/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 is interpreted by / \ | 1 1 | | 0 1 | \ / 1 is interpreted by / \ | 1 1 | | 0 1 | \ / 2 is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 17-rule system { 0 1 2 0 2 -> 0 1 0 2 2 , 0 1 2 0 2 -> 0 1 1 2 2 , 0 1 2 0 2 -> 0 2 1 0 2 , 0 1 2 0 2 -> 0 2 2 1 0 , 1 1 2 0 2 -> 1 0 0 2 2 , 1 1 2 0 2 -> 1 0 1 2 2 , 1 1 2 0 2 -> 1 0 2 0 2 , 1 1 2 0 2 -> 1 0 2 1 2 , 1 1 2 0 2 -> 1 0 2 2 0 , 1 1 2 0 2 -> 1 1 0 2 2 , 1 1 2 0 2 -> 1 2 1 0 2 , 1 2 2 0 2 -> 1 0 2 2 2 , 2 1 1 0 2 -> 2 0 1 0 2 , 2 1 2 0 2 -> 2 0 1 2 2 , 2 1 2 0 2 -> 2 1 0 2 2 , 2 1 2 0 2 -> 2 2 1 0 2 , 2 1 2 0 2 -> 2 2 2 1 0 } 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 153-rule system { [0, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [0, 0] [0, 1] [1, 0] [0, 2] [2, 2] [2, 0] , [0, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [0, 0] [0, 1] [1, 1] [1, 2] [2, 2] [2, 0] , [0, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [0, 0] [0, 2] [2, 1] [1, 0] [0, 2] [2, 0] , [0, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [0, 0] [0, 2] [2, 2] [2, 1] [1, 0] [0, 0] , [0, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [0, 1] [1, 0] [0, 0] [0, 2] [2, 2] [2, 0] , [0, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [0, 1] [1, 0] [0, 1] [1, 2] [2, 2] [2, 0] , [0, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [0, 1] [1, 0] [0, 2] [2, 0] [0, 2] [2, 0] , [0, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [0, 1] [1, 0] [0, 2] [2, 1] [1, 2] [2, 0] , [0, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [0, 1] [1, 0] [0, 2] [2, 2] [2, 0] [0, 0] , [0, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [0, 1] [1, 1] [1, 0] [0, 2] [2, 2] [2, 0] , [0, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [0, 1] [1, 2] [2, 1] [1, 0] [0, 2] [2, 0] , [0, 1] [1, 2] [2, 2] [2, 0] [0, 2] [2, 0] -> [0, 1] [1, 0] [0, 2] [2, 2] [2, 2] [2, 0] , [0, 2] [2, 1] [1, 1] [1, 0] [0, 2] [2, 0] -> [0, 2] [2, 0] [0, 1] [1, 0] [0, 2] [2, 0] , [0, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [0, 2] [2, 0] [0, 1] [1, 2] [2, 2] [2, 0] , [0, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [0, 2] [2, 1] [1, 0] [0, 2] [2, 2] [2, 0] , [0, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [0, 2] [2, 2] [2, 1] [1, 0] [0, 2] [2, 0] , [0, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [0, 2] [2, 2] [2, 2] [2, 1] [1, 0] [0, 0] , [0, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [0, 0] [0, 1] [1, 0] [0, 2] [2, 2] [2, 1] , [0, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [0, 0] [0, 1] [1, 1] [1, 2] [2, 2] [2, 1] , [0, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [0, 0] [0, 2] [2, 1] [1, 0] [0, 2] [2, 1] , [0, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [0, 0] [0, 2] [2, 2] [2, 1] [1, 0] [0, 1] , [0, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [0, 1] [1, 0] [0, 0] [0, 2] [2, 2] [2, 1] , [0, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [0, 1] [1, 0] [0, 1] [1, 2] [2, 2] [2, 1] , [0, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [0, 1] [1, 0] [0, 2] [2, 0] [0, 2] [2, 1] , [0, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [0, 1] [1, 0] [0, 2] [2, 1] [1, 2] [2, 1] , [0, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [0, 1] [1, 0] [0, 2] [2, 2] [2, 0] [0, 1] , [0, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [0, 1] [1, 1] [1, 0] [0, 2] [2, 2] [2, 1] , [0, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [0, 1] [1, 2] [2, 1] [1, 0] [0, 2] [2, 1] , [0, 1] [1, 2] [2, 2] [2, 0] [0, 2] [2, 1] -> [0, 1] [1, 0] [0, 2] [2, 2] [2, 2] [2, 1] , [0, 2] [2, 1] [1, 1] [1, 0] [0, 2] [2, 1] -> [0, 