/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/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 288-rule system { [b, b] [b, b] [b, b] -> [b, c] [c, d] [d, b] , [b, c] [c, c] [c, b] -> [b, d] [d, d] [d, d] [d, b] , [b, c] [c, b] -> [b, g] [g, b] , [b, d] [d, d] [d, b] -> [b, c] [c, f] [f, b] , [b, d] [d, d] [d, d] [d, b] -> [b, g] [g, c] [c, b] , [b, f] [f, b] -> [b, a] [a, g] [g, b] , [b, g] [g, b] -> [b, d] [d, a] [a, b] [b, b] , [b, g] [g, g] [g, b] -> [b, b] [b, c] [c, b] , [b, b] [b, b] [b, c] -> [b, c] [c, d] [d, c] , [b, c] [c, c] [c, c] -> [b, d] [d, d] [d, d] [d, c] , [b, c] [c, c] -> [b, g] [g, c] , [b, d] [d, d] [d, c] -> [b, c] [c, f] [f, c] , [b, d] [d, d] [d, d] [d, c] -> [b, g] [g, c] [c, c] , [b, f] [f, c] -> [b, a] [a, g] [g, c] , [b, g] [g, c] -> [b, d] [d, a] [a, b] [b, c] , [b, g] [g, g] [g, c] -> [b, b] [b, c] [c, c] , [b, b] [b, b] [b, d] -> [b, c] [c, d] [d, d] , [b, c] [c, c] [c, d] -> [b, d] [d, d] [d, d] [d, d] , [b, c] [c, d] -> [b, g] [g, d] , [b, d] [d, d] [d, d] -> [b, c] [c, f] [f, d] , [b, d] [d, d] [d, d] [d, d] -> [b, g] [g, c] [c, d] , [b, f] [f, d] -> [b, a] [a, g] [g, d] , [b, g] [g, d] -> [b, d] [d, a] [a, b] [b, d] , [b, g] [g, g] [g, d] -> [b, b] [b, c] [c, d] , [b, b] [b, b] [b, g] -> [b, c] [c, d] [d, g] , [b, c] [c, c] [c, g] -> [b, d] [d, d] [d, d] [d, g] , [b, c] [c, g] -> [b, g] [g, g] , [b, d] [d, d] [d, g] -> [b, c] [c, f] [f, g] , [b, d] [d, d] [d, d] [d, g] -> [b, g] [g, c] [c, g] , [b, f] [f, g] -> [b, a] [a, g] [g, g] , [b, g] [g, g] -> [b, d] [d, a] [a, b] [b, g] , [b, g] [g, g] [g, g] -> [b, b] [b, c] [c, g] , [b, b] [b, b] [b, f] -> [b, c] [c, d] [d, f] , [b, c] [c, c] [c, f] -> [b, d] [d, d] [d, d] [d, f] , [b, c] [c, f] -> [b, g] [g, f] , [b, d] [d, d] [d, f] -> [b, c] [c, f] [f, f] , [b, d] [d, d] [d, d] [d, f] -> [b, g] [g, c] [c, f] , [b, f] [f, f] -> [b, a] [a, g] [g, f] , [b, g] [g, f] -> [b, d] [d, a] [a, b] [b, f] , [b, g] [g, g] [g, f] -> [b, b] [b, c] [c, f] , [b, b] [b, b] [b, a] -> [b, c] [c, d] [d, a] , [b, c] [c, c] [c, a] -> [b, d] [d, d] [d, d] [d, a] , [b, c] [c, a] -> [b, g] [g, a] , [b, d] [d, d] [d, a] -> [b, c] [c, f] [f, a] , [b, d] [d, d] [d, d] [d, a] -> [b, g] [g, c] [c, a] , [b, f] [f, a] -> [b, a] [a, g] [g, a] , [b, g] [g, a] -> [b, d] [d, a] [a, b] [b, a] , [b, g] [g, g] [g, a] -> [b, b] [b, c] [c, a] , [c, b] [b, b] [b, b] -> [c, c] [c, d] [d, b] , [c, c] [c, c] [c, b] -> [c, d] [d, d] [d, d] [d, b] , [c, c] [c, b] -> [c, g] [g, b] , [c, d] [d, d] [d, b] -> [c, c] [c, f] [f, b] , [c, d] [d, d] [d, d] [d, b] -> [c, g] [g, c] [c, b] , [c, f] [f, b] -> [c, a] [a, g] [g, b] , [c, g] [g, b] -> [c, d] [d, a] [a, b] [b, b] , [c, g] [g, g] [g, b] -> [c, b] [b, c] [c, b] , [c, b] [b, b] [b, c] -> [c, c] [c, d] [d, c] , [c, c] [c, c] [c, c] -> [c, d] [d, d] [d, d] [d, c] , [c, c] [c, c] -> [c, g] [g, c] , [c, d] [d, d] [d, c] -> [c, c] [c, f] [f, c] , [c, d] [d, d] [d, d] [d, c] -> [c, g] [g, c] [c, c] , [c, f] [f, c] -> [c, a] [a, g] [g, c] , [c, g] [g, c] -> [c, d] [d, a] [a, b] [b, c] , [c, g] [g, g] [g, c] -> [c, b] [b, c] [c, c] , [c, b] [b, b] [b, d] -> [c, c] [c, d] [d, d] , [c, c] [c, c] [c, d] -> [c, d] [d, d] [d, d] [d, d] , [c, c] [c, d] -> [c, g] [g, d] , [c, d] [d, d] [d, d] -> [c, c] [c, f] [f, d] , [c, d] [d, d] [d, d] [d, d] -> [c, g] [g, c] [c, d] , [c, f] [f, d] -> [c, a] [a, g] [g, d] , [c, g] [g, d] -> [c, d] [d, a] [a, b] [b, d] , [c, g] [g, g] [g, d] -> [c, b] [b, c] [c, d] , [c, b] [b, b] [b, g] -> [c, c] [c, d] [d, g] , [c, c] [c, c] [c, g] -> [c, d] [d, d] [d, d] [d, g] , [c, c] [c, g] -> [c, g] [g, g] , [c, d] [d, d] [d, g] -> [c, c] [c, f] [f, g] , [c, d] [d, d] [d, d] [d, g] -> [c, g] [g, c] [c, g] , [c, f] [f, g] -> [c, a] [a, g] [g, g] , [c, g] [g, g] -> [c, d] [d, a] [a, b] [b, g] , [c, g] [g, g] [g, g] -> [c, b] [b, c] [c, g] , [c, b] [b, b] [b, f] -> [c, c] [c, d] [d, f] , [c, c] [c, c] [c, f] -> [c, d] [d, d] [d, d] [d, f] , [c, c] [c, f] -> [c, g] [g, f] , [c, d] [d, d] [d, f] -> [c, c] [c, f] [f, f] , [c, d] [d, d] [d, d] [d, f] -> [c, g] [g, c] [c, f] , [c, f] [f, f] -> [c, a] [a, g] [g, f] , [c, g] [g, f] -> [c, d] [d, a] [a, b] [b, f] , [c, g] [g, g] [g, f] -> [c, b] [b, c] [c, f] , [c, b] [b, b] [b, a] -> [c, c] [c, d] [d, a] , [c, c] [c, c] [c, a] -> [c, d] [d, d] [d, d] [d, a] , [c, c] [c, a] -> [c, g] [g, a] , [c, d] [d, d] [d, a] -> [c, c] [c, f] [f, a] , [c, d] [d, d] [d, d] [d, a] -> [c, g] [g, c] [c, a] , [c, f] [f, a] -> [c, a] [a, g] [g, a] , [c, g] [g, a] -> [c, d] [d, a] [a, b] [b, a] , [c, g] [g, g] [g, a] -> [c, b] [b, c] [c, a] , [d, b] [b, b] [b, b] -> [d, c] [c, d] [d, b] , [d, c] [c, c] [c, b] -> [d, d] [d, d] [d, d] [d, b] , [d, c] [c, b] -> [d, g] [g, b] , [d, d] [d, d] [d, b] -> [d, c] [c, f] [f, b] , [d, d] [d, d] [d, d] [d, b] -> [d, g] [g, c] [c, b] , [d, f] [f, b] -> [d, a] [a, g] [g, b] , [d, g] [g, b] -> [d, d] [d, a] [a, b] [b, b] , [d, g] [g, g] [g, b] -> [d, b] [b, c] [c, b] , [d, b] [b, b] [b, c] -> [d, c] [c, d] [d, c] , [d, c] [c, c] [c, c] -> [d, d] [d, d] [d, d] [d, c] , [d, c] [c, c] -> [d, g] [g, c] , [d, d] [d, d] [d, c] -> [d, c] [c, f] [f, c] , [d, d] [d, d] [d, d] [d, c] -> [d, g] [g, c] [c, c] , [d, f] [f, c] -> [d, a] [a, g] [g, c] , [d, g] [g, c] -> [d, d] [d, a] [a, b] [b, c] , [d, g] [g, g] [g, c] -> [d, b] [b, c] [c, c] , [d, b] [b, b] [b, d] -> [d, c] [c, d] [d, d] , [d, c] [c, c] [c, d] -> [d, d] [d, d] [d, d] [d, d] , [d, c] [c, d] -> [d, g] [g, d] , [d, d] [d, d] [d, d] -> [d, c] [c, f] [f, d] , [d, d] [d, d] [d, d] [d, d] -> [d, g] [g, c] [c, d] , [d, f] [f, d] -> [d, a] [a, g] [g, d] , [d, g] [g, d] -> [d, d] [d, a] [a, b] [b, d] , [d, g] [g, g] [g, d] -> [d, b] [b, c] [c, d] , [d, b] [b, b] [b, g] -> [d, c] [c, d] [d, g] , [d, c] [c, c] [c, g] -> [d, d] [d, d] [d, d] [d, g] , [d, c] [c, g] -> [d, g] [g, g] , [d, d] [d, d] [d, g] -> [d, c] [c, f] [f, g] , [d, d] [d, d] [d, d] [d, g] -> [d, g] [g, c] [c, g] , [d, f] [f, g] -> [d, a] [a, g] [g, g] , [d, g] [g, g] -> [d, d] [d, a] [a, b] [b, g] , [d, g] [g, g] [g, g] -> [d, b] [b, c] [c, g] , [d, b] [b, b] [b, f] -> [d, c] [c, d] [d, f] , [d, c] [c, c] [c, f] -> [d, d] [d, d] [d, d] [d, f] , [d, c] [c, f] -> [d, g] [g, f] , [d, d] [d, d] [d, f] -> [d, c] [c, f] [f, f] , [d, d] [d, d] [d, d] [d, f] -> [d, g] [g, c] [c, f] , [d, f] [f, f] -> [d, a] [a, g] [g, f] , [d, g] [g, f] -> [d, d] [d, a] [a, b] [b, f] , [d, g] [g, g] [g, f] -> [d, b] [b, c] [c, f] , [d, b] [b, b] [b, a] -> [d, c] [c, d] [d, a] , [d, c] [c, c] [c, a] -> [d, d] [d, d] [d, d] [d, a] , [d, c] [c, a] -> [d, g] [g, a] , [d, d] [d, d] [d, a] -> [d, c] [c, f] [f, a] , [d, d] [d, d] [d, d] [d, a] -> [d, g] [g, c] [c, a] , [d, f] [f, a] -> [d, a] [a, g] [g, a] , [d, g] [g, a] -> [d, d] [d, a] [a, b] [b, a] , [d, g] [g, g] [g, a] -> [d, b] [b, c] [c, a] , [g, b] [b, b] [b, b] -> [g, c] [c, d] [d, b] , [g, c] [c, c] [c, b] -> [g, d] [d, d] [d, d] [d, b] , [g, c] [c, b] -> [g, g] [g, b] , [g, d] [d, d] [d, b] -> [g, c] [c, f] [f, b] , [g, d] [d, d] [d, d] [d, b] -> [g, g] [g, c] [c, b] , [g, f] [f, b] -> [g, a] [a, g] [g, b] , [g, g] [g, b] -> [g, d] [d, a] [a, b] [b, b] , [g, g] [g, g] [g, b] -> [g, b] [b, c] [c, b] , [g, b] [b, b] [b, c] -> [g, c] [c, d] [d, c] , [g, c] [c, c] [c, c] -> [g, d] [d, d] [d, d] [d, c] , [g, c] [c, c] -> [g, g] [g, c] , [g, d] [d, d] [d, c] -> [g, c] [c, f] [f, c] , [g, d] [d, d] [d, d] [d, c] -> [g, g] [g, c] [c, c] , [g, f] [f, c] -> [g, a] [a, g] [g, c] , [g, g] [g, c] -> [g, d] [d, a] [a, b] [b, c] , [g, g] [g, g] [g, c] -> [g, b] [b, c] [c, c] , [g, b] [b, b] [b, d] -> [g, c] [c, d] [d, d] , [g, c] [c, c] [c, d] -> [g, d] [d, d] [d, d] [d, d] , [g, c] [c, d] -> [g, g] [g, d] , [g, d] [d, d] [d, d] -> [g, c] [c, f] [f, d] , [g, d] [d, d] [d, d] [d, d] -> [g, g] [g, c] [c, d] , [g, f] [f, d] -> [g, a] [a, g] [g, d] , [g, g] [g, d] -> [g, d] [d, a] [a, b] [b, d] , [g, g] [g, g] [g, d] -> [g, b] [b, c] [c, d] , [g, b] [b, b] [b, g] -> [g, c] [c, d] [d, g] , [g, c] [c, c] [c, g] -> [g, d] [d, d] [d, d] [d, g] , [g, c] [c, g] -> [g, g] [g, g] , [g, d] [d, d] [d, g] -> [g, c] [c, f] [f, g] , [g, d] [d, d] [d, d] [d, g] -> [g, g] [g, c] [c, g] , [g, f] [f, g] -> [g, a] [a, g] [g, g] , [g, g] [g, g] -> [g, d] [d, a] [a, b] [b, g] , [g, g] [g, g] [g, g] -> [g, b] [b, c] [c, g] , [g, b] [b, b] [b, f] -> [g, c] [c, d] [d, f] , [g, c] [c, c] [c, f] -> [g, d] [d, d] [d, d] [d, f] , [g, c] [c, f] -> [g, g] [g, f] , [g, d] [d, d] [d, f] -> [g, c] [c, f] [f, f] , [g, d] [d, d] [d, d] [d, f] -> [g, g] [g, c] [c, f] , [g, f] [f, f] -> [g, a] [a, g] [g, f] , [g, g] [g, f] -> [g, d] [d, a] [a, b] [b, f] , [g, g] [g, g] [g, f] -> [g, b] [b, c] [c, f] , [g, b] [b, b] [b, a] -> [g, c] [c, d] [d, a] , [g, c] [c, c] [c, a] -> [g, d] [d, d] [d, d] [d, a] , [g, c] [c, a] -> [g, g] [g, a] , [g, d] [d, d] [d, a] -> [g, c] [c, f] [f, a] , [g, d] [d, d] [d, d] [d, a] -> [g, g] [g, c] [c, a] , [g, f] [f, a] -> [g, a] [a, g] [g, a] , [g, g] [g, a] -> [g, d] [d, a] [a, b] [b, a] , [g, g] [g, g] [g, a] -> [g, b] [b, c] [c, a] , [f, b] [b, b] [b, b] -> [f, c] [c, d] [d, b] , [f, c] [c, c] [c, b] -> [f, d] [d, d] [d, d] [d, b] , [f, c] [c, b] -> [f, g] [g, b] , [f, d] [d, d] [d, b] -> [f, c] [c, f] [f, b] , [f, d] [d, d] [d, d] [d, b] -> [f, g] [g, c] [c, b] , [f, f] [f, b] -> [f, a] [a, g] [g, b] , [f, g] [g, b] -> [f, d] [d, a] [a, b] [b, b] , [f, g] [g, g] [g, b] -> [f, b] [b, c] [c, b] , [f, b] [b, b] [b, c] -> [f, c] [c, d] [d, c] , [f, c] [c, c] [c, c] -> [f, d] [d, d] [d, d] [d, c] , [f, c] [c, c] -> [f, g] [g, c] , [f, d] [d, d] [d, c] -> [f, c] [c, f] [f, c] , [f, d] [d, d] [d, d] [d, c] -> [f, g] [g, c] [c, c] , [f, f] [f, c] -> [f, a] [a, g] [g, c] , [f, g] [g, c] -> [f, d] [d, a] [a, b] [b, c] , [f, g] [g, g] [g, c] -> [f, b] [b, c] [c, c] , [f, b] [b, b] [b, d] -> [f, c] [c, d] [d, d] , [f, c] [c, c] [c, d] -> [f, d] [d, d] [d, d] [d, d] , [f, c] [c, d] -> [f, g] [g, d] , [f, d] [d, d] [d, d] -> [f, c] [c, f] [f, d] , [f, d] [d, d] [d, d] [d, d] -> [f, g] [g, c] [c, d] , [f, f] [f, d] -> [f, a] [a, g] [g, d] , [f, g] [g, d] -> [f, d] [d, a] [a, b] [b, d] , [f, g] [g, g] [g, d] -> [f, b] [b, c] [c, d] , [f, b] [b, b] [b, g] -> [f, c] [c, d] [d, g] , [f, c] [c, c] [c, g] -> [f, d] [d, d] [d, d] [d, g] , [f, c] [c, g] -> [f, g] [g, g] , [f, d] [d, d] [d, g] -> [f, c] [c, f] [f, g] , [f, d] [d, d] [d, d] [d, g] -> [f, g] [g, c] [c, g] , [f, f] [f, g] -> [f, a] [a, g] [g, g] , [f, g] [g, g] -> [f, d] [d, a] [a, b] [b, g] , [f, g] [g, g] [g, g] -> [f, b] [b, c] [c, g] , [f, b] [b, b] [b, f] -> [f, c] [c, d] [d, f] , [f, c] [c, c] [c, f] -> [f, d] [d, d] [d, d] [d, f] , [f, c] [c, f] -> [f, g] [g, f] , [f, d] [d, d] [d, f] -> [f, c] [c, f] [f, f] , [f, d] [d, d] [d, d] [d, f] -> [f, g] [g, c] [c, f] , [f, f] [f, f] -> [f, a] [a, g] [g, f] , [f, g] [g, f] -> [f, d] [d, a] [a, b] [b, f] , [f, g] [g, g] [g, f] -> [f, b] [b, c] [c, f] , [f, b] [b, b] [b, a] -> [f, c] [c, d] [d, a] , [f, c] [c, c] [c, a] -> [f, d] [d, d] [d, d] [d, a] , [f, c] [c, a] -> [f, g] [g, a] , [f, d] [d, d] [d, a] -> [f, c] [c, f] [f, a] , [f, d] [d, d] [d, d] [d, a] -> [f, g] [g, c] [c, a] , [f, f] [f, a] -> [f, a] [a, g] [g, a] , [f, g] [g, a] -> [f, d] [d, a] [a, b] [b, a] , [f, g] [g, g] [g, a] -> [f, b] [b, c] [c, a] , [a, b] [b, b] [b, b] -> [a, c] [c, d] [d, b] , [a, c] [c, c] [c, b] -> [a, d] [d, d] [d, d] [d, b] , [a, c] [c, b] -> [a, g] [g, b] , [a, d] [d, d] [d, b] -> [a, c] [c, f] [f, b] , [a, d] [d, d] [d, d] [d, b] -> [a, g] [g, c] [c, b] , [a, f] [f, b] -> [a, a] [a, g] [g, b] , [a, g] [g, b] -> [a, d] [d, a] [a, b] [b, b] , [a, g] [g, g] [g, b] -> [a, b] [b, c] [c, b] , [a, b] [b, b] [b, c] -> [a, c] [c, d] [d, c] , [a, c] [c, c] [c, c] -> [a, d] [d, d] [d, d] [d, c] , [a, c] [c, c] -> [a, g] [g, c] , [a, d] [d, d] [d, c] -> [a, c] [c, f] [f, c] , [a, d] [d, d] [d, d] [d, c] -> [a, g] [g, c] [c, c] , [a, f] [f, c] -> [a, a] [a, g] [g, c] , [a, g] [g, c] -> [a, d] [d, a] [a, b] [b, c] , [a, g] [g, g] [g, c] -> [a, b] [b, c] [c, c] , [a, b] [b, b] [b, d] -> [a, c] [c, d] [d, d] , [a, c] [c, c] [c, d] -> [a, d] [d, d] [d, d] [d, d] , [a, c] [c, d] -> [a, g] [g, d] , [a, d] [d, d] [d, d] -> [a, c] [c, f] [f, d] , [a, d] [d, d] [d, d] [d, d] -> [a, g] [g, c] [c, d] , [a, f] [f, d] -> [a, a] [a, g] [g, d] , [a, g] [g, d] -> [a, d] [d, a] [a, b] [b, d] , [a, g] [g, g] [g, d] -> [a, b] [b, c] [c, d] , [a, b] [b, b] [b, g] -> [a, c] [c, d] [d, g] , [a, c] [c, c] [c, g] -> [a, d] [d, d] [d, d] [d, g] , [a, c] [c, g] -> [a, g] [g, g] , [a, d] [d, d] [d, g] -> [a, c] [c, f] [f, g] , [a, d] [d, d] [d, d] [d, g] -> [a, g] [g, c] [c, g] , [a, f] [f, g] -> [a, a] [a, g] [g, g] , [a, g] [g, g] -> [a, d] [d, a] [a, b] [b, g] , [a, g] [g, g] [g, g] -> [a, b] [b, c] [c, g] , [a, b] [b, b] [b, f] -> [a, c] [c, d] [d, f] , [a, c] [c, c] [c, f] -> [a, d] [d, d] [d, d] [d, f] , [a, c] [c, f] -> [a, g] [g, f] , [a, d] [d, d] [d, f] -> [a, c] [c, f] [f, f] , [a, d] [d, d] [d, d] [d, f] -> [a, g] [g, c] [c, f] , [a, f] [f, f] -> [a, a] [a, g] [g, f] , [a, g] [g, f] -> [a, d] [d, a] [a, b] [b, f] , [a, g] [g, g] [g, f] -> [a, b] [b, c] [c, f] , [a, b] [b, b] [b, a] -> [a, c] [c, d] [d, a] , [a, c] [c, c] [c, a] -> [a, d] [d, d] [d, d] [d, a] , [a, c] [c, a] -> [a, g] [g, a] , [a, d] [d, d] [d, a] -> [a, c] [c, f] [f, a] , [a, d] [d, d] [d, d] [d, a] -> [a, g] [g, c] [c, a] , [a, f] [f, a] -> [a, a] [a, g] [g, a] , [a, g] [g, a] -> [a, d] [d, a] [a, b] [b, a] , [a, g] [g, g] [g, a] -> [a, b] [b, c] [c, a] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [f, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, f] is