0.00/0.60 YES 1.67/0.62 1.67/0.62 1.67/0.62 Applying context closure of depth 1 in the following form: System R over Sigma 1.67/0.62 maps to { fold(xly) -> fold(xry) | l -> r in R, x,y in Sigma } over Sigma^2, 1.67/0.62 where fold(a_1,...,a_n) = (a_1,a_2)...(a_{n-1}a_{n}) 1.67/0.62 1.67/0.62 Remains to prove termination of the 36-rule system 1.67/0.62 { [a, a] [a, a] -> [a, a] , 1.67/0.62 [a, a] [a, a] [a, a] -> [a, b] [b, a] , 1.67/0.62 [a, b] [b, c] [c, a] -> [a, a] , 1.67/0.62 [a, c] [c, b] [b, a] -> [a, a] [a, b] [b, c] [c, c] [c, a] , 1.67/0.62 [a, a] [a, b] -> [a, b] , 1.67/0.62 [a, a] [a, a] [a, b] -> [a, b] [b, b] , 1.67/0.62 [a, b] [b, c] [c, b] -> [a, b] , 1.67/0.62 [a, c] [c, b] [b, b] -> [a, a] [a, b] [b, c] [c, c] [c, b] , 1.67/0.62 [a, a] [a, c] -> [a, c] , 1.67/0.62 [a, a] [a, a] [a, c] -> [a, b] [b, c] , 1.67/0.62 [a, b] [b, c] [c, c] -> [a, c] , 1.67/0.62 [a, c] [c, b] [b, c] -> [a, a] [a, b] [b, c] [c, c] [c, c] , 1.67/0.62 [b, a] [a, a] -> [b, a] , 1.67/0.62 [b, a] [a, a] [a, a] -> [b, b] [b, a] , 1.67/0.62 [b, b] [b, c] [c, a] -> [b, a] , 1.67/0.62 [b, c] [c, b] [b, a] -> [b, a] [a, b] [b, c] [c, c] [c, a] , 1.67/0.62 [b, a] [a, b] -> [b, b] , 1.67/0.62 [b, a] [a, a] [a, b] -> [b, b] [b, b] , 1.67/0.62 [b, b] [b, c] [c, b] -> [b, b] , 1.67/0.62 [b, c] [c, b] [b, b] -> [b, a] [a, b] [b, c] [c, c] [c, b] , 1.67/0.62 [b, a] [a, c] -> [b, c] , 1.67/0.62 [b, a] [a, a] [a, c] -> [b, b] [b, c] , 1.67/0.62 [b, b] [b, c] [c, c] -> [b, c] , 1.67/0.62 [b, c] [c, b] [b, c] -> [b, a] [a, b] [b, c] [c, c] [c, c] , 1.67/0.62 [c, a] [a, a] -> [c, a] , 1.67/0.62 [c, a] [a, a] [a, a] -> [c, b] [b, a] , 1.67/0.62 [c, b] [b, c] [c, a] -> [c, a] , 1.67/0.62 [c, c] [c, b] [b, a] -> [c, a] [a, b] [b, c] [c, c] [c, a] , 1.67/0.62 [c, a] [a, b] -> [c, b] , 1.67/0.62 [c, a] [a, a] [a, b] -> [c, b] [b, b] , 1.67/0.62 [c, b] [b, c] [c, b] -> [c, b] , 1.67/0.62 [c, c] [c, b] [b, b] -> [c, a] [a, b] [b, c] [c, c] [c, b] , 1.67/0.62 [c, a] [a, c] -> [c, c] , 1.67/0.62 [c, a] [a, a] [a, c] -> [c, b] [b, c] , 1.67/0.62 [c, b] [b, c] [c, c] -> [c, c] , 1.67/0.62 [c, c] [c, b] [b, c] -> [c, a] [a, b] [b, c] [c, c] [c, c] } 1.67/0.62 1.67/0.62 1.67/0.62 1.67/0.62 The system was filtered by the following matrix interpretation 1.67/0.62 of type E_J with J = {1,...,2} and dimension 2: 1.67/0.62 1.67/0.62 [a, a] is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 1 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 [a, b] is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 1 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 [b, a] is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 0 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 [b, c] is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 0 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 [c, a] is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 0 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 [a, c] is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 1 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 [c, b] is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 1 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 [c, c] is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 0 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 [b, b] is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 1 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 1.67/0.62 Remains to prove termination of the 15-rule system 1.67/0.62 { [a, b] [b, c] [c, a] -> [a, a] , 1.67/0.62 [a, c] [c, b] [b, a] -> [a, a] [a, b] [b, c] [c, c] [c, a] , 1.67/0.62 [a, c] [c, b] [b, b] -> [a, a] [a, b] [b, c] [c, c] [c, b] , 1.67/0.62 [a, b] [b, c] [c, c] -> [a, c] , 1.67/0.62 [a, c] [c, b] [b, c] -> [a, a] [a, b] [b, c] [c, c] [c, c] , 1.67/0.62 [b, c] [c, b] [b, a] -> [b, a] [a, b] [b, c] [c, c] [c, a] , 1.67/0.62 [b, a] [a, b] -> [b, b] , 1.67/0.62 [b, a] [a, a] [a, b] -> [b, b] [b, b] , 1.67/0.62 [b, c] [c, b] [b, b] -> [b, a] [a, b] [b, c] [c, c] [c, b] , 1.67/0.62 [b, c] [c, b] [b, c] -> [b, a] [a, b] [b, c] [c, c] [c, c] , 1.67/0.62 [c, c] [c, b] [b, a] -> [c, a] [a, b] [b, c] [c, c] [c, a] , 1.67/0.62 [c, a] [a, b] -> [c, b] , 1.67/0.62 [c, a] [a, a] [a, b] -> [c, b] [b, b] , 1.67/0.62 [c, c] [c, b] [b, b] -> [c, a] [a, b] [b, c] [c, c] [c, b] , 1.67/0.62 [c, c] [c, b] [b, c] -> [c, a] [a, b] [b, c] [c, c] [c, c] } 1.67/0.62 1.67/0.62 1.67/0.62 The dependency pairs transformation was applied. 1.67/0.62 1.67/0.62 Remains to prove termination of the 55-rule system 1.67/0.62 { ([a, c],true) ([c, b],false) ([b, a],false) -> ([a, b],true) ([b, c],false) ([c, c],false) ([c, a],false) , 1.67/0.62 ([a, c],true) ([c, b],false) ([b, a],false) -> ([b, c],true) ([c, c],false) ([c, a],false) , 1.67/0.62 ([a, c],true) ([c, b],false) ([b, a],false) -> ([c, c],true) ([c, a],false) , 1.67/0.62 ([a, c],true) ([c, b],false) ([b, a],false) -> ([c, a],true) , 1.67/0.62 ([a, c],true) ([c, b],false) ([b, b],false) -> ([a, b],true) ([b, c],false) ([c, c],false) ([c, b],false) , 1.67/0.62 ([a, c],true) ([c, b],false) ([b, b],false) -> ([b, c],true) ([c, c],false) ([c, b],false) , 1.67/0.62 ([a, c],true) ([c, b],false) ([b, b],false) -> ([c, c],true) ([c, b],false) , 1.67/0.62 ([a, b],true) ([b, c],false) ([c, c],false) -> ([a, c],true) , 1.67/0.62 ([a, c],true) ([c, b],false) ([b, c],false) -> ([a, b],true) ([b, c],false) ([c, c],false) ([c, c],false) , 1.67/0.62 ([a, c],true) ([c, b],false) ([b, c],false) -> ([b, c],true) ([c, c],false) ([c, c],false) , 1.67/0.62 ([a, c],true) ([c, b],false) ([b, c],false) -> ([c, c],true) ([c, c],false) , 1.67/0.62 ([a, c],true) ([c, b],false) ([b, c],false) -> ([c, c],true) , 1.67/0.62 ([b, c],true) ([c, b],false) ([b, a],false) -> ([b, a],true) ([a, b],false) ([b, c],false) ([c, c],false) ([c, a],false) , 1.67/0.62 ([b, c],true) ([c, b],false) ([b, a],false) -> ([a, b],true) ([b, c],false) ([c, c],false) ([c, a],false) , 1.67/0.62 ([b, c],true) ([c, b],false) ([b, a],false) -> ([b, c],true) ([c, c],false) ([c, a],false) , 1.67/0.62 ([b, c],true) ([c, b],false) ([b, a],false) -> ([c, c],true) ([c, a],false) , 1.67/0.62 ([b, c],true) ([c, b],false) ([b, a],false) -> ([c, a],true) , 1.67/0.62 ([b, c],true) ([c, b],false) ([b, b],false) -> ([b, a],true) ([a, b],false) ([b, c],false) ([c, c],false) ([c, b],false) , 1.67/0.62 ([b, c],true) ([c, b],false) ([b, b],false) -> ([a, b],true) ([b, c],false) ([c, c],false) ([c, b],false) , 1.67/0.62 ([b, c],true) ([c, b],false) ([b, b],false) -> ([b, c],true) ([c, c],false) ([c, b],false) , 1.67/0.62 ([b, c],true) ([c, b],false) ([b, b],false) -> ([c, c],true) ([c, b],false) , 1.67/0.62 ([b, c],true) ([c, b],false) ([b, c],false) -> ([b, a],true) ([a, b],false) ([b, c],false) ([c, c],false) ([c, c],false) , 1.67/0.62 ([b, c],true) ([c, b],false) ([b, c],false) -> ([a, b],true) ([b, c],false) ([c, c],false) ([c, c],false) , 1.67/0.62 ([b, c],true) ([c, b],false) ([b, c],false) -> ([b, c],true) ([c, c],false) ([c, c],false) , 1.67/0.62 ([b, c],true) ([c, b],false) ([b, c],false) -> ([c, c],true) ([c, c],false) , 1.67/0.62 ([b, c],true) ([c, b],false) ([b, c],false) -> ([c, c],true) , 1.67/0.62 ([c, c],true) ([c, b],false) ([b, a],false) -> ([c, a],true) ([a, b],false) ([b, c],false) ([c, c],false) ([c, a],false) , 