2] [2, 0] [0, 1] [1, 0] [0, 2] [2, 1] , [0, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [0, 2] [2, 0] [0, 1] [1, 2] [2, 2] [2, 1] , [0, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [0, 2] [2, 1] [1, 0] [0, 2] [2, 2] [2, 1] , [0, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [0, 2] [2, 2] [2, 1] [1, 0] [0, 2] [2, 1] , [0, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [0, 2] [2, 2] [2, 2] [2, 1] [1, 0] [0, 1] , [0, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [0, 0] [0, 1] [1, 0] [0, 2] [2, 2] [2, 2] , [0, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [0, 0] [0, 1] [1, 1] [1, 2] [2, 2] [2, 2] , [0, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [0, 0] [0, 2] [2, 1] [1, 0] [0, 2] [2, 2] , [0, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [0, 0] [0, 2] [2, 2] [2, 1] [1, 0] [0, 2] , [0, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [0, 1] [1, 0] [0, 0] [0, 2] [2, 2] [2, 2] , [0, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [0, 1] [1, 0] [0, 1] [1, 2] [2, 2] [2, 2] , [0, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [0, 1] [1, 0] [0, 2] [2, 0] [0, 2] [2, 2] , [0, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [0, 1] [1, 0] [0, 2] [2, 1] [1, 2] [2, 2] , [0, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [0, 1] [1, 0] [0, 2] [2, 2] [2, 0] [0, 2] , [0, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [0, 1] [1, 1] [1, 0] [0, 2] [2, 2] [2, 2] , [0, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [0, 1] [1, 2] [2, 1] [1, 0] [0, 2] [2, 2] , [0, 1] [1, 2] [2, 2] [2, 0] [0, 2] [2, 2] -> [0, 1] [1, 0] [0, 2] [2, 2] [2, 2] [2, 2] , [0, 2] [2, 1] [1, 1] [1, 0] [0, 2] [2, 2] -> [0, 2] [2, 0] [0, 1] [1, 0] [0, 2] [2, 2] , [0, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [0, 2] [2, 0] [0, 1] [1, 2] [2, 2] [2, 2] , [0, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [0, 2] [2, 1] [1, 0] [0, 2] [2, 2] [2, 2] , [0, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [0, 2] [2, 2] [2, 1] [1, 0] [0, 2] [2, 2] , [0, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [0, 2] [2, 2] [2, 2] [2, 1] [1, 0] [0, 2] , [1, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [1, 0] [0, 1] [1, 0] [0, 2] [2, 2] [2, 0] , [1, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [1, 0] [0, 1] [1, 1] [1, 2] [2, 2] [2, 0] , [1, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [1, 0] [0, 2] [2, 1] [1, 0] [0, 2] [2, 0] , [1, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [1, 0] [0, 2] [2, 2] [2, 1] [1, 0] [0, 0] , [1, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [1, 1] [1, 0] [0, 0] [0, 2] [2, 2] [2, 0] , [1, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [1, 1] [1, 0] [0, 1] [1, 2] [2, 2] [2, 0] , [1, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [1, 1] [1, 0] [0, 2] [2, 0] [0, 2] [2, 0] , [1, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [1, 1] [1, 0] [0, 2] [2, 1] [1, 2] [2, 0] , [1, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [1, 1] [1, 0] [0, 2] [2, 2] [2, 0] [0, 0] , [1, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [1, 1] [1, 1] [1, 0] [0, 2] [2, 2] [2, 0] , [1, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [1, 1] [1, 2] [2, 1] [1, 0] [0, 2] [2, 0] , [1, 1] [1, 2] [2, 2] [2, 0] [0, 2] [2, 0] -> [1, 1] [1, 0] [0, 2] [2, 2] [2, 2] [2, 0] , [1, 2] [2, 1] [1, 1] [1, 0] [0, 2] [2, 0] -> [1, 2] [2, 0] [0, 1] [1, 0] [0, 2] [2, 0] , [1, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [1, 2] [2, 0] [0, 1] [1, 2] [2, 2] [2, 0] , [1, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [1, 2] [2, 1] [1, 0] [0, 2] [2, 2] [2, 