interpreted by / \ | 1 1 | | 0 1 | \ / [a, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, a] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 282-rule system { [b, b] [b, b] [b, b] -> [b, c] [c, d] [d, b] , [b, c] [c, c] [c, b] -> [b, d] [d, d] [d, d] [d, b] , [b, c] [c, b] -> [b, g] [g, b] , [b, d] [d, d] [d, b] -> [b, c] [c, f] [f, b] , [b, d] [d, d] [d, d] [d, b] -> [b, g] [g, c] [c, b] , [b, f] [f, b] -> [b, a] [a, g] [g, b] , [b, g] [g, b] -> [b, d] [d, a] [a, b] [b, b] , [b, g] [g, g] [g, b] -> [b, b] [b, c] [c, b] , [b, b] [b, b] [b, c] -> [b, c] [c, d] [d, c] , [b, c] [c, c] [c, c] -> [b, d] [d, d] [d, d] [d, c] , [b, c] [c, c] -> [b, g] [g, c] , [b, d] [d, d] [d, c] -> [b, c] [c, f] [f, c] , [b, d] [d, d] [d, d] [d, c] -> [b, g] [g, c] [c, c] , [b, f] [f, c] -> [b, a] [a, g] [g, c] , [b, g] [g, c] -> [b, d] [d, a] [a, b] [b, c] , [b, g] [g, g] [g, c] -> [b, b] [b, c] [c, c] , [b, b] [b, b] [b, d] -> [b, c] [c, d] [d, d] , [b, c] [c, c] [c, d] -> [b, d] [d, d] [d, d] [d, d] , [b, c] [c, d] -> [b, g] [g, d] , [b, d] [d, d] [d, d] -> [b, c] [c, f] [f, d] , [b, d] [d, d] [d, d] [d, d] -> [b, g] [g, c] [c, d] , [b, f] [f, d] -> [b, a] [a, g] [g, d] , [b, g] [g, d] -> [b, d] [d, a] [a, b] [b, d] , [b, g] [g, g] [g, d] -> [b, b] [b, c] [c, d] , [b, b] [b, b] [b, g] -> [b, c] [c, d] [d, g] , [b, c] [c, c] [c, g] -> [b, d] [d, d] [d, d] [d, g] , [b, c] [c, g] -> [b, g] [g, g] , [b, d] [d, d] [d, g] -> [b, c] [c, f] [f, g] , [b, d] [d, d] [d, d] [d, g] -> [b, g] [g, c] [c, g] , [b, f] [f, g] -> [b, a] [a, g] [g, g] , [b, g] [g, g] -> [b, d] [d, a] [a, b] [b, g] , [b, g] [g, g] [g, g] -> [b, b] [b, c] [c, g] , [b, b] [b, b] [b, f] -> [b, c] [c, d] [d, f] , [b, c] [c, c] [c, f] -> [b, d] [d, d] [d, d] [d, f] , [b, c] [c, f] -> [b, g] [g, f] , [b, d] [d, d] [d, f] -> [b, c] [c, f] [f, f] , [b, d] [d, d] [d, d] [d, f] -> [b, g] [g, c] [c, f] , [b, f] [f, f] -> [b, a] [a, g] [g, f] , [b, g] [g, f] -> [b, d] [d, a] [a, b] [b, f] , [b, g] [g, g] [g, f] -> [b, b] [b, c] [c, f] , [b, b] [b, b] [b, a] -> [b, c] [c, d] [d, a] , [b, c] [c, c] [c, a] -> [b, d] [d, d] [d, d] [d, a] , [b, c] [c, a] -> [b, g] [g, a] , [b, d] [d, d] [d, a] -> [b, c] [c, f] [f, a] , [b, d] [d, d] [d, d] [d, a] -> [b, g] [g, c] [c, a] , [b, f] [f, a] -> [b, a] [a, g] [g, a] , [b, g] [g, a] -> [b, d] [d, a] [a, b] [b, a] , [b, g] [g, g] [g, a] -> [b, b] [b, c] [c, a] , [c, b] [b, b] [b, b] -> [c, c] [c, d] [d, b] , [c, c] [c, c] [c, b] -> [c, d] [d, d] [d, d] [d, b] , [c, c] [c, b] -> [c, g] [g, b] , [c, d] [d, d] [d, b] -> [c, c] [c, f] [f, b] , [c, d] [d, d] [d, d] [d, b] -> [c, g] [g, c] [c, b] , [c, f] [f, b] -> [c, a] [a, g] [g, b] , [c, g] [g, b] -> [c, d] [d, a] [a, b] [b, b] , [c, g] [g, g] [g, b] -> [c, b] [b, c] [c, b] , [c, b] [b, b] [b, c] -> [c, c] [c, d] [d, c] , [c, c] [c, c] [c, c] -> [c, d] [d, d] [d, d] [d, c] , [c, c] [c, c] -> [c, g] [g, c] , [c, d] [d, d] [d, c] -> [c, c] [c, f] [f, c] , [c, d] [d, d] [d, d] [d, c] -> [c, g] [g, c] [c, c] , [c, f] [f, c] -> [c, a] [a, g] [g, c] , [c, g] [g, c] -> [c, d] [d, a] [a, b] [b, c] , [c, g] [g, g] [g, c] -> [c, b] [b, c] [c, c] , [c, b] [b, b] [b, d] -> [c, c] [c, d] [d, d] , [c, c] [c, c] [c, d] -> [c, d] [d, d] [d, d] [d, d] , [c, c] [c, d] -> [c, g] [g, d] , [c, d] [d, d] [d, d] -> [c, c] [c, f] [f, d] , [c, d] [d, d] [d, d] [d, d] -> [c, g] [g, c] [c, d] , [c, f] [f, d] -> [c, a] [a, g] [g, d] , [c, g] [g, d] -> [c, d] [d, a] [a, b] [b, d] , [c, g] [g, g] [g, d] -> [c, b] [b, c] [c, d] , [c, b] [b, b] [b, g] -> [c, c] [c, d] [d, g] , [c, c] [c, c] [c, g] -> [c, d] [d, d] [d, d] [d, g] , [c, c] [c, g] -> [c, g] [g, g] , [c, d] [d, d] [d, g] -> [c, c] [c, f] [f, g] , [c, d] [d, d] [d, d] [d, g] -> [c, g] [g, c] [c, g] , [c, f] [f, g] -> [c, a] [a, g] [g, g] , [c, g] [g, g] -> [c, d] [d, a] [a, b] [b, g] , [c, g] [g, g] [g, g] -> [c, b] [b, c] [c, g] , [c, b] [b, b] [b, f] -> [c, c] [c, d] [d, f] , [c, c] [c, c] [c, f] -> [c, d] [d, d] [d, d] [d, f] , [c, c] [c, f] -> [c, g] [g, f] , [c, d] [d, d] [d, f] -> [c, c] [c, f] [f, f] , [c, d] [d, d] [d, d] [d, f] -> [c, g] [g, c] [c, f] , [c, f] [f, f] -> [c, a] [a, g] [g, f] , [c, g] [g, f] -> [c, d] [d, a] [a, b] [b, f] , [c, g] [g, g] [g, f] -> [c, b] [b, c] [c, f] , [c, b] [b, b] [b, a] -> [c, c] [c, d] [d, a] , [c, c] [c, c] [c, a] -> [c, d] [d, d] [d, d] [d, a] , [c, c] [c, a] -> [c, g] [g, a] , [c, d] [d, d] [d, a] -> [c, c] [c, f] [f, a] , [c, d] [d, d] [d, d] [d, a] -> [c, g] [g, c] [c, a] , [c, f] [f, a] -> [c, a] [a, g] [g, a] , [c, g] [g, a] -> [c, d] [d, a] [a, b] [b, a] , [c, g] [g, g] [g, a] -> [c, b] [b, c] [c, a] , [d, b] [b, b] [b, b] -> [d, c] [c, d] [d, b] , [d, c] [c, c] [c, b] -> [d, d] [d, d] [d, d] [d, b] , [d, c] [c, b] -> [d, g] [g, b] , [d, d] [d, d] [d, b] -> [d, c] [c, f] [f, b] , [d, d] [d, d] [d, d] [d, b] -> [d, g] [g, c] [c, b] , [d, f] [f, b] -> [d, a] [a, g] [g, b] , [d, g] [g, b] -> [d, d] [d, a] [a, b] [b, b] , [d, g] [g, g] [g, b] -> [d, b] [b, c] [c, b] , [d, b] [b, b] [b, c] -> [d, c] [c, d] [d, c] , [d, c] [c, c] [c, c] -> [d, d] [d, d] [d, d] [d, c] , [d, c] [c, c] -> [d, g] [g, c] , [d, d] [d, d] [d, c] -> [d, c] [c, f] [f, c] , [d, d] [d, d] [d, d] [d, c] -> [d, g] [g, c] [c, c] , [d, f] [f, c] -> [d, a] [a, g] [g, c] , [d, g] [g, c] -> [d, d] [d, a] [a, b] [b, c] , [d, g] [g, g] [g, c] -> [d, b] [b, c] [c, c] , [d, b] [b, b] [b, d] -> [d, c] [c, d] [d, d] , [d, c] [c, c] [c, d] -> [d, d] [d, d] [d, d] [d, d] , [d, c] [c, d] -> [d, g] [g, d] , [d, d] [d, d] [d, d] -> [d, c] [c, f] [f, d] , [d, d] [d, d] [d, d] [d, d] -> [d, g] [g, c] [c, d] , [d, f] [f, d] -> [d, a] [a, g] [g, d] , [d, g] [g, d] -> [d, d] [d, a] [a, b] [b, d] , [d, g] [g, g] [g, d] -> [d, b] [b, c] [c, d] , [d, b] [b, b] [b, g] -> [d, c] [c, d] [d, g] , [d, c] [c, c] [c, g] -> [d, d] [d, d] [d, d] [d, g] , [d, c] [c, g] -> [d, g] [g, g] , [d, d] [d, d] [d, g] -> [d, c] [c, f] [f, g] , [d, d] [d, d] [d, d] [d, g] -> [d, g] [g, c] [c, g] , [d, f] [f, g] -> [d, a] [a, g] [g, g] , [d, g] [g, g] -> [d, d] [d, a] [a, b] [b, g] , [d, g] [g, g] [g, g] -> [d, b] [b, c] [c, g] , [d, b] [b, b] [b, f] -> [d, c] [c, d] [d, f] , [d, c] [c, c] [c, f] -> [d, d] [d, d] [d, d] [d, f] , [d, c] [c, f] -> [d, g] [g, f] , [d, d] [d, d] [d, f] -> [d, c] [c, f] [f, f] , [d, d] [d, d] [d, d] [d, f] -> [d, g] [g, c] [c, f] , [d, f] [f, f] -> [d, a] [a, g] [g, f] , [d, g] [g, f] -> [d, d] [d, a] [a, b] [b, f] , [d, g] [g, g] [g, f] -> [d, b] [b, c] [c, f] , [d, b] [b, b] [b, a] -> [d, c] [c, d] [d, a] , [d, c] [c, c] [c, a] -> [d, d] [d, d] [d, d] [d, a] , [d, c] [c, a] -> [d, g] [g, a] , [d, d] [d, d] [d, a] -> [d, c] [c, f] [f, a] , [d, d] [d, d] [d, d] [d, a] -> [d, g] [g, c] [c, a] , [d, f] [f, a] -> [d, a] [a, g] [g, a] , [d, g] [g, a] -> [d, d] [d, a] [a, b] [b, a] , [d, g] [g, g] [g, a] -> [d, b] [b, c] [c, a] , [g, b] [b, b] [b, b] -> [g, c] [c, d] [d, b] , [g, c] [c, c] [c, b] -> [g, d] [d, d] [d, d] [d, b] , [g, c] [c, b] -> [g, g] [g, b] , [g, d] [d, d] [d, b] -> [g, c] [c, f] [f, b] , [g, d] [d, d] [d, d] [d, b] -> [g, g] [g, c] [c, b] , [g, f] [f, b] -> [g, a] [a, g] [g, b] , [g, g] [g, b] -> [g, d] [d, a] [a, b] [b, b] , [g, g] [g, g] [g, b] -> [g, b] [b, c] [c, b] , [g, b] [b, b] [b, c] -> [g, c] [c, d] [d, c] , [g, c] [c, c] [c, c] -> [g, d] [d, d] [d, d] [d, c] , [g, c] [c, c] -> [g, g] [g, c] , [g, d] [d, d] [d, c] -> [g, c] [c, f] [f, c] , [g, d] [d, d] [d, d] [d, c] -> [g, g] [g, c] [c, c] , [g, f] [f, c] -> [g, a] [a, g] [g, c] , [g, g] [g, c] -> [g, d] [d, a] [a, b] [b, c] , [g, g] [g, g] [g, c] -> [g, b] [b, c] [c, c] , [g, b] [b, b] [b, d] -> [g, c] [c, d] [d, d] , [g, c] [c, c] [c, d] -> [g, d] [d, d] [d, d] [d, d] , [g, c] [c, d] -> [g, g] [g, d] , [g, d] [d, d] [d, d] -> [g, c] [c, f] [f, d] , [g, d] [d, d] [d, d] [d, d] -> [g, g] [g, c] [c, d] , [g, f] [f, d] -> [g, a] [a, g] [g, d] , [g, g] [g, d] -> [g, d] [d, a] [a, b] [b, d] , [g, g] [g, g] [g, d] -> [g, b] [b, c] [c, d] , [g, b] [b, b] [b, g] -> [g, c] [c, d] [d, g] , [g, c] [c, c] [c, g] -> [g, d] [d, d] [d, d] [d, g] , [g, c] [c, g] -> [g, g] [g, g] , [g, d] [d, d] [d, g] -> [g, c] [c, f] [f, g] , [g, d] [d, d] [d, d] [d, g] -> [g, g] [g, c] [c, g] , [g, f] [f, g] -> [g, a] [a, g] [g, g] , [g, g] [g, g] -> [g, d] [d, a] [a, b] [b, g] , [g, g] [g, g] [g, g] -> [g, b] [b, c] [c, g] , [g, b] [b, b] [b, f] -> [g, c] [c, d] [d, f] , [g, c] [c, c] [c, f] -> [g, d] [d, d] [d, d] [d, f] , [g, c] [c, f] -> [g, g] [g, f] , [g, d] [d, d] [d, f] -> [g, c] [c, f] [f, f] , [g, d] [d, d] [d, d] [d, f] -> [g, g] [g, c] [c, f] , [g, f] [f, f] -> [g, a] [a, g] [g, f] , [g, g] [g, f] -> [g, d] [d, a] [a, b] [b, f] , [g, g] [g, g] [g, f] -> [g, b] [b, c] [c, f] , [g, b] [b, b] [b, a] -> [g, c] [c, d] [d, a] , [g, c] [c, c] [c, a] -> [g, d] [d, d] [d, d] [d, a] , [g, c] [c, a] -> [g, g] [g, a] , [g, d] [d, d] [d, a] -> [g, c] [c, f] [f, a] , [g, d] [d, d] [d, d] [d, a] -> [g, g] [g, c] [c, a] , [g, f] [f, a] -> [g, a] [a, g] [g, a] , [g, g] [g, a] -> [g, d] [d, a] [a, b] [b, a] , [g, g] [g, g] [g, a] -> [g, b] [b, c] [c, a] , [f, b] [b, b] [b, b] -> [f, c] [c, d] [d, b] , [f, c] [c, c] [c, b] -> [f, d] [d, d] [d, d] [d, b] , [f, c] [c, b] -> [f, g] [g, b] , [f, d] [d, d] [d, b] -> [f, c] [c, f] [f, b] , [f, d] [d, d] [d, d] [d, b] -> [f, g] [g, c] [c, b] , [f, f] [f, b] -> [f, a] [a, g] [g, b] , [f, g] [g, b] -> [f, d] [d, a] [a, b] [b, b] , [f, g] [g, g] [g, b] -> [f, b] [b, c] [c, b] , [f, b] [b, b] [b, c] -> [f, c] [c, d] [d, c] , [f, c] [c, c] [c, c] -> [f, d] [d, d] [d, d] [d, c] , [f, c] [c, c] -> [f, g] [g, c] , [f, d] [d, d] [d, c] -> [f, c] [c, f] [f, c] , [f, d] [d, d] [d, d] [d, c] -> [f, g] [g, c] [c, c] , [f, f] [f, c] -> [f, a] [a, g] [g, c] , [f, g] [g, c] -> [f, d] [d, a] [a, b] [b, c] , [f, g] [g, g] [g, c] -> [f, b] [b, c] [c, c] , [f, b] [b, b] [b, d] -> [f, c] [c, d] [d, d] , [f, c] [c, c] [c, d] -> [f, d] [d, d] [d, d] [d, d] , [f, c] [c, d] -> [f, g] [g, d] , [f, d] [d, d] [d, d] -> [f, c] [c, f] [f, d] , [f, d] [d, d] [d, d] [d, d] -> [f, g] [g, c] [c, d] , [f, f] [f, d] -> [f, a] [a, g] [g, d] , [f, g] [g, d] -> [f, d] [d, a] [a, b] [b, d] , [f, g] [g, g] [g, d] -> [f, b] [b, c] [c, d] , [f, b] [b, b] [b, g] -> [f, c] [c, d] [d, g] , [f, c] [c, c] [c, g] -> [f, d] [d, d] [d, d] [d, g] , [f, c] [c, g] -> [f, g] [g, g] , [f, d] [d, d] [d, g] -> [f, c] [c, f] [f, g] , [f, d] [d, d] [d, d] [d, g] -> [f, g] [g, c] [c, g] , [f, f] [f, g] -> [f, a] [a, g] [g, g] , [f, g] [g, g] -> [f, d] [d, a] [a, b] [b, g] , [f, g] [g, g] [g, g] -> [f, b] [b, c] [c, g] , [f, b] [b, b] [b, f] -> [f, c] [c, d] [d, f] , [f, c] [c, c] [c, f] -> [f, d] [d, d] [d, d] [d, f] , [f, c] [c, f] -> [f, g] [g, f] , [f, d] [d, d] [d, f] -> [f, c] [c, f] [f, f] , [f, d] [d, d] [d, d] [d, f] -> [f, g] [g, c] [c, f] , [f, f] [f, f] -> [f, a] [a, g] [g, f] , [f, g] [g, f] -> [f, d] [d, a] [a, b] [b, f] , [f, g] [g, g] [g, f] -> [f, b] [b, c] [c, f] , [f, b] [b, b] [b, a] -> [f, c] [c, d] [d, a] , [f, c] [c, c] [c, a] -> [f, d] [d, d] [d, d] [d, a] , [f, c] [c, a] -> [f, g] [g, a] , [f, d] [d, d] [d, a] -> [f, c] [c, f] [f, a] , [f, d] [d, d] [d, d] [d, a] -> [f, g] [g, c] [c, a] , [f, f] [f, a] -> [f, a] [a, g] [g, a] , [f, g] [g, a] -> [f, d] [d, a] [a, b] [b, a] , [f, g] [g, g] [g, a] -> [f, b] [b, c] [c, a] , [a, b] [b, b] [b, b] -> [a, c] [c, d] [d, b] , [a, c] [c, c] [c, b] -> [a, d] [d, d] [d, d] [d, b] , [a, c] [c, b] -> [a, g] [g, b] , [a, d] [d, d] [d, b] -> [a, c] [c, f] [f, b] , [a, d] [d, d] [d, d] [d, b] -> [a, g] [g, c] [c, b] , [a, g] [g, b] -> [a, d] [d, a] [a, b] [b, b] , [a, g] [g, g] [g, b] -> [a, b] [b, c] [c, b] , [a, b] [b, b] [b, c] -> [a, c] [c, d] [d, c] , [a, c] [c, c] [c, c] -> [a, d] [d, d] [d, d] [d, c] , [a, c] [c, c] -> [a, g] [g, c] , [a, d] [d, d] [d, c] -> [a, c] [c, f] [f, c] , [a, d] [d, d] [d, d] [d, c] -> [a, g] [g, c] [c, c] , [a, g] [g, c] -> [a, d] [d, a] [a, b] [b, c] , [a, g] [g, g] [g, c] -> [a, b] [b, c] [c, c] , [a, b] [b, b] [b, d] -> [a, c] [c, d] [d, d] , [a, c] [c, c] [c, d] -> [a, d] [d, d] [d, d] [d, d] , [a, c] [c, d] -> [a, g] [g, d] , [a, d] [d, d] [d, d] -> [a, c] [c, f] [f, d] , [a, d] [d, d] [d, d] [d, d] -> [a, g] [g, c] [c, d] , [a, g] [g, d] -> [a, d] [d, a] [a, b] [b, d] , [a, g] [g, g] [g, d] -> [a, b] [b, c] [c, d] , [a, b] [b, b] [b, g] -> [a, c] [c, d] [d, g] , [a, c] [c, c] [c, g] -> [a, d] [d, d] [d, d] [d, g] , [a, c] [c, g] -> [a, g] [g, g] , [a, d] [d, d] [d, g] -> [a, c] [c, f] [f, g] , [a, d] [d, d] [d, d] [d, g] -> [a, g] [g, c] [c, g] , [a, g] [g, g] -> [a, d] [d, a] [a, b] [b, g] , [a, g] [g, g] [g, g] -> [a, b] [b, c] [c, g] , [a, b] [b, b] [b, f] -> [a, c] [c, d] [d, f] , [a, c] [c, c] [c, f] -> [a, d] [d, d] [d, d] [d, f] , [a, c] [c, f] -> [a, g] [g, f] , [a, d] [d, d] [d, f] -> [a, c] [c, f] [f, f] , [a, d] [d, d] [d, d] [d, f] -> [a, g] [g, c] [c, f] , [a, g] [g, f] -> [a, d] [d, a] [a, b] [b, f] , [a, g] [g, g] [g, f] -> [a, b] [b, c] [c, f] , [a, b] [b, b] [b, a] -> [a, c] [c, d] [d, a] , [a, c] [c, c] [c, a] -> [a, d] [d, d] [d, d] [d, a] , [a, c] [c, a] -> [a, g] [g, a] , [a, d] [d, d] [d, a] -> [a, c] [c, f] [f, a] , [a, d] [d, d] [d, d] [d, a] -> [a, g] [g, c] [c, a] , [a, g] [g, a] -> [a, d] [d, a] [a, b] [b, a] , [a, g] [g, g] [g, a] -> [a, b] [b, c] [c, a] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [f, a] is interpreted by / \ | 1 2 | | 0 1 | \ / [a, c] is interpreted by / \ | 1 2 | | 0 1 | \ / [a, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, b] is interpreted by / \ | 1 5 | | 0 1 | \ / [b, c] is interpreted by / \ | 1 5 | | 0 1 | \ / [c, d] is interpreted by / \ | 1 4 | | 0 1 | \ / [d, b] is interpreted by / \ | 1 6 | | 0 1 | \ / [c, c] is interpreted by / \ | 1 6 | | 0 1 | \ / [c, b] is interpreted by / \ | 1 6 | | 0 1 | \ / [b, d] is interpreted by / \ | 1 3 | | 0 1 | \ / [d, d] is interpreted by / \ | 1 4 | | 0 1 | \ / [b, g] is interpreted by / \ | 1 5 | | 0 1 | \ / [g, b] is interpreted by / \ | 1 6 | | 0 1 | \ / [c, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, b] is interpreted by / \ | 1 8 | | 0 1 | \ / [g, c] is interpreted by / \ | 1 6 | | 0 1 | \ / [b, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, g] is interpreted by / \ | 1 2 | | 0 1 | \ / [d, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, b] is interpreted by / \ | 1 2 | | 0 1 | \ / [g, g] is interpreted by / \ | 1 6 | | 0 1 | \ / [d, c] is interpreted by / \ | 1 6 | | 0 1 | \ / [f, c] is interpreted by / \ | 1 8 | | 0 1 | \ / [g, d] is interpreted by / \ | 1 4 | | 0 1 | \ / [f, d] is interpreted by / \ | 1 6 | | 0 1 | \ / [d, g] is interpreted by / \ | 1 6 | | 0 1 | \ / [c, g] is interpreted by / \ | 1 6 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 8 | | 0 1 | \ / [d, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 2 | | 0 1 | \ / [c, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, a] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 210-rule system { [b, b] [b, b] [b, b] -> [b, c] [c, d] [d, b] , [b, c] [c, c] [c, b] -> [b, d] [d, d] [d, d] [d, b] , [b, c] [c, b] -> [b, g] [g, b] , [b, d] [d, d] [d, b] -> [b, c] [c, f] [f, b] , [b, d] [d, d] [d, d] [d, b] -> [b, g] [g, c] [c, b] , [b, f] [f, b] -> [b, a] [a, g] [g, b] , [b, b] [b, b] [b, c] -> [b, c] [c, d] [d, c] , [b, c] [c, c] [c, c] -> [b, d] [d, d] [d, d] [d, c] , [b, c] [c, c] -> [b, g] [g, c] , [b, d] [d, d] [d, c] -> [b, c] [c, f] [f, c] , [b, d] [d, d] [d, d] [d, c] -> [b, g] [g, c] [c, c] , [b, f] [f, c] -> [b, a] [a, g] [g, c] , [b, b] [b, b] [b, d] -> [b, c] [c, d] [d, d] , [b, c] [c, c] [c, d] -> [b, d] [d, d] [d, d] [d, d] , [b, c] [c, d] -> [b, g] [g, d] , [b, d] [d, d] [d, d] -> [b, c] [c, f] [f, d] , [b, d] [d, d] [d, d] [d, d] -> [b, g] [g, c] [c, d] , [b, f] [f, d] -> [b, a] [a, g] [g, d] , [b, b] [b, b] [b, g] -> [b, c] [c, d] [d, g] , [b, c] [c, c] [c, g] -> [b, d] [d, d] [d, d] [d, g] , [b, c] [c, g] -> [b, g] [g, g] , [b, d] [d, d] [d, g] -> [b, c] [c, f] [f, g] , [b, d] [d, d] [d, d] [d, g] -> [b, g] [g, c] [c, g] , [b, f] [f, g] -> [b, a] [a, g] [g, g] , [b, c] [c, c] [c, f] -> [b, d] [d, d] [d, d] [d, f] , [b, c] [c, f] -> [b, g] [g, f] , [b, d] [d, d] [d, f] -> [b, c] [c, f] [f, f] , [b, d] [d, d] [d, d] [d, f] -> [b, g] [g, c] [c, f] , [b, f] [f, f] -> [b, a] [a, g] [g, f] , [b, g] [g, f] -> [b, d] [d, a] [a, b] [b, f] , [b, c] [c, c] [c, a] -> [b, d] [d, d] [d, d] [d, a] , [b, c] [c, a] -> [b, g] [g, a] , [b, d] [d, d] [d, a] -> [b, c] [c, f] [f, a] , [b, d] [d, d] [d, d] [d, a] -> [b, g] [g, c] [c, a] , [b, f] [f, a] -> [b, a] [a, g] [g, a] , [b, g] [g, a] -> [b, d] [d, a] [a, b] [b, a] , [c, b] [b, b] [b, b] -> [c, c] [c, d] [d, b] , [c, c] [c, c] [c, b] -> [c, d] [d, d] [d, d] [d, b] , [c, c] [c, b] -> [c, g] [g, b] , [c, d] [d, d] [d, b] -> [c, c] [c, f] [f, b] , [c, d] [d, d] [d, d] [d, b] -> [c, g] [g, c] [c, b] , [c, f] [f, b] -> [c, a] [a, g] [g, b] , [c, b] [b, b] [b, c] -> [c, c] [c, d] [d, c] , [c, c] [c, c] [c, c] -> [c, d] [d, d] [d, d] [d, c] , [c, c] [c, c] -> [c, g] [g, c] , [c, d] [d, d] [d, c] -> [c, c] [c, f] [f, c] , [c, d] [d, d] [d, d] [d, c] -> [c, g] [g, c] [c, c] , [c, f] [f, c] -> [c, a] [a, g] [g, c] , [c, b] [b, b] [b, d] -> [c, c] [c, d] [d, d] , [c, c] [c, c] [c, d] -> [c, d] [d, d] [d, d] [d, d] , [c, c] [c, d] -> [c, g] [g, d] , [c, d] [d, d] [d, d] -> [c, c] [c, f] [f, d] , [c, d] [d, d] [d, d] [d, d] -> [c, g] [g, c] [c, d] , [c, f] [f, d] -> [c, a] [a, g] [g, d] , [c, b] [b, b] [b, g] -> [c, c] [c, d] [d, g] , [c, c] [c, c] [c, g] -> [c, d] [d, d] [d, d] [d, g] , [c, c] [c, g] -> [c, g] [g, g] , [c, d] [d, d] [d, g] -> [c, c] [c, f] [f, g] , [c, d] [d, d] [d, d] [d, g] -> [c, g] [g, c] [c, g] , [c, f] [f, g] -> [c, a] [a, g] [g, g] , [c, c] [c, c] [c, f] -> [c, d] [d, d] [d, d] [d, f] , [c, c] [c, f] -> [c, g] [g, f] , [c, d] [d, d] [d, f] -> [c, c] [c, f] [f, f] , [c, d] [d, d] [d, d] [d, f] -> [c, g] [g, c] [c, f] , [c, f] [f, f] -> [c, a] [a, g] [g, f] , [c, g] [g, f] -> [c, d] [d, a] [a, b] [b, f] , [c, c] [c, c] [c, a] -> [c, d] [d, d] [d, d] [d, a] , [c, c] [c, a] -> [c, g] [g, a] , [c, d] [d, d] [d, a] -> [c, c] [c, f] [f, a] , [c, d] [d, d] [d, d] [d, a] -> [c, g] [g, c] [c, a] , [c, f] [f, a] -> [c, a] [a, g] [g, a] , [c, g] [g, a] -> [c, d] [d, a] [a, b] [b, a] , [d, b] [b, b] [b, b] -> [d, c] [c, d] [d, b] , [d, c] [c, c] [c, b] -> [d, d] [d, d] [d, d] [d, b] , [d, c] [c, b] -> [d, g] [g, b] , [d, d] [d, d] [d, b] -> [d, c] [c, f] [f, b] , [d, d] [d, d] [d, d] [d, b] -> [d, g] [g, c] [c, b] , [d, f] [f, b] -> [d, a] [a, g] [g, b] , [d, b] [b, b] [b, c] -> [d, c] [c, d] [d, c] , [d, c] [c, c] [c, c] -> [d, d] [d, d] [d, d] [d, c] , [d, c] [c, c] -> [d, g] [g, c] , [d, d] [d, d] [d, c] -> [d, c] [c, f] [f, c] , [d, d] [d, d] [d, d] [d, c] -> [d, g] [g, c] [c, c] , [d, f] [f, c] -> [d, a] [a, g] [g, c] , [d, b] [b, b] [b, d] -> [d, c] [c, d] [d, d] , [d, c] [c, c] [c, d] -> [d, d] [d, d] [d, d] [d, d] , [d, c] [c, d] -> [d, g] [g, d] , [d, d] [d, d] [d, d] -> [d, c] [c, f] [f, d] , [d, d] [d, d] [d, d] [d, d] -> [d, g] [g, c] [c, d] , [d, f] [f, d] -> [d, a] [a, g] [g, d] , [d, b] [b, b] [b, g] -> [d, c] [c, d] [d, g] , [d, c] [c, c] [c, g] -> [d, d] [d, d] [d, d] [d, g] , [d, c] [c, g] -> [d, g] [g, g] , [d, d] [d, d] [d, g] -> [d, c] [c, f] [f, g] , [d, d] [d, d] [d, d] [d, g] -> [d, g] [g, c] [c, g] , [d, f] [f, g] -> [d, a] [a, g] [g, g] , [d, c] [c, c] [c, f] -> [d, d] [d, d] [d, d] [d, f] , [d, c] [c, f] -> [d, g] [g, f] , [d, d] [d, d] [d, f] -> [d, c] [c, f] [f, f] , [d, d] [d, d] [d, d] [d, f] -> [d, g] [g, c] [c, f] , [d, f] [f, f] -> [d, a] [a, g] [g, f] , [d, g] [g, f] -> [d, d] [d, a] [a, b] [b, f] , [d, c] [c, c] [c, a] -> [d, d] [d, d] [d, d] [d, a] , [d, c] [c, a] -> [d, g] [g, a] , [d, d] [d, d] [d, a] -> [d, c] [c, f] [f, a] , [d, d] [d, d] [d, d] [d, a] -> [d, g] [g, c] [c, a] , [d, f] [f, a] -> [d, a] [a, g] [g, a] , [d, g] [g, a] -> [d, d] [d, a] [a, b] [b, a] , [g, b] [b, b] [b, b] -> [g, c] [c, d] [d, b] , [g, c] [c, c] [c, b] -> [g, d] [d, d] [d, d] [d, b] , [g, c] [c, b] -> [g, g] [g, b] , [g, d] [d, d] [d, b] -> [g, c] [c, f] [f, b] , [g, d] [d, d] [d, d] [d, b] -> [g, g] [g, c] [c, b] , [g, f] [f, b] -> [g, a] [a, g] [g, b] , [g, b] [b, b] [b, c] -> [g, c] [c, d] [d, c] , [g, c] [c, c] [c, c] -> [g, d] [d, d] [d, d] [d, c] , [g, c] [c, c] -> [g, g] [g, c] , [g, d] [d, d] [d, c] -> [g, c] [c, f] [f, c] , [g, d] [d, d] [d, d] [d, c] -> [g, g] [g, c] [c, c] , [g, f] [f, c] -> [g, a] [a, g] [g, c] , [g, b] [b, b] [b, d] -> [g, c] [c, d] [d, d] , [g, c] [c, c] [c, d] -> [g, d] [d, d] [d, d] [d, d] , [g, c] [c, d] -> [g, g] [g, d] , [g, d] [d, d] [d, d] -> [g, c] [c, f] [f, d] , [g, d] [d, d] [d, d] [d, d] -> [g, g] [g, c] [c, d] , [g, f] [f, d] -> [g, a] [a, g] [g, d] , [g, b] [b, b] [b, g] -> [g, c] [c, d] [d, g] , [g, c] [c, c] [c, g] -> [g, d] [d, d] [d, d] [d, g] , [g, c] [c, g] -> [g, g] [g, g] , [g, d] [d, d] [d, g] -> [g, c] [c, f] [f, g] , [g, d] [d, d] [d, d] [d, g] -> [g, g] [g, c] [c, g] , [g, f] [f, g] -> [g, a] [a, g] [g, g] , [g, c] [c, c] [c, f] -> [g, d] [d, d] [d, d] [d, f] , [g, c] [c, f] -> [g, g] [g, f] , [g, d] [d, d] [d, f] -> [g, c] [c, f] [f, f] , [g, d] [d, d] [d, d] [d, f] -> [g, g] [g, c] [c, f] , [g, f] [f, f] -> [g, a] [a, g] [g, f] , [g, g] [g, f] -> [g, d] [d, a] [a, b] [b, f] , [g, c] [c, c] [c, a] -> [g, d] [d, d] [d, d] [d, a] , [g, c] [c, a] -> [g, g] [g, a] , [g, d] [d, d] [d, a] -> [g, c] [c, f] [f, a] , [g, d] [d, d] [d, d] [d, a] -> [g, g] [g, c] [c, a] , [g, f] [f, a] -> [g, a] [a, g] [g, a] , [g, g] [g, a] -> [g, d] [d, a] [a, b] [b, a] , [f, b] [b, b] [b, b] -> [f, c] [c, d] [d, b] , [f, c] [c, c] [c, b] -> [f, d] [d, d] [d, d] [d, b] , [f, c] [c, b] -> [f, g] [g, b] , [f, d] [d, d] [d, b] -> [f, c] [c, f] [f, b] , [f, d] [d, d] [d, d] [d, b] -> [f, g] [g, c] [c, b] , [f, f] [f, b] -> [f, a] [a, g] [g, b] , [f, b] [b, b] [b, c] -> [f, c] [c, d] [d, c] , [f, c] [c, c] [c, c] -> [f, d] [d, d] [d, d] [d, c] , [f, c] [c, c] -> [f, g] [g, c] , [f, d] [d, d] [d, c] -> [f, c] [c, f] [f, c] , [f, d] [d, d] [d, d] [d, c] -> [f, g] [g, c] [c, c] , [f, f] [f, c] -> [f, a] [a, g] [g, c] , [f, b] [b, b] [b, d] -> [f, c] [c, d] [d, d] , [f, c] [c, c] [c, d] -> [f, d] [d, d] [d, d] [d, d] , [f, c] [c, d] -> [f, g] [g, d] , [f, d] [d, d] [d, d] -> [f, c] [c, f] [f, d] , [f, d] [d, d] [d, d] [d, d] -> [f, g] [g, c] [c, d] , [f, f] [f, d] -> [f, a] [a, g] [g, d] , [f, b] [b, b] [b, g] -> [f, c] [c, d] [d, g] , [f, c] [c, c] [c, g] -> [f, d] [d, d] [d, d] [d, g] , [f, c] [c, g] -> [f, g] [g, g] , [f, d] [d, d] [d, g] -> [f, c] [c, f] [f, g] , [f, d] [d, d] [d, d] [d, g] -> [f, g] [g, c] [c, g] , [f, f] [f, g] -> [f, a] [a, g] [g, g] , [f, c] [c, c] [c, f] -> [f, d] [d, d] [d, d] [d, f] , [f, c] [c, f] -> [f, g] [g, f] , [f, d] [d, d] [d, f] -> [f, c] [c, f] [f, f] , [f, d] [d, d] [d, d] [d, f] -> [f, g] [g, c] [c, f] , [f, f] [f, f] -> [f, a] [a, g] [g, f] , [f, g] [g, f] -> [f, d] [d, a] [a, b] [b, f] , [f, c] [c, c] [c, a] -> [f, d] [d, d] [d, d] [d, a] , [f, c] [c, a] -> [f, g] [g, a] , [f, d] [d, d] [d, a] -> [f, c] [c, f] [f, a] , [f, d] [d, d] [d, d] [d, a] -> [f, g] [g, c] [c, a] , [f, f] [f, a] -> [f, a] [a, g] [g, a] , [f, g] [g, a] -> [f, d] [d, a] [a, b] [b, a] , [a, b] [b, b] [b, b] -> [a, c] [c, d] [d, b] , [a, c] [c, c] [c, b] -> [a, d] [d, d] [d, d] [d, b] , [a, c] [c, b] -> [a, g] [g, b] , [a, d] [d, d] [d, b] -> [a, c] [c, f] [f, b] , [a, d] [d, d] [d, d] [d, b] -> [a, g] [g, c] [c, b] , [a, b] [b, b] [b, c] -> [a, c] [c, d] [d, c] , [a, c] [c, c] [c, c] -> [a, d] [d, d] [d, d] [d, c] , [a, c] [c, c] -> [a, g] [g, c] , [a, d] [d, d] [d, c] -> [a, c] [c, f] [f, c] , [a, d] [d, d] [d, d] [d, c] -> [a, g] [g, c] [c, c] , [a, b] [b, b] [b, d] -> [a, c] [c, d] [d, d] , [a, c] [c, c] [c, d] -> [a, d] [d, d] [d, d] [d, d] , [a, c] [c, d] -> [a, g] [g, d] , [a, d] [d, d] [d, d] -> [a, c] [c, f] [f, d] , [a, d] [d, d] [d, d] [d, d] -> [a, g] [g, c] [c, d] , [a, b] [b, b] [b, g] -> [a, c] [c, d] [d, g] , [a, c] [c, c] [c, g] -> [a, d] [d, d] [d, d] [d, g] , [a, c] [c, g] -> [a, g] [g, g] , [a, d] [d, d] [d, g] -> [a, c] [c, f] [f, g] , [a, d] [d, d] [d, d] [d, g] -> [a, g] [g, c] [c, g] , [a, c] [c, c] [c, f] -> [a, d] [d, d] [d, d] [d, f] , [a, c] [c, f] -> [a, g] [g, f] , [a, d] [d, d] [d, f] -> [a, c] [c, f] [f, f] , [a, d] [d, d] [d, d] [d, f] -> [a, g] [g, c] [c, f] , [a, g] [g, f] -> [a, d] [d, a] [a, b] [b, f] , [a, c] [c, c] [c, a] -> [a, d] [d, d] [d, d] [d, a] , [a, c] [c, a] -> [a, g] [g, a] , [a, d] [d, d] [d, a] -> [a, c] [c, f] [f, a] , [a, d] [d, d] [d, d] [d, a] -> [a, g] [g, c] [c, a] , [a, g] [g, a] -> [a, d] [d, a] [a, b] [b, a] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [f, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, b] is interpreted by / \ | 1 1 | | 0 1 | \ / [b, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, a] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 186-rule system { [b, c] [c, c] [c, b] -> [b, d] [d, d] [d, d] [d, b] , [b, c] [c, b] -> [b, g] [g, b] , [b, d] [d, d] [d, b] -> [b, c] [c, f] [f, b] , [b, d] [d, d] [d, d] [d, b] -> [b, g] [g, c] [c, b] , [b, f] [f, b] -> [b, a] [a, g] [g, b] , [b, c] [c, c] [c, c] -> [b, d] [d, d] [d, d] [d, c] , [b, c] [c, c] -> [b, g] [g, c] , [b, d] [d, d] [d, c] -> [b, c] [c, f] [f, c] , [b, d] [d, d] [d, d] [d, c] -> [b, g] [g, c] [c, c] , [b, f] [f, c] -> [b, a] [a, g] [g, c] , [b, c] [c, c] [c, d] -> [b, d] [d, d] [d, d] [d, d] , [b, c] [c, d] -> [b, g] [g, d] , [b, d] [d, d] [d, d] -> [b, c] [c, f] [f, d] , [b, d] [d, d] [d, d] [d, d] -> [b, g] [g, c] [c, d] , [b, f] [f, d] -> [b, a] [a, g] [g, d] , [b, c] [c, c] [c, g] -> [b, d] [d, d] [d, d] [d, g] , [b, c] [c, g] -> [b, g] [g, g] , [b, d] [d, d] [d, g] -> [b, c] [c, f] [f, g] , [b, d] [d, d] [d, d] [d, g] -> [b, g] [g, c] [c, g] , [b, f] [f, g] -> [b, a] [a, g] [g, g] , [b, c] [c, c] [c, f] -> [b, d] [d, d] [d, d] [d, f] , [b, c] [c, f] -> [b, g] [g, f] , [b, d] [d, d] [d, f] -> [b, c] [c, f] [f, f] , [b, d] [d, d] [d, d] [d, f] -> [b, g] [g, c] [c, f] , [b, f] [f, f] -> [b, a] [a, g] [g, f] , [b, g] [g, f] -> [b, d] [d, a] [a, b] [b, f] , [b, c] [c, c] [c, a] -> [b, d] [d, d] [d, d] [d, a] , [b, c] [c, a] -> [b, g] [g, a] , [b, d] [d, d] [d, a] -> [b, c] [c, f] [f, a] , [b, d] [d, d] [d, d] [d, a] -> [b, g] [g, c] [c, a] , [b, f] [f, a] -> [b, a] [a, g] [g, a] , [b, g] [g, a] -> [b, d] [d, a] [a, b] [b, a] , [c, c] [c, c] [c, b] -> [c, d] [d, d] [d, d] [d, b] , [c, c] [c, b] -> [c, g] [g, b] , [c, d] [d, d] [d, b] -> [c, c] [c, f] [f, b] , [c, d] [d, d] [d, d] [d, b] -> [c, g] [g, c] [c, b] , [c, f] [f, b] -> [c, a] [a, g] [g, b] , [c, c] [c, c] [c, c] -> [c, d] [d, d] [d, d] [d, c] , [c, c] [c, c] -> [c, g] [g, c] , [c, d] [d, d] [d, c] -> [c, c] [c, f] [f, c] , [c, d] [d, d] [d, d] [d, c] -> [c, g] [g, c] [c, c] , [c, f] [f, c] -> [c, a