/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Applying context closure of depth 1 in the following form: System R over Sigma maps to { fold(xly) -> fold(xry) | l -> r in R, x,y in Sigma } over Sigma^2, where fold(a_1,...,a_n) = (a_1,a_2)...(a_{n-1}a_{n}) Remains to prove termination of the 16-rule system { [a, a] [a, b] [b, a] -> [a, b] [b, b] [b, b] [b, a] , [a, b] [b, a] [a, a] -> [a, a] [a, a] [a, a] [a, a] , [a, a] [a, a] -> [a, a] , [a, b] [b, a] -> [a, a] , [a, a] [a, b] [b, b] -> [a, b] [b, b] [b, b] [b, b] , [a, b] [b, a] [a, b] -> [a, a] [a, a] [a, a] [a, b] , [a, a] [a, b] -> [a, b] , [a, b] [b, b] -> [a, b] , [b, a] [a, b] [b, a] -> [b, b] [b, b] [b, b] [b, a] , [b, b] [b, a] [a, a] -> [b, a] [a, a] [a, a] [a, a] , [b, a] [a, a] -> [b, a] , [b, b] [b, a] -> [b, a] , [b, a] [a, b] [b, b] -> [b, b] [b, b] [b, b] [b, b] , [b, b] [b, a] [a, b] -> [b, a] [a, a] [a, a] [a, b] , [b, a] [a, b] -> [b, b] , [b, b] [b, b] -> [b, b] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [a, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, b] is interpreted by / \ | 1 1 | | 0 1 | \ / [b, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, b] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 10-rule system { [a, a] [a, b] [b, a] -> [a, b] [b, b] [b, b] [b, a] , [a, a] [a, a] -> [a, a] , [a, a] [a, b] [b, b] -> [a, b] [b, b] [b, b] [b, b] , [a, a] [a, b] -> [a, b] , [a, b] [b, b] -> [a, b] , [b, b] [b, a] [a, a] -> [b, a] [a, a] [a, a] [a, a] , [b, a] [a, a] -> [b, a] , [b, b] [b, a] -> [b, a] , [b, b] [b, a] [a, b] -> [b, a] [a, a] [a, a] [a, b] , [b, b] [b, b] -> [b, b] } The dependency pairs transformation was applied. Remains to prove termination of the 32-rule system { ([a, a],true) ([a, b],false) ([b, a],false) -> ([a, b],true) ([b, b],false) ([b, b],false) ([b, a],false) , ([a, a],true) ([a, b],false) ([b, a],false) -> ([b, b],true) ([b, b],false) ([b, a],false) , ([a, a],true) ([a, b],false) ([b, a],false) -> ([b, b],true) ([b, a],false) , ([a, a],true) ([a, b],false) ([b, a],false) -> ([b, a],true) , ([a, a],true) ([a, a],false) -> ([a, a],true) , ([a, a],true) ([a, b],false) ([b, b],false) -> ([a, b],true) ([b, b],false) ([b, b],false) ([b, b],false) , ([a, a],true) ([a, b],false) ([b, b],false) -> ([b, b],true) ([b, b],false) ([b, b],false) , ([a, a],true) ([a, b],false) ([b, b],false) -> ([b, b],true) ([b, b],false) , ([a, a],true) ([a, b],false) ([b, b],false) -> ([b, b],true) , ([a, a],true) ([a, b],false) -> ([a, b],true) , ([a, b],true) ([b, b],false) -> ([a, b],true) , ([b, b],true) ([b, a],false) ([a, a],false) -> ([b, a],true) ([a, a],false) ([a, a],false) ([a, a],false) , ([b, b],true) ([b, a],false) ([a, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) , ([b, b],true) ([b, a],false) ([a, a],false) -> ([a, a],true) ([a, a],false) , ([b, b],true) ([b, a],false) ([a, a],false) -> ([a, a],true) , ([b, a],true) ([a, a],false) -> ([b, a],true) , ([b, b],true) ([b, a],false) -> ([b, a],true) , ([b, b],true) ([b, a],false) ([a, b],false) -> ([b, a],true) ([a, a],false) ([a, a],false) ([a, b],false) , ([b, b],true) ([b, a],false) ([a, b],false) -> ([a, a],true) ([a, a],false) ([a, b],false) , ([b, b],true) ([b, a],false) ([a, b],false) -> ([a, a],true) ([a, b],false) , ([b, b],true) ([b, a],false) ([a, b],false) -> ([a, b],true) , ([b, b],true) ([b, b],false) -> ([b, b],true) , ([a, a],false) ([a, b],false) ([b, a],false) ->= ([a, b],false) ([b, b],false) ([b, b],false) ([b, a],false) , ([a, a],false) ([a, a],false) ->= ([a, a],false) , ([a, a],false) ([a, b],false) ([b, b],false) ->= ([a, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([a, a],false) ([a, b],false) ->= ([a, b],false) , ([a, b],false) ([b, b],false) ->= ([a, b],false) , ([b, b],false) ([b, a],false) ([a, a],false) ->= ([b, a],false) ([a, a],false) ([a, a],false) ([a, a],false) , ([b, a],false) ([a, a],false) ->= ([b, a],false) , ([b, b],false) ([b, a],false) ->= ([b, a],false) , ([b, b],false) ([b, a],false) ([a, b],false) ->= ([b, a],false) ([a, a],false) ([a, a],false) ([a, b],false) , ([b, b],false) ([b, b],false) ->= ([b, b],false) } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: ([a, a],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, b],false) is interpreted by / \ | 1 1 | | 0 1 | \ / ([b, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, b],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, b],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, a],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 