0] , [1, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [1, 2] [2, 2] [2, 1] [1, 0] [0, 2] [2, 0] , [1, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [1, 2] [2, 2] [2, 2] [2, 1] [1, 0] [0, 0] , [1, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [1, 0] [0, 1] [1, 0] [0, 2] [2, 2] [2, 1] , [1, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [1, 0] [0, 1] [1, 1] [1, 2] [2, 2] [2, 1] , [1, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [1, 0] [0, 2] [2, 1] [1, 0] [0, 2] [2, 1] , [1, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [1, 0] [0, 2] [2, 2] [2, 1] [1, 0] [0, 1] , [1, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [1, 1] [1, 0] [0, 0] [0, 2] [2, 2] [2, 1] , [1, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [1, 1] [1, 0] [0, 1] [1, 2] [2, 2] [2, 1] , [1, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [1, 1] [1, 0] [0, 2] [2, 0] [0, 2] [2, 1] , [1, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [1, 1] [1, 0] [0, 2] [2, 1] [1, 2] [2, 1] , [1, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [1, 1] [1, 0] [0, 2] [2, 2] [2, 0] [0, 1] , [1, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [1, 1] [1, 1] [1, 0] [0, 2] [2, 2] [2, 1] , [1, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [1, 1] [1, 2] [2, 1] [1, 0] [0, 2] [2, 1] , [1, 1] [1, 2] [2, 2] [2, 0] [0, 2] [2, 1] -> [1, 1] [1, 0] [0, 2] [2, 2] [2, 2] [2, 1] , [1, 2] [2, 1] [1, 1] [1, 0] [0, 2] [2, 1] -> [1, 2] [2, 0] [0, 1] [1, 0] [0, 2] [2, 1] , [1, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [1, 2] [2, 0] [0, 1] [1, 2] [2, 2] [2, 1] , [1, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [1, 2] [2, 1] [1, 0] [0, 2] [2, 2] [2, 1] , [1, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [1, 2] [2, 2] [2, 1] [1, 0] [0, 2] [2, 1] , [1, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [1, 2] [2, 2] [2, 2] [2, 1] [1, 0] [0, 1] , [1, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [1, 0] [0, 1] [1, 0] [0, 2] [2, 2] [2, 2] , [1, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [1, 0] [0, 1] [1, 1] [1, 2] [2, 2] [2, 2] , [1, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [1, 0] [0, 2] [2, 1] [1, 0] [0, 2] [2, 2] , [1, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [1, 0] [0, 2] [2, 2] [2, 1] [1, 0] [0, 2] , [1, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [1, 1] [1, 0] [0, 0] [0, 2] [2, 2] [2, 2] , [1, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [1, 1] [1, 0] [0, 1] [1, 2] [2, 2] [2, 2] , [1, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [1, 1] [1, 0] [0, 2] [2, 0] [0, 2] [2, 2] , [1, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [1, 1] [1, 0] [0, 2] [2, 1] [1, 2] [2, 2] , [1, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [1, 1] [1, 0] [0, 2] [2, 2] [2, 0] [0, 2] , [1, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [1, 1] [1, 1] [1, 0] [0, 2] [2, 2] [2, 2] , [1, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [1, 1] [1, 2] [2, 1] [1, 0] [0, 2] [2, 2] , [1, 1] [1, 2] [2, 2] [2, 0] [0, 2] [2, 2] -> [1, 1] [1, 0] [0, 2] [2, 2] [2, 2] [2, 2] , [1, 2] [2, 1] [1, 1] [1, 0] [0, 2] [2, 2] -> [1, 2] [2, 0] [0, 1] [1, 0] [0, 2] [2, 2] , [1, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [1, 2] [2, 0] [0, 1] [1, 2] [2, 2] [2, 2] , [1, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [1, 2] [2, 1] [1, 0] [0, 2] [2, 2] [2, 2] , [1, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [1, 2] [2, 2] [2, 1] [1, 0] [0, 2] [2, 2] , [1, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [1, 2] [2, 2] [2, 2] [2, 1] [1, 0] [0, 2] , [2, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [2, 0] [0, 1] [1, 0] [0, 2] [2, 2] [2, 