 8.53/2.46 ([c, a],true) ([c, c],false) ([b, c],false) -> ([c, a],true) ([a, c],false) ([b, a],false) , 8.53/2.46 ([c, a],true) ([c, c],false) ([b, c],false) -> ([a, c],true) ([b, a],false) , 8.53/2.46 ([c, b],true) ([b, c],false) -> ([b, b],true) ([b, b],false) , 8.53/2.46 ([c, b],true) ([b, c],false) -> ([b, b],true) , 8.53/2.46 ([c, b],true) ([c, c],false) ([b, c],false) -> ([c, b],true) ([a, c],false) ([b, a],false) , 8.53/2.46 ([c, b],true) ([c, c],false) ([b, c],false) -> ([a, c],true) ([b, a],false) , 8.53/2.46 ([b, c],true) ([a, b],false) ([b, a],false) -> ([a, c],true) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, c],true) ([c, c],false) ([b, c],false) -> ([c, c],true) ([a, c],false) ([b, a],false) , 8.53/2.46 ([c, c],true) ([c, c],false) ([b, c],false) -> ([a, c],true) ([b, a],false) , 8.53/2.46 ([b, c],true) ([a, b],false) ([c, a],false) -> ([a, c],true) ([c, a],false) ([b, c],false) ([c, b],false) , 8.53/2.46 ([b, a],false) ([a, b],false) ([a, a],false) ->= ([a, a],false) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, a],false) ([a, c],false) ->= ([b, a],false) ([a, b],false) , 8.53/2.46 ([c, a],false) ([c, c],false) ([a, c],false) ->= ([c, a],false) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, b],false) ([a, b],false) ([a, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, b],false) ([a, c],false) ->= ([b, b],false) ([a, b],false) , 8.53/2.46 ([c, b],false) ([c, c],false) ([a, c],false) ->= ([c, b],false) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, c],false) ([a, b],false) ([a, a],false) ->= ([a, c],false) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, c],false) ([c, c],false) ([a, c],false) ->= ([c, c],false) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, a],false) ([a, b],false) ([b, a],false) ->= ([a, a],false) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, a],false) ([b, c],false) ->= ([b, a],false) ([b, b],false) , 8.53/2.46 ([c, a],false) ([c, c],false) ([b, c],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, b],false) ([a, b],false) ([b, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, b],false) ([b, c],false) ->= ([b, b],false) ([b, b],false) , 8.53/2.46 ([c, b],false) ([c, c],false) ([b, c],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, c],false) ([a, b],false) ([b, a],false) ->= ([a, c],false) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, c],false) ([c, c],false) ([b, c],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, a],false) ([a, b],false) ([c, a],false) ->= ([a, a],false) ([c, a],false) ([b, c],false) ([c, b],false) , 8.53/2.46 ([b, b],false) ([a, b],false) ([c, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([c, b],false) , 8.53/2.46 ([a, c],false) ([c, a],false) ->= ([c, c],false) , 8.53/2.46 ([b, c],false) ([a, b],false) ([c, a],false) ->= ([a, c],false) ([c, a],false) ([b, c],false) ([c, b],false) } 8.53/2.46 8.53/2.46 8.53/2.46 The system was filtered by the following matrix interpretation 8.53/2.46 of type E_J with J = {1,...,2} and dimension 2: 8.53/2.46 8.53/2.46 ([b, a],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([a, b],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([a, a],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([c, a],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 1 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([b, c],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([b, c],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([a, c],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([c, c],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([a, c],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([b, b],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([c, b],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([c, a],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([c, c],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([b, a],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([b, b],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([c, b],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 8.53/2.46 Remains to prove termination of the 36-rule system 8.53/2.46 { ([c, a],true) ([c, c],false) ([a, c],false) -> ([c, a],true) ([a, c],false) ([a, a],false) , 8.53/2.46 ([c, b],true) ([a, c],false) -> ([b, b],true) ([a, b],false) , 8.53/2.46 ([c, b],true) ([c, c],false) ([a, c],false) -> ([c, b],true) ([a, c],false) ([a, a],false) , 8.53/2.46 ([c, b],true) ([c, c],false) ([a, c],false) -> ([a, c],true) ([a, a],false) , 8.53/2.46 ([b, c],true) ([a, b],false) ([a, a],false) -> ([a, c],true) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, c],true) ([c, c],false) ([a, c],false) -> ([c, c],true) ([a, c],false) ([a, a],false) , 8.53/2.46 ([c, c],true) ([c, c],false) ([a, c],false) -> ([a, c],true) ([a, a],false) , 8.53/2.46 ([c, a],true) ([c, c],false) ([b, c],false) -> ([c, a],true) ([a, c],false) ([b, a],false) , 8.53/2.46 ([c, b],true) ([b, c],false) -> ([b, b],true) ([b, b],false) , 8.53/2.46 ([c, b],true) ([b, c],false) -> ([b, b],true) , 8.53/2.46 ([c, b],true) ([c, c],false) ([b, c],false) -> ([c, b],true) ([a, c],false) ([b, a],false) , 8.53/2.46 ([c, b],true) ([c, c],false) ([b, c],false) -> ([a, c],true) ([b, a],false) , 