22-rule system { ([a, a],true) ([a, a],false) -> ([a, a],true) , ([a, b],true) ([b, b],false) -> ([a, b],true) , ([b, b],true) ([b, a],false) ([a, a],false) -> ([b, a],true) ([a, a],false) ([a, a],false) ([a, a],false) , ([b, b],true) ([b, a],false) ([a, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) , ([b, b],true) ([b, a],false) ([a, a],false) -> ([a, a],true) ([a, a],false) , ([b, b],true) ([b, a],false) ([a, a],false) -> ([a, a],true) , ([b, a],true) ([a, a],false) -> ([b, a],true) , ([b, b],true) ([b, a],false) -> ([b, a],true) , ([b, b],true) ([b, a],false) ([a, b],false) -> ([b, a],true) ([a, a],false) ([a, a],false) ([a, b],false) , ([b, b],true) ([b, a],false) ([a, b],false) -> ([a, a],true) ([a, a],false) ([a, b],false) , ([b, b],true) ([b, a],false) ([a, b],false) -> ([a, a],true) ([a, b],false) , ([b, b],true) ([b, b],false) -> ([b, b],true) , ([a, a],false) ([a, b],false) ([b, a],false) ->= ([a, b],false) ([b, b],false) ([b, b],false) ([b, a],false) , ([a, a],false) ([a, a],false) ->= ([a, a],false) , ([a, a],false) ([a, b],false) ([b, b],false) ->= ([a, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([a, a],false) ([a, b],false) ->= ([a, b],false) , ([a, b],false) ([b, b],false) ->= ([a, b],false) , ([b, b],false) ([b, a],false) ([a, a],false) ->= ([b, a],false) ([a, a],false) ([a, a],false) ([a, a],false) , ([b, a],false) ([a, a],false) ->= ([b, a],false) , ([b, b],false) ([b, a],false) ->= ([b, a],false) , ([b, b],false) ([b, a],false) ([a, b],false) ->= ([b, a],false) ([a, a],false) ([a, a],false) ([a, b],false) , ([b, b],false) ([b, b],false) ->= ([b, b],false) } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: ([a, a],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, a],false) is interpreted by / \ | 1 1 | | 0 1 | \ / ([a, b],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, b],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, a],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 14-rule system { ([a, a],true) ([a, a],false) -> ([a, a],true) , ([a, b],true) ([b, b],false) -> ([a, b],true) , ([b, a],true) ([a, a],false) -> ([b, a],true) , ([b, b],true) ([b, b],false) -> ([b, b],true) , ([a, a],false) ([a, b],false) ([b, a],false) ->= ([a, b],false) ([b, b],false) ([b, b],false) ([b, a],false) , ([a, a],false) ([a, a],false) ->= ([a, a],false) , ([a, a],false) ([a, b],false) ([b, b],false) ->= ([a, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([a, a],false) ([a, b],false) ->= ([a, b],false) , ([a, b],false) ([b, b],false) ->= ([a, b],false) , ([b, b],false) ([b, a],false) ([a, a],false) ->= ([b, a],false) ([a, a],false) ([a, a],false) ([a, a],false) , ([b, a],false) ([a, a],false) ->= ([b, a],false) , ([b, b],false) ([b, a],false) ->= ([b, a],false) , ([b, b],false) ([b, a],false) ([a, b],false) ->= ([b, a],false) ([a, a],false) ([a, a],false) ([a, b],false) , ([b, b],false) ([b, b],false) ->= ([b, b],false) } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 3: ([a, a],true) is interpreted by / \ | 1 0 1 | | 0 1 0 | | 0 0 0 | \ / ([a, b],false) is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / ([b, a],false) is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / ([a, b],true) is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / ([b, b],false) is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / ([b, b],true) is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / ([b, a],true) is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / ([a, a],false) is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 1 1 | \ / Remains to prove termination of the 13-rule system { ([a, b],true) ([b, b],false) -> ([a, b],true) , ([b, a],true) ([a, a],false) -> ([b, a],true) , ([b, b],true) ([b, b],false) -> ([b, b],true) , ([a, a],false) ([a, b],false) ([b, a],false) ->= ([a, b],false) ([b, b],false) ([b, b],false) ([b, a],false) , ([a, a],false) ([a, a],false) ->= ([a, a],false) , ([a, a],false) ([a, b],false) ([b, b],false) ->= ([a, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([a, a],false) ([a, b],false) ->= ([a, b],false) , ([a, b],false) ([b, b],false) ->= ([a, b],false) , ([b, b],false) ([b, a],false) ([a, a],false) ->= ([b, a],false) ([a, a],false) ([a, a],false) ([a, a],false) , ([b, a],false) ([a, a],false) ->= ([b, a],false) , ([b, b],false) ([b, a],false) ->= ([b, a],false) , ([b, b],false) ([b, a],false) ([a, b],false) ->= ([b, a],false) ([a, a],false) ([a, a],false) ([a, b],false) , ([b, b],false) ([b, b],false) ->= ([b, b],false) } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 