0] , [2, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [2, 0] [0, 1] [1, 1] [1, 2] [2, 2] [2, 0] , [2, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [2, 0] [0, 2] [2, 1] [1, 0] [0, 2] [2, 0] , [2, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [2, 0] [0, 2] [2, 2] [2, 1] [1, 0] [0, 0] , [2, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [2, 1] [1, 0] [0, 0] [0, 2] [2, 2] [2, 0] , [2, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [2, 1] [1, 0] [0, 1] [1, 2] [2, 2] [2, 0] , [2, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [2, 1] [1, 0] [0, 2] [2, 0] [0, 2] [2, 0] , [2, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [2, 1] [1, 0] [0, 2] [2, 1] [1, 2] [2, 0] , [2, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [2, 1] [1, 0] [0, 2] [2, 2] [2, 0] [0, 0] , [2, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [2, 1] [1, 1] [1, 0] [0, 2] [2, 2] [2, 0] , [2, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [2, 1] [1, 2] [2, 1] [1, 0] [0, 2] [2, 0] , [2, 1] [1, 2] [2, 2] [2, 0] [0, 2] [2, 0] -> [2, 1] [1, 0] [0, 2] [2, 2] [2, 2] [2, 0] , [2, 2] [2, 1] [1, 1] [1, 0] [0, 2] [2, 0] -> [2, 2] [2, 0] [0, 1] [1, 0] [0, 2] [2, 0] , [2, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [2, 2] [2, 0] [0, 1] [1, 2] [2, 2] [2, 0] , [2, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [2, 2] [2, 1] [1, 0] [0, 2] [2, 2] [2, 0] , [2, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [2, 2] [2, 2] [2, 1] [1, 0] [0, 2] [2, 0] , [2, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [2, 2] [2, 2] [2, 2] [2, 1] [1, 0] [0, 0] , [2, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [2, 0] [0, 1] [1, 0] [0, 2] [2, 2] [2, 1] , [2, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [2, 0] [0, 1] [1, 1] [1, 2] [2, 2] [2, 1] , [2, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [2, 0] [0, 2] [2, 1] [1, 0] [0, 2] [2, 1] , [2, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [2, 0] [0, 2] [2, 2] [2, 1] [1, 0] [0, 1] , [2, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [2, 1] [1, 0] [0, 0] [0, 2] [2, 2] [2, 1] , [2, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [2, 1] [1, 0] [0, 1] [1, 2] [2, 2] [2, 1] , [2, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [2, 1] [1, 0] [0, 2] [2, 0] [0, 2] [2, 1] , [2, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [2, 1] [1, 0] [0, 2] [2, 1] [1, 2] [2, 1] , [2, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [2, 1] [1, 0] [0, 2] [2, 2] [2, 0] [0, 1] , [2, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [2, 1] [1, 1] [1, 0] [0, 2] [2, 2] [2, 1] , [2, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [2, 1] [1, 2] [2, 1] [1, 0] [0, 2] [2, 1] , [2, 1] [1, 2] [2, 2] [2, 0] [0, 2] [2, 1] -> [2, 1] [1, 0] [0, 2] [2, 2] [2, 2] [2, 1] , [2, 2] [2, 1] [1, 1] [1, 0] [0, 2] [2, 1] -> [2, 2] [2, 0] [0, 1] [1, 0] [0, 2] [2, 1] , [2, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [2, 2] [2, 0] [0, 1] [1, 2] [2, 2] [2, 1] , [2, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [2, 2] [2, 1] [1, 0] [0, 2] [2, 2] [2, 1] , [2, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [2, 2] [2, 2] [2, 1] [1, 0] [0, 2] [2, 1] , [2, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [2, 2] [2, 2] [2, 2] [2, 1] [1, 0] [0, 1] , [2, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [2, 0] [0, 1] [1, 0] [0, 2] [2, 2] [2, 2] , [2, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [2, 0] [0, 1] [1, 1] [1, 2] [2, 2] [2, 2] , [2, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [2, 0] [0, 2] [2, 1] [1, 0] [0, 2] [2, 2] , [2, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [2, 