8.53/2.46 ([b, c],true) ([a, b],false) ([b, a],false) -> ([a, c],true) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, c],true) ([c, c],false) ([b, c],false) -> ([c, c],true) ([a, c],false) ([b, a],false) , 8.53/2.46 ([c, c],true) ([c, c],false) ([b, c],false) -> ([a, c],true) ([b, a],false) , 8.53/2.46 ([b, c],true) ([a, b],false) ([c, a],false) -> ([a, c],true) ([c, a],false) ([b, c],false) ([c, b],false) , 8.53/2.46 ([b, a],false) ([a, b],false) ([a, a],false) ->= ([a, a],false) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, a],false) ([a, c],false) ->= ([b, a],false) ([a, b],false) , 8.53/2.46 ([c, a],false) ([c, c],false) ([a, c],false) ->= ([c, a],false) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, b],false) ([a, b],false) ([a, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, b],false) ([a, c],false) ->= ([b, b],false) ([a, b],false) , 8.53/2.46 ([c, b],false) ([c, c],false) ([a, c],false) ->= ([c, b],false) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, c],false) ([a, b],false) ([a, a],false) ->= ([a, c],false) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, c],false) ([c, c],false) ([a, c],false) ->= ([c, c],false) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, a],false) ([a, b],false) ([b, a],false) ->= ([a, a],false) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, a],false) ([b, c],false) ->= ([b, a],false) ([b, b],false) , 8.53/2.46 ([c, a],false) ([c, c],false) ([b, c],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, b],false) ([a, b],false) ([b, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, b],false) ([b, c],false) ->= ([b, b],false) ([b, b],false) , 8.53/2.46 ([c, b],false) ([c, c],false) ([b, c],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, c],false) ([a, b],false) ([b, a],false) ->= ([a, c],false) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, c],false) ([c, c],false) ([b, c],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, a],false) ([a, b],false) ([c, a],false) ->= ([a, a],false) ([c, a],false) ([b, c],false) ([c, b],false) , 8.53/2.46 ([b, b],false) ([a, b],false) ([c, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([c, b],false) , 8.53/2.46 ([a, c],false) ([c, a],false) ->= ([c, c],false) , 8.53/2.46 ([b, c],false) ([a, b],false) ([c, a],false) ->= ([a, c],false) ([c, a],false) ([b, c],false) ([c, b],false) } 8.53/2.46 8.53/2.46 8.53/2.46 The system was filtered by the following matrix interpretation 8.53/2.46 of type E_J with J = {1,...,2} and dimension 2: 8.53/2.46 8.53/2.46 ([b, a],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([a, b],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([a, a],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([c, a],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([b, c],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([b, c],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 1 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([a, c],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([c, c],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([a, c],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([b, b],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([c, b],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([c, a],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([c, c],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([b, a],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([b, b],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([c, b],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 8.53/2.46 Remains to prove termination of the 33-rule system 8.53/2.46 { ([c, a],true) ([c, c],false) ([a, c],false) -> ([c, a],true) ([a, c],false) ([a, a],false) , 8.53/2.46 ([c, b],true) ([a, c],false) -> ([b, b],true) ([a, b],false) , 8.53/2.46 ([c, b],true) ([c, c],false) ([a, c],false) -> ([c, b],true) ([a, c],false) ([a, a],false) , 8.53/2.46 ([c, b],true) ([c, c],false) ([a, c],false) -> ([a, c],true) ([a, a],false) , 8.53/2.46 ([c, c],true) ([c, c],false) ([a, c],false) -> ([c, c],true) ([a, c],false) ([a, a],false) , 8.53/2.46 ([c, c],true) ([c, c],false) ([a, c],false) -> ([a, c],true) ([a, a],false) , 8.53/2.46 ([c, a],true) ([c, c],false) ([b, c],false) -> ([c, a],true) ([a, c],false) ([b, a],false) , 8.53/2.46 ([c, b],true) ([b, c],false) -> ([b, b],true) ([b, b],false) , 8.53/2.46 ([c, b],true) ([b, c],false) -> ([b, b],true) , 8.53/2.46 ([c, b],true) ([c, c],false) ([b, c],false) -> ([c, b],true) ([a, c],false) ([b, a],false) , 8.53/2.46 ([c, b],true) ([c, c],false) ([b, c],false) -> ([a, c],true) ([b, a],false) , 8.53/2.46 ([c, c],true) ([c, c],false) ([b, c],false) -> ([c, c],true) ([a, c],false) ([b, a],false) , 8.53/2.46 ([c, c],true) ([c, c],false) ([b, c],false) -> ([a, c],true) ([b, a],false) , 8.53/2.46 ([b, a],false) ([a, b],false) ([a, a],false) ->= ([a, a],false) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, a],false) ([a, c],false) ->= ([b, a],false) ([a, b],false) , 8.53/2.46 ([c, a],false) ([c, c],false) ([a, c],false) ->= ([c, a],false) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, b],false) ([a, b],false) ([a, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, b],false) ([a, c],false) ->= ([b, b],false) ([a, b],false) , 