3: ([a, a],true) is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / ([a, b],false) is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / ([b, a],false) is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / ([a, b],true) is interpreted by / \ | 1 0 1 | | 0 1 0 | | 0 0 0 | \ / ([b, b],false) is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 1 1 | \ / ([b, b],true) is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / ([b, a],true) is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / ([a, a],false) is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / Remains to prove termination of the 12-rule system { ([b, a],true) ([a, a],false) -> ([b, a],true) , ([b, b],true) ([b, b],false) -> ([b, b],true) , ([a, a],false) ([a, b],false) ([b, a],false) ->= ([a, b],false) ([b, b],false) ([b, b],false) ([b, a],false) , ([a, a],false) ([a, a],false) ->= ([a, a],false) , ([a, a],false) ([a, b],false) ([b, b],false) ->= ([a, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([a, a],false) ([a, b],false) ->= ([a, b],false) , ([a, b],false) ([b, b],false) ->= ([a, b],false) , ([b, b],false) ([b, a],false) ([a, a],false) ->= ([b, a],false) ([a, a],false) ([a, a],false) ([a, a],false) , ([b, a],false) ([a, a],false) ->= ([b, a],false) , ([b, b],false) ([b, a],false) ->= ([b, a],false) , ([b, b],false) ([b, a],false) ([a, b],false) ->= ([b, a],false) ([a, a],false) ([a, a],false) ([a, b],false) , ([b, b],false) ([b, b],false) ->= ([b, b],false) } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 3: ([a, a],true) is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / ([a, b],false) is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / ([b, a],false) is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / ([a, b],true) is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / ([b, b],false) is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / ([b, b],true) is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / ([b, a],true) is interpreted by / \ | 1 0 1 | | 0 1 0 | | 0 0 0 | \ / ([a, a],false) is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 1 1 | \ / Remains to prove termination of the 11-rule system { ([b, b],true) ([b, b],false) -> ([b, b],true) , ([a, a],false) ([a, b],false) ([b, a],false) ->= ([a, b],false) ([b, b],false) ([b, b],false) ([b, a],false) , ([a, a],false) ([a, a],false) ->= ([a, a],false) , ([a, a],false) ([a, b],false) ([b, b],false) ->= ([a, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([a, a],false) ([a, b],false) ->= ([a, b],false) , ([a, b],false) ([b, b],false) ->= ([a, b],false) , ([b, b],false) ([b, a],false) ([a, a],false) ->= ([b, a],false) ([a, a],false) ([a, a],false) ([a, a],false) , ([b, a],false) ([a, a],false) ->= ([b, a],false) , ([b, b],false) ([b, a],false) ->= ([b, a],false) , ([b, b],false) ([b, a],false) ([a, b],false) ->= ([b, a],false) ([a, a],false) ([a, a],false) ([a, b],false) , ([b, b],false) ([b, b],false) ->= ([b, b],false) } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 3: ([a, a],true) is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / ([a, b],false) is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / ([b, a],false) is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / ([a, b],true) is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / ([b, b],false) is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 1 1 | \ / ([b, b],true) is interpreted by / \ | 1 0 1 | | 0 1 0 | | 0 0 0 | \ / ([b, a],true) is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / ([a, a],false) is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / Remains to prove termination of the 10-rule system { ([a, a],false) ([a, b],false) ([b, a],false) ->= ([a, b],false) ([b, b],false) ([b, b],false) ([b, a],false) , ([a, a],false) ([a, a],false) ->= ([a, a],false) , ([a, a],false) ([a, b],false) ([b, b],false) ->= ([a, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([a, a],false) ([a, b],false) ->= ([a, b],false) , ([a, b],false) ([b, b],false) ->= ([a, b],false) , ([b, b],false) ([b, a],false) ([a, a],false) ->= ([b, a],false) ([a, a],false) ([a, a],false) ([a, a],false) , ([b, a],false) ([a, a],false) ->= ([b, a],false) , ([b, b],false) ([b, a],false) ->= ([b, a],false) , ([b, b],false) ([b, a],false) ([a, b],false) ->= ([b, a],false) ([a, a],false) ([a, a],false) ([a, b],false) , ([b, b],false) ([b, b],false) ->= ([b, b],false) } The system is trivially terminating.