0] [0, 2] [2, 2] [2, 1] [1, 0] [0, 2] , [2, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [2, 1] [1, 0] [0, 0] [0, 2] [2, 2] [2, 2] , [2, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [2, 1] [1, 0] [0, 1] [1, 2] [2, 2] [2, 2] , [2, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [2, 1] [1, 0] [0, 2] [2, 0] [0, 2] [2, 2] , [2, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [2, 1] [1, 0] [0, 2] [2, 1] [1, 2] [2, 2] , [2, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [2, 1] [1, 0] [0, 2] [2, 2] [2, 0] [0, 2] , [2, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [2, 1] [1, 1] [1, 0] [0, 2] [2, 2] [2, 2] , [2, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [2, 1] [1, 2] [2, 1] [1, 0] [0, 2] [2, 2] , [2, 1] [1, 2] [2, 2] [2, 0] [0, 2] [2, 2] -> [2, 1] [1, 0] [0, 2] [2, 2] [2, 2] [2, 2] , [2, 2] [2, 1] [1, 1] [1, 0] [0, 2] [2, 2] -> [2, 2] [2, 0] [0, 1] [1, 0] [0, 2] [2, 2] , [2, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [2, 2] [2, 0] [0, 1] [1, 2] [2, 2] [2, 2] , [2, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [2, 2] [2, 1] [1, 0] [0, 2] [2, 2] [2, 2] , [2, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [2, 2] [2, 2] [2, 1] [1, 0] [0, 2] [2, 2] , [2, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [2, 2] [2, 2] [2, 2] [2, 1] [1, 0] [0, 2] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [0, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 1] is interpreted by / \ | 1 0 | | 0 1 | \ / [1, 2] is interpreted by / \ | 1 1 | | 0 1 | \ / [2, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 2] is interpreted by / \ | 1 0 | | 0 1 | \ / [1, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [2, 2] is interpreted by / \ | 1 0 | | 0 1 | \ / [1, 1] is interpreted by / \ | 1 0 | | 0 1 | \ / [2, 1] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 54-rule system { [0, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [0, 0] [0, 1] [1, 1] [1, 2] [2, 2] [2, 0] , [0, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [0, 1] [1, 0] [0, 1] [1, 2] [2, 2] [2, 0] , [0, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [0, 1] [1, 0] [0, 2] [2, 1] [1, 2] [2, 0] , [0, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [0, 1] [1, 2] [2, 1] [1, 0] [0, 2] [2, 0] , [0, 2] [2, 1] [1, 1] [1, 0] [0, 2] [2, 0] -> [0, 2] [2, 0] [0, 1] [1, 0] [0, 2] [2, 0] , [0, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [0, 2] [2, 0] [0, 1] [1, 2] [2, 2] [2, 0] , [0, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [0, 0] [0, 1] [1, 1] [1, 2] [2, 2] [2, 1] , [0, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [0, 1] [1, 0] [0, 1] [1, 2] [2, 2] [2, 1] , [0, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [0, 1] [1, 0] [0, 2] [2, 1] [1, 2] [2, 1] , [0, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [0, 1] [1, 2] [2, 1] [1, 0] [0, 2] [2, 1] , [0, 2] [2, 1] [1, 1] [1, 0] [0, 2] [2, 1] -> [0, 2] [2, 0] [0, 1] [1, 0] [0, 2] [2, 1] , [0, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [0, 2] [2, 0] [0, 1] [1, 2] [2, 2] [2, 1] , [0, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [0, 0] [0, 1] [1, 1] [1, 2] [2, 2] [2, 2] , [0, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [0, 1] [1, 0] [0, 1] [1, 2] [2, 2] [2, 2] , [0, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [0, 1] [1, 0] [0, 2] [2, 1] [1, 2] [2, 2] , [0, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [0, 1] [1, 2] [2, 1] [1, 0] [0, 2] [2, 2] , [0, 2] [2, 1] [1, 1] [1, 0] [0, 2] [2, 2] -> [0, 2] [2, 0] [0, 1] [1, 0] [0, 2] [2, 2] , [0, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [0, 2] [2, 0] [0, 1] [1, 2] [2, 2] [2, 