8.53/2.46 ([c, b],false) ([c, c],false) ([a, c],false) ->= ([c, b],false) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, c],false) ([a, b],false) ([a, a],false) ->= ([a, c],false) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, c],false) ([c, c],false) ([a, c],false) ->= ([c, c],false) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, a],false) ([a, b],false) ([b, a],false) ->= ([a, a],false) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, a],false) ([b, c],false) ->= ([b, a],false) ([b, b],false) , 8.53/2.46 ([c, a],false) ([c, c],false) ([b, c],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, b],false) ([a, b],false) ([b, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, b],false) ([b, c],false) ->= ([b, b],false) ([b, b],false) , 8.53/2.46 ([c, b],false) ([c, c],false) ([b, c],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, c],false) ([a, b],false) ([b, a],false) ->= ([a, c],false) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, c],false) ([c, c],false) ([b, c],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, a],false) ([a, b],false) ([c, a],false) ->= ([a, a],false) ([c, a],false) ([b, c],false) ([c, b],false) , 8.53/2.46 ([b, b],false) ([a, b],false) ([c, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([c, b],false) , 8.53/2.46 ([a, c],false) ([c, a],false) ->= ([c, c],false) , 8.53/2.46 ([b, c],false) ([a, b],false) ([c, a],false) ->= ([a, c],false) ([c, a],false) ([b, c],false) ([c, b],false) } 8.53/2.46 8.53/2.46 8.53/2.46 The system was filtered by the following matrix interpretation 8.53/2.46 of type E_J with J = {1,...,2} and dimension 2: 8.53/2.46 8.53/2.46 ([b, a],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([a, b],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([a, a],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([c, a],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([b, c],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([b, c],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([a, c],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([c, c],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([a, c],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([b, b],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([c, b],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 1 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([c, a],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([c, c],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([b, a],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([b, b],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([c, b],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 8.53/2.46 Remains to prove termination of the 28-rule system 8.53/2.46 { ([c, a],true) ([c, c],false) ([a, c],false) -> ([c, a],true) ([a, c],false) ([a, a],false) , 8.53/2.46 ([c, b],true) ([c, c],false) ([a, c],false) -> ([c, b],true) ([a, c],false) ([a, a],false) , 8.53/2.46 ([c, c],true) ([c, c],false) ([a, c],false) -> ([c, c],true) ([a, c],false) ([a, a],false) , 8.53/2.46 ([c, c],true) ([c, c],false) ([a, c],false) -> ([a, c],true) ([a, a],false) , 8.53/2.46 ([c, a],true) ([c, c],false) ([b, c],false) -> ([c, a],true) ([a, c],false) ([b, a],false) , 8.53/2.46 ([c, b],true) ([c, c],false) ([b, c],false) -> ([c, b],true) ([a, c],false) ([b, a],false) , 8.53/2.46 ([c, c],true) ([c, c],false) ([b, c],false) -> ([c, c],true) ([a, c],false) ([b, a],false) , 8.53/2.46 ([c, c],true) ([c, c],false) ([b, c],false) -> ([a, c],true) ([b, a],false) , 8.53/2.46 ([b, a],false) ([a, b],false) ([a, a],false) ->= ([a, a],false) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, a],false) ([a, c],false) ->= ([b, a],false) ([a, b],false) , 8.53/2.46 ([c, a],false) ([c, c],false) ([a, c],false) ->= ([c, a],false) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, b],false) ([a, b],false) ([a, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, b],false) ([a, c],false) ->= ([b, b],false) ([a, b],false) , 8.53/2.46 ([c, b],false) ([c, c],false) ([a, c],false) ->= ([c, b],false) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, c],false) ([a, b],false) ([a, a],false) ->= ([a, c],false) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, c],false) ([c, c],false) ([a, c],false) ->= ([c, c],false) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, a],false) ([a, b],false) ([b, a],false) ->= ([a, a],false) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, a],false) ([b, c],false) ->= ([b, a],false) ([b, b],false) , 8.53/2.46 ([c, a],false) ([c, c],false) ([b, c],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, b],false) ([a, b],false) ([b, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, b],false) ([b, c],false) ->= ([b, b],false) ([b, b],false) , 8.53/2.46 ([c, b],false) ([c, c],false) ([b, c],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, c],false) ([a, b],false) ([b, a],false) ->= ([a, c],false) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, c],false) ([c, c],false) ([b, c],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, a],false) ([a, b],false) ([c, a],false) ->= ([a, a],false) ([c, a],false) ([b, c],false) ([c, b],false) , 