1.67/0.62 ([c, c],true) ([c, b],false) ([b, a],false) -> ([a, b],true) ([b, c],false) ([c, c],false) ([c, a],false) , 1.67/0.62 ([c, c],true) ([c, b],false) ([b, a],false) -> ([b, c],true) ([c, c],false) ([c, a],false) , 1.67/0.62 ([c, c],true) ([c, b],false) ([b, a],false) -> ([c, c],true) ([c, a],false) , 1.67/0.62 ([c, c],true) ([c, b],false) ([b, a],false) -> ([c, a],true) , 1.67/0.62 ([c, c],true) ([c, b],false) ([b, b],false) -> ([c, a],true) ([a, b],false) ([b, c],false) ([c, c],false) ([c, b],false) , 1.67/0.62 ([c, c],true) ([c, b],false) ([b, b],false) -> ([a, b],true) ([b, c],false) ([c, c],false) ([c, b],false) , 1.67/0.62 ([c, c],true) ([c, b],false) ([b, b],false) -> ([b, c],true) ([c, c],false) ([c, b],false) , 1.67/0.62 ([c, c],true) ([c, b],false) ([b, b],false) -> ([c, c],true) ([c, b],false) , 1.67/0.62 ([c, c],true) ([c, b],false) ([b, c],false) -> ([c, a],true) ([a, b],false) ([b, c],false) ([c, c],false) ([c, c],false) , 1.67/0.62 ([c, c],true) ([c, b],false) ([b, c],false) -> ([a, b],true) ([b, c],false) ([c, c],false) ([c, c],false) , 1.67/0.62 ([c, c],true) ([c, b],false) ([b, c],false) -> ([b, c],true) ([c, c],false) ([c, c],false) , 1.67/0.62 ([c, c],true) ([c, b],false) ([b, c],false) -> ([c, c],true) ([c, c],false) , 1.67/0.62 ([c, c],true) ([c, b],false) ([b, c],false) -> ([c, c],true) , 1.67/0.62 ([a, b],false) ([b, c],false) ([c, a],false) ->= ([a, a],false) , 1.67/0.62 ([a, c],false) ([c, b],false) ([b, a],false) ->= ([a, a],false) ([a, b],false) ([b, c],false) ([c, c],false) ([c, a],false) , 1.67/0.62 ([a, c],false) ([c, b],false) ([b, b],false) ->= ([a, a],false) ([a, b],false) ([b, c],false) ([c, c],false) ([c, b],false) , 1.67/0.62 ([a, b],false) ([b, c],false) ([c, c],false) ->= ([a, c],false) , 1.67/0.62 ([a, c],false) ([c, b],false) ([b, c],false) ->= ([a, a],false) ([a, b],false) ([b, c],false) ([c, c],false) ([c, c],false) , 1.67/0.62 ([b, c],false) ([c, b],false) ([b, a],false) ->= ([b, a],false) ([a, b],false) ([b, c],false) ([c, c],false) ([c, a],false) , 1.67/0.62 ([b, a],false) ([a, b],false) ->= ([b, b],false) , 1.67/0.62 ([b, a],false) ([a, a],false) ([a, b],false) ->= ([b, b],false) ([b, b],false) , 1.67/0.62 ([b, c],false) ([c, b],false) ([b, b],false) ->= ([b, a],false) ([a, b],false) ([b, c],false) ([c, c],false) ([c, b],false) , 1.67/0.62 ([b, c],false) ([c, b],false) ([b, c],false) ->= ([b, a],false) ([a, b],false) ([b, c],false) ([c, c],false) ([c, c],false) , 1.67/0.62 ([c, c],false) ([c, b],false) ([b, a],false) ->= ([c, a],false) ([a, b],false) ([b, c],false) ([c, c],false) ([c, a],false) , 1.67/0.62 ([c, a],false) ([a, b],false) ->= ([c, b],false) , 1.67/0.62 ([c, a],false) ([a, a],false) ([a, b],false) ->= ([c, b],false) ([b, b],false) , 1.67/0.62 ([c, c],false) ([c, b],false) ([b, b],false) ->= ([c, a],false) ([a, b],false) ([b, c],false) ([c, c],false) ([c, b],false) , 1.67/0.62 ([c, c],false) ([c, b],false) ([b, c],false) ->= ([c, a],false) ([a, b],false) ([b, c],false) ([c, c],false) ([c, c],false) } 1.67/0.62 1.67/0.62 1.67/0.62 1.67/0.62 1.67/0.62 The system was filtered by the following matrix interpretation 1.67/0.62 of type E_J with J = {1,...,2} and dimension 2: 1.67/0.62 1.67/0.62 ([a, c],true) is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 0 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 ([c, b],false) is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 1 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 ([b, a],false) is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 1 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 ([a, b],true) is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 0 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 ([b, c],false) is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 0 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 ([c, c],false) is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 0 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 ([c, a],false) is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 1 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 ([b, c],true) is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 0 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 ([c, c],true) is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 0 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 ([c, a],true) is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 0 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 ([b, b],false) is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 1 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 ([b, a],true) is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 0 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 ([a, b],false) is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 0 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 ([a, a],false) is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 1 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 ([a, c],false) is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 0 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 1.67/0.62 Remains to prove termination of the 16-rule system 1.67/0.62 { ([a, b],true) ([b, c],false) ([c, c],false) -> ([a, c],true) , 1.67/0.62 ([a, b],false) ([b, c],false) ([c, a],false) ->= ([a, a],false) , 1.67/0.62 ([a, c],false) ([c, b],false) ([b, a],false) ->= ([a, a],false) ([a, b],false) ([b, c],false) ([c, c],false) ([c, a],false) , 1.67/0.62 ([a, c],false) ([c, b],false) ([b, b],false) ->= ([a, a],false) ([a, b],false) ([b, c],false) ([c, c],false) ([c, b],false) , 1.67/0.62 ([a, b],false) ([b, c],false) ([c, c],false) ->= ([a, c],false) , 1.67/0.62 ([a, c],false) ([c, b],false) ([b, c],false) ->= ([a, a],false) ([a, b],false) ([b, c],false) ([c, c],false) ([c, c],false) , 1.67/0.62 ([b, c],false) ([c, b],false) ([b, a],false) ->= ([b, a],false) ([a, b],false) ([b, c],false) ([c, c],false) ([c, a],false) , 1.67/0.62 ([b, a],false) ([a, b],false) ->= ([b, b],false) , 1.67/0.62 ([b, a],false) ([a, a],false) ([a, b],false) ->= ([b, b],false) ([b, b],false) , 1.67/0.62 ([b, c],false) ([c, b],false) ([b, b],false) ->= ([b, a],false) ([a, b],false) ([b, c],false) ([c, c],false) ([c, b],false) , 1.67/0.62 ([b, c],false) ([c, b],false) ([b, c],false) ->= ([b, a],false) ([a, b],false) ([b, c],false) ([c, c],false) ([c, c],false) , 1.67/0.62 ([c, c],false) ([c, b],false) ([b, a],false) ->= ([c, a],false) ([a, b],false) ([b, c],false) ([c, c],false) ([c, a],false) , 1.67/0.62 ([c, a],false) ([a, b],false) ->= ([c, b],false) , 1.67/0.62 ([c, a],false) ([a, a],false) ([a, b],false) ->= ([c, b],false) ([b, b],false) , 1.67/0.62 ([c, c],false) ([c, b],false) ([b, b],false) ->= ([c, a],false) ([a, b],false) ([b, c],false) ([c, c],false) ([c, b],false) , 1.67/0.62 ([c, c],false) ([c, b],false) ([b, c],false) ->= ([c, a],false) ([a, b],false) ([b, c],false) ([c, c],false) ([c, c],false) } 1.67/0.62 1.67/0.62 1.67/0.62 The system was filtered by the following matrix interpretation 1.67/0.62 of type E_J with J = {1,...,2} and dimension 2: 1.67/0.62 1.67/0.62 ([a, c],true) is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 0 