2] , [1, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [1, 0] [0, 1] [1, 1] [1, 2] [2, 2] [2, 0] , [1, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [1, 1] [1, 0] [0, 1] [1, 2] [2, 2] [2, 0] , [1, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [1, 1] [1, 0] [0, 2] [2, 1] [1, 2] [2, 0] , [1, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [1, 1] [1, 2] [2, 1] [1, 0] [0, 2] [2, 0] , [1, 2] [2, 1] [1, 1] [1, 0] [0, 2] [2, 0] -> [1, 2] [2, 0] [0, 1] [1, 0] [0, 2] [2, 0] , [1, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [1, 2] [2, 0] [0, 1] [1, 2] [2, 2] [2, 0] , [1, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [1, 0] [0, 1] [1, 1] [1, 2] [2, 2] [2, 1] , [1, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [1, 1] [1, 0] [0, 1] [1, 2] [2, 2] [2, 1] , [1, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [1, 1] [1, 0] [0, 2] [2, 1] [1, 2] [2, 1] , [1, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [1, 1] [1, 2] [2, 1] [1, 0] [0, 2] [2, 1] , [1, 2] [2, 1] [1, 1] [1, 0] [0, 2] [2, 1] -> [1, 2] [2, 0] [0, 1] [1, 0] [0, 2] [2, 1] , [1, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [1, 2] [2, 0] [0, 1] [1, 2] [2, 2] [2, 1] , [1, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [1, 0] [0, 1] [1, 1] [1, 2] [2, 2] [2, 2] , [1, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [1, 1] [1, 0] [0, 1] [1, 2] [2, 2] [2, 2] , [1, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [1, 1] [1, 0] [0, 2] [2, 1] [1, 2] [2, 2] , [1, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [1, 1] [1, 2] [2, 1] [1, 0] [0, 2] [2, 2] , [1, 2] [2, 1] [1, 1] [1, 0] [0, 2] [2, 2] -> [1, 2] [2, 0] [0, 1] [1, 0] [0, 2] [2, 2] , [1, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [1, 2] [2, 0] [0, 1] [1, 2] [2, 2] [2, 2] , [2, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [2, 0] [0, 1] [1, 1] [1, 2] [2, 2] [2, 0] , [2, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [2, 1] [1, 0] [0, 1] [1, 2] [2, 2] [2, 0] , [2, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [2, 1] [1, 0] [0, 2] [2, 1] [1, 2] [2, 0] , [2, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [2, 1] [1, 2] [2, 1] [1, 0] [0, 2] [2, 0] , [2, 2] [2, 1] [1, 1] [1, 0] [0, 2] [2, 0] -> [2, 2] [2, 0] [0, 1] [1, 0] [0, 2] [2, 0] , [2, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [2, 2] [2, 0] [0, 1] [1, 2] [2, 2] [2, 0] , [2, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [2, 0] [0, 1] [1, 1] [1, 2] [2, 2] [2, 1] , [2, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [2, 1] [1, 0] [0, 1] [1, 2] [2, 2] [2, 1] , [2, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [2, 1] [1, 0] [0, 2] [2, 1] [1, 2] [2, 1] , [2, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [2, 1] [1, 2] [2, 1] [1, 0] [0, 2] [2, 1] , [2, 2] [2, 1] [1, 1] [1, 0] [0, 2] [2, 1] -> [2, 2] [2, 0] [0, 1] [1, 0] [0, 2] [2, 1] , [2, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [2, 2] [2, 0] [0, 1] [1, 2] [2, 2] [2, 1] , [2, 0] [0, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [2, 0] [0, 1] [1, 1] [1, 2] [2, 2] [2, 2] , [2, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [2, 1] [1, 0] [0, 1] [1, 2] [2, 2] [2, 2] , [2, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [2, 1] [1, 0] [0, 2] [2, 1] [1, 2] [2, 2] , [2, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [2, 1] [1, 2] [2, 1] [1, 0] [0, 2] [2, 2] , [2, 2] [2, 1] [1, 1] [1, 0] [0, 2] [2, 2] -> [2, 2] [2, 0] [0, 1] [1, 0] [0, 2] [2, 2] , [2, 2] [2, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [2, 2] [2, 0] [0, 1] [1, 2] [2, 2] [2, 2] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [0, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 