8.53/2.46 ([b, b],false) ([a, b],false) ([c, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([c, b],false) , 8.53/2.46 ([a, c],false) ([c, a],false) ->= ([c, c],false) , 8.53/2.46 ([b, c],false) ([a, b],false) ([c, a],false) ->= ([a, c],false) ([c, a],false) ([b, c],false) ([c, b],false) } 8.53/2.46 8.53/2.46 8.53/2.46 The system was filtered by the following matrix interpretation 8.53/2.46 of type E_J with J = {1,...,2} and dimension 2: 8.53/2.46 8.53/2.46 ([b, a],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([a, b],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([a, a],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([c, a],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([b, c],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([b, c],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([a, c],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([c, c],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([a, c],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([b, b],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([c, b],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([c, a],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([c, c],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 1 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([b, a],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([b, b],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 ([c, b],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 | 8.53/2.46 | 0 1 | 8.53/2.46 \ / 8.53/2.46 8.53/2.46 Remains to prove termination of the 26-rule system 8.53/2.46 { ([c, a],true) ([c, c],false) ([a, c],false) -> ([c, a],true) ([a, c],false) ([a, a],false) , 8.53/2.46 ([c, b],true) ([c, c],false) ([a, c],false) -> ([c, b],true) ([a, c],false) ([a, a],false) , 8.53/2.46 ([c, c],true) ([c, c],false) ([a, c],false) -> ([c, c],true) ([a, c],false) ([a, a],false) , 8.53/2.46 ([c, a],true) ([c, c],false) ([b, c],false) -> ([c, a],true) ([a, c],false) ([b, a],false) , 8.53/2.46 ([c, b],true) ([c, c],false) ([b, c],false) -> ([c, b],true) ([a, c],false) ([b, a],false) , 8.53/2.46 ([c, c],true) ([c, c],false) ([b, c],false) -> ([c, c],true) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, a],false) ([a, b],false) ([a, a],false) ->= ([a, a],false) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, a],false) ([a, c],false) ->= ([b, a],false) ([a, b],false) , 8.53/2.46 ([c, a],false) ([c, c],false) ([a, c],false) ->= ([c, a],false) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, b],false) ([a, b],false) ([a, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, b],false) ([a, c],false) ->= ([b, b],false) ([a, b],false) , 8.53/2.46 ([c, b],false) ([c, c],false) ([a, c],false) ->= ([c, b],false) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, c],false) ([a, b],false) ([a, a],false) ->= ([a, c],false) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, c],false) ([c, c],false) ([a, c],false) ->= ([c, c],false) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, a],false) ([a, b],false) ([b, a],false) ->= ([a, a],false) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, a],false) ([b, c],false) ->= ([b, a],false) ([b, b],false) , 8.53/2.46 ([c, a],false) ([c, c],false) ([b, c],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, b],false) ([a, b],false) ([b, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, b],false) ([b, c],false) ->= ([b, b],false) ([b, b],false) , 8.53/2.46 ([c, b],false) ([c, c],false) ([b, c],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, c],false) ([a, b],false) ([b, a],false) ->= ([a, c],false) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, c],false) ([c, c],false) ([b, c],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, a],false) ([a, b],false) ([c, a],false) ->= ([a, a],false) ([c, a],false) ([b, c],false) ([c, b],false) , 8.53/2.46 ([b, b],false) ([a, b],false) ([c, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([c, b],false) , 8.53/2.46 ([a, c],false) ([c, a],false) ->= ([c, c],false) , 8.53/2.46 ([b, c],false) ([a, b],false) ([c, a],false) ->= ([a, c],false) ([c, a],false) ([b, c],false) ([c, b],false) } 8.53/2.46 8.53/2.46 8.53/2.46 The system was filtered by the following matrix interpretation 8.53/2.46 of type E_J with J = {1,...,2} and dimension 5: 8.53/2.46 8.53/2.46 ([b, a],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([a, b],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([a, a],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([c, a],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([b, c],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([b, c],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([a, c],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 1 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([c, c],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 1 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([a, c],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([b, b],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([c, b],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([c, a],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 1 0 | 8.53/2.46 \ / 8.53/2.46 ([c, c],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 1 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([b, a],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([b, b],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([c, b],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 8.53/2.46 Remains to prove termination of the 25-rule system 8.53/2.46 { ([c, a],true) ([c, c],false) ([a, c],false) -> ([c, a],true) ([a, c],false) ([a, a],false) , 8.53/2.46 ([c, b],true) ([c, c],false) ([a, c],false) -> ([c, b],true) ([a, c],false) ([a, a],false) , 8.53/2.46 ([c, c],true) ([c, c],false) ([a, c],false) -> ([c, c],true) ([a, c],false) ([a, a],false) , 8.53/2.46 ([c, a],true) ([c, c],false) ([b, c],false) -> ([c, a],true) ([a, c],false) ([b, a],false) , 8.53/2.46 ([c, b],true) ([c, c],false) ([b, c],false) -> ([c, b],true) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, a],false) ([a, b],false) ([a, a],false) ->= ([a, a],false) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, a],false) ([a, c],false) ->= ([b, a],false) ([a, b],false) , 8.53/2.46 ([c, a],false) ([c, c],false) ([a, c],false) ->= ([c, a],false) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, b],false) ([a, b],false) ([a, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, b],false) ([a, c],false) ->= ([b, b],false) ([a, b],false) , 8.53/2.46 ([c, b],false) ([c, c],false) ([a, c],false) ->= ([c, b],false) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, c],false) ([a, b],false) ([a, a],false) ->= ([a, c],false) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, c],false) ([c, c],false) ([a, c],false) ->= ([c, c],false) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, a],false) ([a, b],false) ([b, a],false) ->= ([a, a],false) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, a],false) ([b, c],false) ->= ([b, a],false) ([b, b],false) , 8.53/2.46 ([c, a],false) ([c, c],false) ([b, c],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, b],false) ([a, b],false) ([b, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, b],false) ([b, c],false) ->= ([b, b],false) ([b, b],false) , 8.53/2.46 ([c, b],false) ([c, c],false) ([b, c],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, c],false) ([a, b],false) ([b, a],false) ->= ([a, c],false) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, c],false) ([c, c],false) ([b, c],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, a],false) ([a, b],false) ([c, a],false) ->= ([a, a],false) ([c, a],false) ([b, c],false) ([c, b],false) , 8.53/2.46 ([b, b],false) ([a, b],false) ([c, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([c, b],false) , 8.53/2.46 ([a, c],false) ([c, a],false) ->= ([c, c],false) , 8.53/2.46 ([b, c],false) ([a, b],false) ([c, a],false) ->= ([a, c],false) ([c, a],false) ([b, c],false) ([c, b],false) } 8.53/2.46 8.53/2.46 8.53/2.46 The system was filtered by the following matrix interpretation 8.53/2.46 of type E_J with J = {1,...,2} and dimension 5: 8.53/2.46 8.53/2.46 ([b, a],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([a, b],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([a, a],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([c, a],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 1 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([b, c],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([b, c],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([a, c],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 1 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([c, c],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 1 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([a, c],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([b, b],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([c, b],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([c, a],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 1 0 | 8.53/2.46 \ / 8.53/2.46 ([c, c],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([b, a],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([b, b],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([c, b],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 8.53/2.46 Remains to prove termination of the 24-rule system 8.53/2.46 { ([c, a],true) ([c, c],false) ([a, c],false) -> ([c, a],true) ([a, c],false) ([a, a],false) , 8.53/2.46 ([c, b],true) ([c, c],false) ([a, c],false) -> ([c, b],true) ([a, c],false) ([a, a],false) , 8.53/2.46 ([c, c],true) ([c, c],false) ([a, c],false) -> ([c, c],true) ([a, c],false) ([a, a],false) , 8.53/2.46 ([c, b],true) ([c, c],false) ([b, c],false) -> ([c, b],true) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, a],false) ([a, b],false) ([a, a],false) ->= ([a, a],false) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, a],false) ([a, c],false) ->= ([b, a],false) ([a, b],false) , 8.53/2.46 ([c, a],false) ([c, c],false) ([a, c],false) ->= ([c, a],false) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, b],false) ([a, b],false) ([a, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, b],false) ([a, c],false) ->= ([b, b],false) ([a, b],false) , 8.53/2.46 ([c, b],false) ([c, c],false) ([a, c],false) ->= ([c, b],false) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, c],false) ([a, b],false) ([a, a],false) ->= ([a, c],false) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, c],false) ([c, c],false) ([a, c],false) ->= ([c, c],false) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, a],false) ([a, b],false) ([b, a],false) ->= ([a, a],false) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, a],false) ([b, c],false) ->= ([b, a],false) ([b, b],false) , 8.53/2.46 ([c, a],false) ([c, c],false) ([b, c],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, b],false) ([a, b],false) ([b, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, b],false) ([b, c],false) ->= ([b, b],false) ([b, b],false) , 8.53/2.46 ([c, b],false) ([c, c],false) ([b, c],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, c],false) ([a, b],false) ([b, a],false) ->= ([a, c],false) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, c],false) ([c, c],false) ([b, c],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, a],false) ([a, b],false) ([c, a],false) ->= ([a, a],false) ([c, a],false) ([b, c],false) ([c, b],false) , 8.53/2.46 ([b, b],false) ([a, b],false) ([c, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([c, b],false) , 8.53/2.46 ([a, c],false) ([c, a],false) ->= ([c, c],false) , 8.53/2.46 ([b, c],false) ([a, b],false) ([c, a],false) ->= ([a, c],false) ([c, a],false) ([b, c],false) ([c, b],false) } 8.53/2.46 8.53/2.46 8.53/2.46 The system was filtered by the following matrix interpretation 8.53/2.46 of type E_J with J = {1,...,2} and dimension 5: 8.53/2.46 8.53/2.46 ([b, a],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([a, b],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([a, a],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([c, a],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([b, c],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([b, c],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([a, c],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 1 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([c, c],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 1 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([a, c],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([b, b],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([c, b],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 1 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([c, a],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 1 0 | 8.53/2.46 \ / 8.53/2.46 ([c, c],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([b, a],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([b, b],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([c, b],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 8.53/2.46 Remains to prove termination of the 23-rule system 8.53/2.46 { ([c, a],true) ([c, c],false) ([a, c],false) -> ([c, a],true) ([a, c],false) ([a, a],false) , 8.53/2.46 ([c, b],true) ([c, c],false) ([a, c],false) -> ([c, b],true) ([a, c],false) ([a, a],false) , 8.53/2.46 ([c, c],true) ([c, c],false) ([a, c],false) -> ([c, c],true) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, a],false) ([a, b],false) ([a, a],false) ->= ([a, a],false) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, a],false) ([a, c],false) ->= ([b, a],false) ([a, b],false) , 8.53/2.46 ([c, a],false) ([c, c],false) ([a, c],false) ->= ([c, a],false) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, b],false) ([a, b],false) ([a, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, b],false) ([a, c],false) ->= ([b, b],false) ([a, b],false) , 8.53/2.46 ([c, b],false) ([c, c],false) ([a, c],false) ->= ([c, b],false) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, c],false) ([a, b],false) ([a, a],false) ->= ([a, c],false) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, c],false) ([c, c],false) ([a, c],false) ->= ([c, c],false) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, a],false) ([a, b],false) ([b, a],false) ->= ([a, a],false) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, a],false) ([b, c],false) ->= ([b, a],false) ([b, b],false) , 8.53/2.46 ([c, a],false) ([c, c],false) ([b, c],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, b],false) ([a, b],false) ([b, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, b],false) ([b, c],false) ->= ([b, b],false) ([b, b],false) , 8.53/2.46 ([c, b],false) ([c, c],false) ([b, c],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, c],false) ([a, b],false) ([b, a],false) ->= ([a, c],false) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, c],false) ([c, c],false) ([b, c],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, a],false) ([a, b],false) ([c, a],false) ->= ([a, a],false) ([c, a],false) ([b, c],false) ([c, b],false) , 8.53/2.46 ([b, b],false) ([a, b],false) ([c, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([c, b],false) , 8.53/2.46 ([a, c],false) ([c, a],false) ->= ([c, c],false) , 8.53/2.46 ([b, c],false) ([a, b],false) ([c, a],false) ->= ([a, c],false) ([c, a],false) ([b, c],false) ([c, b],false) } 8.53/2.46 8.53/2.46 8.53/2.46 The system was filtered by the following matrix interpretation 8.53/2.46 of type E_J with J = {1,...,2} and dimension 5: 8.53/2.46 