] [a, g] [g, c] , [c, c] [c, c] [c, d] -> [c, d] [d, d] [d, d] [d, d] , [c, c] [c, d] -> [c, g] [g, d] , [c, d] [d, d] [d, d] -> [c, c] [c, f] [f, d] , [c, d] [d, d] [d, d] [d, d] -> [c, g] [g, c] [c, d] , [c, f] [f, d] -> [c, a] [a, g] [g, d] , [c, c] [c, c] [c, g] -> [c, d] [d, d] [d, d] [d, g] , [c, c] [c, g] -> [c, g] [g, g] , [c, d] [d, d] [d, g] -> [c, c] [c, f] [f, g] , [c, d] [d, d] [d, d] [d, g] -> [c, g] [g, c] [c, g] , [c, f] [f, g] -> [c, a] [a, g] [g, g] , [c, c] [c, c] [c, f] -> [c, d] [d, d] [d, d] [d, f] , [c, c] [c, f] -> [c, g] [g, f] , [c, d] [d, d] [d, f] -> [c, c] [c, f] [f, f] , [c, d] [d, d] [d, d] [d, f] -> [c, g] [g, c] [c, f] , [c, f] [f, f] -> [c, a] [a, g] [g, f] , [c, g] [g, f] -> [c, d] [d, a] [a, b] [b, f] , [c, c] [c, c] [c, a] -> [c, d] [d, d] [d, d] [d, a] , [c, c] [c, a] -> [c, g] [g, a] , [c, d] [d, d] [d, a] -> [c, c] [c, f] [f, a] , [c, d] [d, d] [d, d] [d, a] -> [c, g] [g, c] [c, a] , [c, f] [f, a] -> [c, a] [a, g] [g, a] , [c, g] [g, a] -> [c, d] [d, a] [a, b] [b, a] , [d, c] [c, c] [c, b] -> [d, d] [d, d] [d, d] [d, b] , [d, c] [c, b] -> [d, g] [g, b] , [d, d] [d, d] [d, b] -> [d, c] [c, f] [f, b] , [d, d] [d, d] [d, d] [d, b] -> [d, g] [g, c] [c, b] , [d, f] [f, b] -> [d, a] [a, g] [g, b] , [d, c] [c, c] [c, c] -> [d, d] [d, d] [d, d] [d, c] , [d, c] [c, c] -> [d, g] [g, c] , [d, d] [d, d] [d, c] -> [d, c] [c, f] [f, c] , [d, d] [d, d] [d, d] [d, c] -> [d, g] [g, c] [c, c] , [d, f] [f, c] -> [d, a] [a, g] [g, c] , [d, c] [c, c] [c, d] -> [d, d] [d, d] [d, d] [d, d] , [d, c] [c, d] -> [d, g] [g, d] , [d, d] [d, d] [d, d] -> [d, c] [c, f] [f, d] , [d, d] [d, d] [d, d] [d, d] -> [d, g] [g, c] [c, d] , [d, f] [f, d] -> [d, a] [a, g] [g, d] , [d, c] [c, c] [c, g] -> [d, d] [d, d] [d, d] [d, g] , [d, c] [c, g] -> [d, g] [g, g] , [d, d] [d, d] [d, g] -> [d, c] [c, f] [f, g] , [d, d] [d, d] [d, d] [d, g] -> [d, g] [g, c] [c, g] , [d, f] [f, g] -> [d, a] [a, g] [g, g] , [d, c] [c, c] [c, f] -> [d, d] [d, d] [d, d] [d, f] , [d, c] [c, f] -> [d, g] [g, f] , [d, d] [d, d] [d, f] -> [d, c] [c, f] [f, f] , [d, d] [d, d] [d, d] [d, f] -> [d, g] [g, c] [c, f] , [d, f] [f, f] -> [d, a] [a, g] [g, f] , [d, g] [g, f] -> [d, d] [d, a] [a, b] [b, f] , [d, c] [c, c] [c, a] -> [d, d] [d, d] [d, d] [d, a] , [d, c] [c, a] -> [d, g] [g, a] , [d, d] [d, d] [d, a] -> [d, c] [c, f] [f, a] , [d, d] [d, d] [d, d] [d, a] -> [d, g] [g, c] [c, a] , [d, f] [f, a] -> [d, a] [a, g] [g, a] , [d, g] [g, a] -> [d, d] [d, a] [a, b] [b, a] , [g, c] [c, c] [c, b] -> [g, d] [d, d] [d, d] [d, b] , [g, c] [c, b] -> [g, g] [g, b] , [g, d] [d, d] [d, b] -> [g, c] [c, f] [f, b] , [g, d] [d, d] [d, d] [d, b] -> [g, g] [g, c] [c, b] , [g, f] [f, b] -> [g, a] [a, g] [g, b] , [g, c] [c, c] [c, c] -> [g, d] [d, d] [d, d] [d, c] , [g, c] [c, c] -> [g, g] [g, c] , [g, d] [d, d] [d, c] -> [g, c] [c, f] [f, c] , [g, d] [d, d] [d, d] [d, c] -> [g, g] [g, c] [c, c] , [g, f] [f, c] -> [g, a] [a, g] [g, c] , [g, c] [c, c] [c, d] -> [g, d] [d, d] [d, d] [d, d] , [g, c] [c, d] -> [g, g] [g, d] , [g, d] [d, d] [d, d] -> [g, c] [c, f] [f, d] , [g, d] [d, d] [d, d] [d, d] -> [g, g] [g, c] [c, d] , [g, f] [f, d] -> [g, a] [a, g] [g, d] , [g, c] [c, c] [c, g] -> [g, d] [d, d] [d, d] [d, g] , [g, c] [c, g] -> [g, g] [g, g] , [g, d] [d, d] [d, g] -> [g, c] [c, f] [f, g] , [g, d] [d, d] [d, d] [d, g] -> [g, g] [g, c] [c, g] , [g, f] [f, g] -> [g, a] [a, g] [g, g] , [g, c] [c, c] [c, f] -> [g, d] [d, d] [d, d] [d, f] , [g, c] [c, f] -> [g, g] [g, f] , [g, d] [d, d] [d, f] -> [g, c] [c, f] [f, f] , [g, d] [d, d] [d, d] [d, f] -> [g, g] [g, c] [c, f] , [g, f] [f, f] -> [g, a] [a, g] [g, f] , [g, g] [g, f] -> [g, d] [d, a] [a, b] [b, f] , [g, c] [c, c] [c, a] -> [g, d] [d, d] [d, d] [d, a] , [g, c] [c, a] -> [g, g] [g, a] , [g, d] [d, d] [d, a] -> [g, c] [c, f] [f, a] , [g, d] [d, d] [d, d] [d, a] -> [g, g] [g, c] [c, a] , [g, f] [f, a] -> [g, a] [a, g] [g, a] , [g, g] [g, a] -> [g, d] [d, a] [a, b] [b, a] , [f, c] [c, c] [c, b] -> [f, d] [d, d] [d, d] [d, b] , [f, c] [c, b] -> [f, g] [g, b] , [f, d] [d, d] [d, b] -> [f, c] [c, f] [f, b] , [f, d] [d, d] [d, d] [d, b] -> [f, g] [g, c] [c, b] , [f, f] [f, b] -> [f, a] [a, g] [g, b] , [f, c] [c, c] [c, c] -> [f, d] [d, d] [d, d] [d, c] , [f, c] [c, c] -> [f, g] [g, c] , [f, d] [d, d] [d, c] -> [f, c] [c, f] [f, c] , [f, d] [d, d] [d, d] [d, c] -> [f, g] [g, c] [c, c] , [f, f] [f, c] -> [f, a] [a, g] [g, c] , [f, c] [c, c] [c, d] -> [f, d] [d, d] [d, d] [d, d] , [f, c] [c, d] -> [f, g] [g, d] , [f, d] [d, d] [d, d] -> [f, c] [c, f] [f, d] , [f, d] [d, d] [d, d] [d, d] -> [f, g] [g, c] [c, d] , [f, f] [f, d] -> [f, a] [a, g] [g, d] , [f, c] [c, c] [c, g] -> [f, d] [d, d] [d, d] [d, g] , [f, c] [c, g] -> [f, g] [g, g] , [f, d] [d, d] [d, g] -> [f, c] [c, f] [f, g] , [f, d] [d, d] [d, d] [d, g] -> [f, g] [g, c] [c, g] , [f, f] [f, g] -> [f, a] [a, g] [g, g] , [f, c] [c, c] [c, f] -> [f, d] [d, d] [d, d] [d, f] , [f, c] [c, f] -> [f, g] [g, f] , [f, d] [d, d] [d, f] -> [f, c] [c, f] [f, f] , [f, d] [d, d] [d, d] [d, f] -> [f, g] [g, c] [c, f] , [f, f] [f, f] -> [f, a] [a, g] [g, f] , [f, g] [g, f] -> [f, d] [d, a] [a, b] [b, f] , [f, c] [c, c] [c, a] -> [f, d] [d, d] [d, d] [d, a] , [f, c] [c, a] -> [f, g] [g, a] , [f, d] [d, d] [d, a] -> [f, c] [c, f] [f, a] , [f, d] [d, d] [d, d] [d, a] -> [f, g] [g, c] [c, a] , [f, f] [f, a] -> [f, a] [a, g] [g, a] , [f, g] [g, a] -> [f, d] [d, a] [a, b] [b, a] , [a, c] [c, c] [c, b] -> [a, d] [d, d] [d, d] [d, b] , [a, c] [c, b] -> [a, g] [g, b] , [a, d] [d, d] [d, b] -> [a, c] [c, f] [f, b] , [a, d] [d, d] [d, d] [d, b] -> [a, g] [g, c] [c, b] , [a, c] [c, c] [c, c] -> [a, d] [d, d] [d, d] [d, c] , [a, c] [c, c] -> [a, g] [g, c] , [a, d] [d, d] [d, c] -> [a, c] [c, f] [f, c] , [a, d] [d, d] [d, d] [d, c] -> [a, g] [g, c] [c, c] , [a, c] [c, c] [c, d] -> [a, d] [d, d] [d, d] [d, d] , [a, c] [c, d] -> [a, g] [g, d] , [a, d] [d, d] [d, d] -> [a, c] [c, f] [f, d] , [a, d] [d, d] [d, d] [d, d] -> [a, g] [g, c] [c, d] , [a, c] [c, c] [c, g] -> [a, d] [d, d] [d, d] [d, g] , [a, c] [c, g] -> [a, g] [g, g] , [a, d] [d, d] [d, g] -> [a, c] [c, f] [f, g] , [a, d] [d, d] [d, d] [d, g] -> [a, g] [g, c] [c, g] , [a, c] [c, c] [c, f] -> [a, d] [d, d] [d, d] [d, f] , [a, c] [c, f] -> [a, g] [g, f] , [a, d] [d, d] [d, f] -> [a, c] [c, f] [f, f] , [a, d] [d, d] [d, d] [d, f] -> [a, g] [g, c] [c, f] , [a, g] [g, f] -> [a, d] [d, a] [a, b] [b, f] , [a, c] [c, c] [c, a] -> [a, d] [d, d] [d, d] [d, a] , [a, c] [c, a] -> [a, g] [g, a] , [a, d] [d, d] [d, a] -> [a, c] [c, f] [f, a] , [a, d] [d, d] [d, d] [d, a] -> [a, g] [g, c] [c, a] , [a, g] [g, a] -> [a, d] [d, a] [a, b] [b, a] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [f, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, b] is