1] is interpreted by / \ | 1 0 | | 0 1 | \ / [1, 2] is interpreted by / \ | 1 0 | | 0 1 | \ / [2, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 2] is interpreted by / \ | 1 1 | | 0 1 | \ / [1, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [2, 2] is interpreted by / \ | 1 0 | | 0 1 | \ / [1, 1] is interpreted by / \ | 1 0 | | 0 1 | \ / [2, 1] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 27-rule system { [0, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [0, 1] [1, 0] [0, 2] [2, 1] [1, 2] [2, 0] , [0, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [0, 1] [1, 2] [2, 1] [1, 0] [0, 2] [2, 0] , [0, 2] [2, 1] [1, 1] [1, 0] [0, 2] [2, 0] -> [0, 2] [2, 0] [0, 1] [1, 0] [0, 2] [2, 0] , [0, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [0, 1] [1, 0] [0, 2] [2, 1] [1, 2] [2, 1] , [0, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [0, 1] [1, 2] [2, 1] [1, 0] [0, 2] [2, 1] , [0, 2] [2, 1] [1, 1] [1, 0] [0, 2] [2, 1] -> [0, 2] [2, 0] [0, 1] [1, 0] [0, 2] [2, 1] , [0, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [0, 1] [1, 0] [0, 2] [2, 1] [1, 2] [2, 2] , [0, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [0, 1] [1, 2] [2, 1] [1, 0] [0, 2] [2, 2] , [0, 2] [2, 1] [1, 1] [1, 0] [0, 2] [2, 2] -> [0, 2] [2, 0] [0, 1] [1, 0] [0, 2] [2, 2] , [1, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [1, 1] [1, 0] [0, 2] [2, 1] [1, 2] [2, 0] , [1, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [1, 1] [1, 2] [2, 1] [1, 0] [0, 2] [2, 0] , [1, 2] [2, 1] [1, 1] [1, 0] [0, 2] [2, 0] -> [1, 2] [2, 0] [0, 1] [1, 0] [0, 2] [2, 0] , [1, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [1, 1] [1, 0] [0, 2] [2, 1] [1, 2] [2, 1] , [1, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [1, 1] [1, 2] [2, 1] [1, 0] [0, 2] [2, 1] , [1, 2] [2, 1] [1, 1] [1, 0] [0, 2] [2, 1] -> [1, 2] [2, 0] [0, 1] [1, 0] [0, 2] [2, 1] , [1, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [1, 1] [1, 0] [0, 2] [2, 1] [1, 2] [2, 2] , [1, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [1, 1] [1, 2] [2, 1] [1, 0] [0, 2] [2, 2] , [1, 2] [2, 1] [1, 1] [1, 0] [0, 2] [2, 2] -> [1, 2] [2, 0] [0, 1] [1, 0] [0, 2] [2, 2] , [2, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [2, 1] [1, 0] [0, 2] [2, 1] [1, 2] [2, 0] , [2, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 0] -> [2, 1] [1, 2] [2, 1] [1, 0] [0, 2] [2, 0] , [2, 2] [2, 1] [1, 1] [1, 0] [0, 2] [2, 0] -> [2, 2] [2, 0] [0, 1] [1, 0] [0, 2] [2, 0] , [2, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [2, 1] [1, 0] [0, 2] [2, 1] [1, 2] [2, 1] , [2, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 1] -> [2, 1] [1, 2] [2, 1] [1, 0] [0, 2] [2, 1] , [2, 2] [2, 1] [1, 1] [1, 0] [0, 2] [2, 1] -> [2, 2] [2, 0] [0, 1] [1, 0] [0, 2] [2, 1] , [2, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [2, 1] [1, 0] [0, 2] [2, 1] [1, 2] [2, 2] , [2, 1] [1, 1] [1, 2] [2, 0] [0, 2] [2, 2] -> [2, 1] [1, 2] [2, 1] [1, 0] [0, 2] [2, 2] , [2, 2] [2, 1] [1, 1] [1, 0] [0, 2] [2, 2] -> [2, 2] [2, 0] [0, 1] [1, 0] [0, 2] [2, 2] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [0, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 1] is interpreted by / \ | 1 0 | | 0 1 | \ / [1, 2] is interpreted by / \ | 1 0 | | 0 1 | \ / [2, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 2] is interpreted by / \ | 1 0 | | 0 1 | \ / [1, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [2, 2] is interpreted by / \ | 1 0 | | 0 1 | \ / [1, 1] is interpreted by / \ | 1 1 | | 0 1 | \ / [2, 1] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 0-rule system { } The system is trivially terminating.