8.53/2.46 ([b, a],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([a, b],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([a, a],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([c, a],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 1 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([b, c],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([b, c],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([a, c],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 1 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([c, c],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 1 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([a, c],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([b, b],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([c, b],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([c, a],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 1 0 | 8.53/2.46 \ / 8.53/2.46 ([c, c],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([b, a],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([b, b],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([c, b],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 8.53/2.46 Remains to prove termination of the 22-rule system 8.53/2.46 { ([c, b],true) ([c, c],false) ([a, c],false) -> ([c, b],true) ([a, c],false) ([a, a],false) , 8.53/2.46 ([c, c],true) ([c, c],false) ([a, c],false) -> ([c, c],true) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, a],false) ([a, b],false) ([a, a],false) ->= ([a, a],false) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, a],false) ([a, c],false) ->= ([b, a],false) ([a, b],false) , 8.53/2.46 ([c, a],false) ([c, c],false) ([a, c],false) ->= ([c, a],false) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, b],false) ([a, b],false) ([a, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, b],false) ([a, c],false) ->= ([b, b],false) ([a, b],false) , 8.53/2.46 ([c, b],false) ([c, c],false) ([a, c],false) ->= ([c, b],false) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, c],false) ([a, b],false) ([a, a],false) ->= ([a, c],false) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, c],false) ([c, c],false) ([a, c],false) ->= ([c, c],false) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, a],false) ([a, b],false) ([b, a],false) ->= ([a, a],false) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, a],false) ([b, c],false) ->= ([b, a],false) ([b, b],false) , 8.53/2.46 ([c, a],false) ([c, c],false) ([b, c],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, b],false) ([a, b],false) ([b, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, b],false) ([b, c],false) ->= ([b, b],false) ([b, b],false) , 8.53/2.46 ([c, b],false) ([c, c],false) ([b, c],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, c],false) ([a, b],false) ([b, a],false) ->= ([a, c],false) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, c],false) ([c, c],false) ([b, c],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, a],false) ([a, b],false) ([c, a],false) ->= ([a, a],false) ([c, a],false) ([b, c],false) ([c, b],false) , 8.53/2.46 ([b, b],false) ([a, b],false) ([c, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([c, b],false) , 8.53/2.46 ([a, c],false) ([c, a],false) ->= ([c, c],false) , 8.53/2.46 ([b, c],false) ([a, b],false) ([c, a],false) ->= ([a, c],false) ([c, a],false) ([b, c],false) ([c, b],false) } 8.53/2.46 8.53/2.46 8.53/2.46 The system was filtered by the following matrix interpretation 8.53/2.46 of type E_J with J = {1,...,2} and dimension 5: 8.53/2.46 8.53/2.46 ([b, a],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([a, b],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([a, a],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([c, a],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([b, c],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([b, c],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([a, c],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 1 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([c, c],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 1 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([a, c],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([b, b],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([c, b],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([c, a],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 1 0 | 8.53/2.46 \ / 8.53/2.46 ([c, c],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 1 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([b, a],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([b, b],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([c, b],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 8.53/2.46 Remains to prove termination of the 21-rule system 8.53/2.46 { ([c, b],true) ([c, c],false) ([a, c],false) -> ([c, b],true) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, a],false) ([a, b],false) ([a, a],false) ->= ([a, a],false) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, a],false) ([a, c],false) ->= ([b, a],false) ([a, b],false) , 8.53/2.46 ([c, a],false) ([c, c],false) ([a, c],false) ->= ([c, a],false) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, b],false) ([a, b],false) ([a, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, b],false) ([a, c],false) ->= ([b, b],false) ([a, b],false) , 8.53/2.46 ([c, b],false) ([c, c],false) ([a, c],false) ->= ([c, b],false) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, c],false) ([a, b],false) ([a, a],false) ->= ([a, c],false) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, c],false) ([c, c],false) ([a, c],false) ->= ([c, c],false) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, a],false) ([a, b],false) ([b, a],false) ->= ([a, a],false) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, a],false) ([b, c],false) ->= ([b, a],false) ([b, b],false) , 8.53/2.46 ([c, a],false) ([c, c],false) ([b, c],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, b],false) ([a, b],false) ([b, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, b],false) ([b, c],false) ->= ([b, b],false) ([b, b],false) , 8.53/2.46 ([c, b],false) ([c, c],false) ([b, c],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, c],false) ([a, b],false) ([b, a],false) ->= ([a, c],false) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, c],false) ([c, c],false) ([b, c],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, a],false) ([a, b],false) ([c, a],false) ->= ([a, a],false) ([c, a],false) ([b, c],false) ([c, b],false) , 8.53/2.46 ([b, b],false) ([a, b],false) ([c, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([c, b],false) , 8.53/2.46 ([a, c],false) ([c, a],false) ->= ([c, c],false) , 8.53/2.46 ([b, c],false) ([a, b],false) ([c, a],false) ->= ([a, c],false) ([c, a],false) ([b, c],false) ([c, b],false) } 8.53/2.46 8.53/2.46 8.53/2.46 The system was filtered by the following matrix interpretation 8.53/2.46 of type E_J with J = {1,...,2} and dimension 5: 8.53/2.46 8.53/2.46 ([b, a],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([a, b],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([a, a],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([c, a],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([b, c],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([b, c],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([a, c],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 1 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([c, c],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 1 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([a, c],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([b, b],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([c, b],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 1 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([c, a],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 1 0 | 8.53/2.46 \ / 8.53/2.46 ([c, c],true) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([b, a],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([b, b],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 ([c, b],false) is interpreted by 8.53/2.46 / \ 8.53/2.46 | 1 0 0 0 0 | 8.53/2.46 | 0 1 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 | 0 0 0 0 0 | 8.53/2.46 \ / 8.53/2.46 8.53/2.46 Remains to prove termination of the 20-rule system 8.53/2.46 { ([b, a],false) ([a, b],false) ([a, a],false) ->= ([a, a],false) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, a],false) ([a, c],false) ->= ([b, a],false) ([a, b],false) , 8.53/2.46 ([c, a],false) ([c, c],false) ([a, c],false) ->= ([c, a],false) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, b],false) ([a, b],false) ([a, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, b],false) ([a, c],false) ->= ([b, b],false) ([a, b],false) , 8.53/2.46 ([c, b],false) ([c, c],false) ([a, c],false) ->= ([c, b],false) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, c],false) ([a, b],false) ([a, a],false) ->= ([a, c],false) ([c, a],false) ([b, c],false) ([a, b],false) , 8.53/2.46 ([c, c],false) ([c, c],false) ([a, c],false) ->= ([c, c],false) ([a, c],false) ([a, a],false) , 8.53/2.46 ([b, a],false) ([a, b],false) ([b, a],false) ->= ([a, a],false) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, a],false) ([b, c],false) ->= ([b, a],false) ([b, b],false) , 8.53/2.46 ([c, a],false) ([c, c],false) ([b, c],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, b],false) ([a, b],false) ([b, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, b],false) ([b, c],false) ->= ([b, b],false) ([b, b],false) , 8.53/2.46 ([c, b],false) ([c, c],false) ([b, c],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, c],false) ([a, b],false) ([b, a],false) ->= ([a, c],false) ([c, a],false) ([b, c],false) ([b, b],false) , 8.53/2.46 ([c, c],false) ([c, c],false) ([b, c],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) , 8.53/2.46 ([b, a],false) ([a, b],false) ([c, a],false) ->= ([a, a],false) ([c, a],false) ([b, c],false) ([c, b],false) , 8.53/2.46 ([b, b],false) ([a, b],false) ([c, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([c, b],false) , 8.53/2.46 ([a, c],false) ([c, a],false) ->= ([c, c],false) , 8.53/2.46 ([b, c],false) ([a, b],false) ([c, a],false) ->= ([a, c],false) ([c, a],false) ([b, c],false) ([c, b],false) } 8.53/2.46 8.53/2.46 8.53/2.46 The system is trivially terminating. 8.83/2.51 EOF