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 ([c, b],false) is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 0 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 ([b, a],false) is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 0 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 ([a, b],true) is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 1 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 ([b, c],false) is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 0 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 ([c, c],false) is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 0 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 ([c, a],false) is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 0 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 ([b, c],true) is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 0 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 ([c, c],true) is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 0 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 ([c, a],true) is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 0 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 ([b, b],false) is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 0 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 ([b, a],true) is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 0 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 ([a, b],false) is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 0 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 ([a, a],false) is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 0 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 ([a, c],false) is interpreted by 1.67/0.62 / \ 1.67/0.62 | 1 0 | 1.67/0.62 | 0 1 | 1.67/0.62 \ / 1.67/0.62 1.67/0.62 Remains to prove termination of the 15-rule system 1.67/0.62 { ([a, b],false) ([b, c],false) ([c, a],false) ->= ([a, a],false) , 1.67/0.62 ([a, c],false) ([c, b],false) ([b, a],false) ->= ([a, a],false) ([a, b],false) ([b, c],false) ([c, c],false) ([c, a],false) , 1.67/0.62 ([a, c],false) ([c, b],false) ([b, b],false) ->= ([a, a],false) ([a, b],false) ([b, c],false) ([c, c],false) ([c, b],false) , 1.67/0.62 ([a, b],false) ([b, c],false) ([c, c],false) ->= ([a, c],false) , 1.67/0.62 ([a, c],false) ([c, b],false) ([b, c],false) ->= ([a, a],false) ([a, b],false) ([b, c],false) ([c, c],false) ([c, c],false) , 1.67/0.62 ([b, c],false) ([c, b],false) ([b, a],false) ->= ([b, a],false) ([a, b],false) ([b, c],false) ([c, c],false) ([c, a],false) , 1.67/0.62 ([b, a],false) ([a, b],false) ->= ([b, b],false) , 1.67/0.62 ([b, a],false) ([a, a],false) ([a, b],false) ->= ([b, b],false) ([b, b],false) , 1.67/0.62 ([b, c],false) ([c, b],false) ([b, b],false) ->= ([b, a],false) ([a, b],false) ([b, c],false) ([c, c],false) ([c, b],false) , 1.67/0.62 ([b, c],false) ([c, b],false) ([b, c],false) ->= ([b, a],false) ([a, b],false) ([b, c],false) ([c, c],false) ([c, c],false) , 1.67/0.62 ([c, c],false) ([c, b],false) ([b, a],false) ->= ([c, a],false) ([a, b],false) ([b, c],false) ([c, c],false) ([c, a],false) , 1.67/0.62 ([c, a],false) ([a, b],false) ->= ([c, b],false) , 1.67/0.62 ([c, a],false) ([a, a],false) ([a, b],false) ->= ([c, b],false) ([b, b],false) , 1.67/0.62 ([c, c],false) ([c, b],false) ([b, b],false) ->= ([c, a],false) ([a, b],false) ([b, c],false) ([c, c],false) ([c, b],false) , 1.67/0.62 ([c, c],false) ([c, b],false) ([b, c],false) ->= ([c, a],false) ([a, b],false) ([b, c],false) ([c, c],false) ([c, c],false) } 1.67/0.62 1.67/0.62 1.67/0.62 The system is trivially terminating. 1.76/0.66 EOF