interpreted by / \ | 1 1 | | 0 1 | \ / [c, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, b] is interpreted by / \ | 1 1 | | 0 1 | \ / [b, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, b] is interpreted by / \ | 1 1 | | 0 1 | \ / [g, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, a] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 175-rule system { [b, c] [c, c] [c, b] -> [b, d] [d, d] [d, d] [d, b] , [b, d] [d, d] [d, b] -> [b, c] [c, f] [f, b] , [b, d] [d, d] [d, d] [d, b] -> [b, g] [g, c] [c, b] , [b, c] [c, c] [c, c] -> [b, d] [d, d] [d, d] [d, c] , [b, c] [c, c] -> [b, g] [g, c] , [b, d] [d, d] [d, c] -> [b, c] [c, f] [f, c] , [b, d] [d, d] [d, d] [d, c] -> [b, g] [g, c] [c, c] , [b, f] [f, c] -> [b, a] [a, g] [g, c] , [b, c] [c, c] [c, d] -> [b, d] [d, d] [d, d] [d, d] , [b, c] [c, d] -> [b, g] [g, d] , [b, d] [d, d] [d, d] -> [b, c] [c, f] [f, d] , [b, d] [d, d] [d, d] [d, d] -> [b, g] [g, c] [c, d] , [b, f] [f, d] -> [b, a] [a, g] [g, d] , [b, c] [c, c] [c, g] -> [b, d] [d, d] [d, d] [d, g] , [b, c] [c, g] -> [b, g] [g, g] , [b, d] [d, d] [d, g] -> [b, c] [c, f] [f, g] , [b, d] [d, d] [d, d] [d, g] -> [b, g] [g, c] [c, g] , [b, f] [f, g] -> [b, a] [a, g] [g, g] , [b, c] [c, c] [c, f] -> [b, d] [d, d] [d, d] [d, f] , [b, c] [c, f] -> [b, g] [g, f] , [b, d] [d, d] [d, f] -> [b, c] [c, f] [f, f] , [b, d] [d, d] [d, d] [d, f] -> [b, g] [g, c] [c, f] , [b, f] [f, f] -> [b, a] [a, g] [g, f] , [b, g] [g, f] -> [b, d] [d, a] [a, b] [b, f] , [b, c] [c, c] [c, a] -> [b, d] [d, d] [d, d] [d, a] , [b, c] [c, a] -> [b, g] [g, a] , [b, d] [d, d] [d, a] -> [b, c] [c, f] [f, a] , [b, d] [d, d] [d, d] [d, a] -> [b, g] [g, c] [c, a] , [b, f] [f, a] -> [b, a] [a, g] [g, a] , [b, g] [g, a] -> [b, d] [d, a] [a, b] [b, a] , [c, c] [c, c] [c, b] -> [c, d] [d, d] [d, d] [d, b] , [c, d] [d, d] [d, b] -> [c, c] [c, f] [f, b] , [c, d] [d, d] [d, d] [d, b] -> [c, g] [g, c] [c, b] , [c, c] [c, c] [c, c] -> [c, d] [d, d] [d, d] [d, c] , [c, c] [c, c] -> [c, g] [g, c] , [c, d] [d, d] [d, c] -> [c, c] [c, f] [f, c] , [c, d] [d, d] [d, d] [d, c] -> [c, g] [g, c] [c, c] , [c, f] [f, c] -> [c, a] [a, g] [g, c] , [c, c] [c, c] [c, d] -> [c, d] [d, d] [d, d] [d, d] , [c, c] [c, d] -> [c, g] [g, d] , [c, d] [d, d] [d, d] -> [c, c] [c, f] [f, d] , [c, d] [d, d] [d, d] [d, d] -> [c, g] [g, c] [c, d] , [c, f] [f, d] -> [c, a] [a, g] [g, d] , [c, c] [c, c] [c, g] -> [c, d] [d, d] [d, d] [d, g] , [c, c] [c, g] -> [c, g] [g, g] , [c, d] [d, d] [d, g] -> [c, c] [c, f] [f, g] , [c, d] [d, d] [d, d] [d, g] -> [c, g] [g, c] [c, g] , [c, f] [f, g] -> [c, a] [a, g] [g, g] , [c, c] [c, c] [c, f] -> [c, d] [d, d] [d, d] [d, f] , [c, c] [c, f] -> [c, g] [g, f] , [c, d] [d, d] [d, f] -> [c, c] [c, f] [f, f] , [c, d] [d, d] [d, d] [d, f] -> [c, g] [g, c] [c, f] , [c, f] [f, f] -> [c, a] [a, g] [g, f] , [c, g] [g, f] -> [c, d] [d, a] [a, b] [b, f] , [c, c] [c, c] [c, a] -> [c, d] [d, d] [d, d] [d, a] , [c, c] [c, a] -> [c, g] [g, a] , [c, d] [d, d] [d, a] -> [c, c] [c, f] [f, a] , [c, d] [d, d] [d, d] [d, a] -> [c, g] [g, c] [c, a] , [c, f] [f, a] -> [c, a] [a, g] [g, a] , [c, g] [g, a] -> [c, d] [d, a] [a, b] [b, a] , [d, c] [c, c] [c, b] -> [d, d] [d, d] [d, d] [d, b] , [d, d] [d, d] [d, b] -> [d, c] [c, f] [f, b] , [d, d] [d, d] [d, d] [d, b] -> [d, g] [g, c] [c, b] , [d, c] [c, c] [c, c] -> [d, d] [d, d] [d, d] [d, c] , [d, c] [c, c] -> [d, g] [g, c] , [d, d] [d, d] [d, c] -> [d, c] [c, f] [f, c] , [d, d] [d, d] [d, d] [d, c] -> [d, g] [g, c] [c, c] , [d, f] [f, c] -> [d, a] [a, g] [g, c] , [d, c] [c, c] [c, d] -> [d, d] [d, d] [d, d] [d, d] , [d, c] [c, d] -> [d, g] [g, d] , [d, d] [d, d] [d, d] -> [d, c] [c, f] [f, d] , [d, d] [d, d] [d, d] [d, d] -> [d, g] [g, c] [c, d] , [d, f] [f, d] -> [d, a] [a, g] [g, d] , [d, c] [c, c] [c, g] -> [d, d] [d, d] [d, d] [d, g] , [d, c] [c, g] -> [d, g] [g, g] , [d, d] [d, d] [d, g] -> [d, c] [c, f] [f, g] , [d, d] [d, d] [d, d] [d, g] -> [d, g] [g, c] [c, g] , [d, f] [f, g] -> [d, a] [a, g] [g, g] , [d, c] [c, c] [c, f] -> [d, d] [d, d] [d, d] [d, f] , [d, c] [c, f] -> [d, g] [g, f] , [d, d] [d, d] [d, f] -> [d, c] [c, f] [f, f] , [d, d] [d, d] [d, d] [d, f] -> [d, g] [g, c] [c, f] , [d, f] [f, f] -> [d, a] [a, g] [g, f] , [d, g] [g, f] -> [d, d] [d, a] [a, b] [b, f] , [d, c] [c, c] [c, a] -> [d, d] [d, d] [d, d] [d, a] , [d, c] [c, a] -> [d, g] [g, a] , [d, d] [d, d] [d, a] -> [d, c] [c, f] [f, a] , [d, d] [d, d] [d, d] [d, a] -> [d, g] [g, c] [c, a] , [d, f] [f, a] -> [d, a] [a, g] [g, a] , [d, g] [g, a] -> [d, d] [d, a] [a, b] [b, a] , [g, c] [c, c] [c, b] -> [g, d] [d, d] [d, d] [d, b] , [g, d] [d, d] [d, b] -> [g, c] [c, f] [f, b] , [g, d] [d, d] [d, d] [d, b] -> [g, g] [g, c] [c, b] , [g, c] [c, c] [c, c] -> [g, d] [d, d] [d, d] [d, c] , [g, c] [c, c] -> [g, g] [g, c] , [g, d] [d, d] [d, c] -> [g, c] [c, f] [f, c] , [g, d] [d, d] [d, d] [d, c] -> [g, g] [g, c] [c, c] , [g, f] [f, c] -> [g, a] [a, g] [g, c] , [g, c] [c, c] [c, d] -> [g, d] [d, d] [d, d] [d, d] , [g, c] [c, d] -> [g, g] [g, d] , [g, d] [d, d] [d, d] -> [g, c] [c, f] [f, d] , [g, d] [d, d] [d, d] [d, d] -> [g, g] [g, c] [c, d] , [g, f] [f, d] -> [g, a] [a, g] [g, d] , [g, c] [c, c] [c, g] -> [g, d] [d, d] [d, d] [d, g] , [g, c] [c, g] -> [g, g] [g, g] , [g, d] [d, d] [d, g] -> [g, c] [c, f] [f, g] , [g, d] [d, d] [d, d] [d, g] -> [g, g] [g, c] [c, g] , [g, f] [f, g] -> [g, a] [a, g] [g, g] , [g, c] [c, c] [c, f] -> [g, d] [d, d] [d, d] [d, f] , [g, c] [c, f] -> [g, g] [g, f] , [g, d] [d, d] [d, f] -> [g, c] [c, f] [f, f] , [g, d] [d, d] [d, d] [d, f] -> [g, g] [g, c] [c, f] , [g, f] [f, f] -> [g, a] [a, g] [g, f] , [g, g] [g, f] -> [g, d] [d, a] [a, b] [b, f] , [g, c] [c, c] [c, a] -> [g, d] [d, d] [d, d] [d, a] , [g, c] [c, a] -> [g, g] [g, a] , [g, d] [d, d] [d, a] -> [g, c] [c, f] [f, a] , [g, d] [d, d] [d, d] [d, a] -> [g, g] [g, c] [c, a] , [g, f] [f, a] -> [g, a] [a, g] [g, a] , [g, g] [g, a] -> [g, d] [d, a] [a, b] [b, a] , [f, c] [c, c] [c, b] -> [f, d] [d, d] [d, d] [d, b] , [f, d] [d, d] [d, b] -> [f, c] [c, f] [f, b] , [f, d] [d, d] [d, d] [d, b] -> [f, g] [g, c] [c, b] , [f, c] [c, c] [c, c] -> [f, d] [d, d] [d, d] [d, c] , [f, c] [c, c] -> [f, g] [g, c] , [f, d] [d, d] [d, c] -> [f, c] [c, f] [f, c] , [f, d] [d, d] [d, d] [d, c] -> [f, g] [g, c] [c, c] , [f, f] [f, c] -> [f, a] [a, g] [g, c] , [f, c] [c, c] [c, d] -> [f, d] [d, d] [d, d] [d, d] , [f, c] [c, d] -> [f, g] [g, d] , [f, d] [d, d] [d, d] -> [f, c] [c, f] [f, d] , [f, d] [d, d] [d, d] [d, d] -> [f, g] [g, c] [c, d] , [f, f] [f, d] -> [f, a] [a, g] [g, d] , [f, c] [c, c] [c, g] -> [f, d] [d, d] [d, d] [d, g] , [f, c] [c, g] -> [f, g] [g, g] , [f, d] [d, d] [d, g] -> [f, c] [c, f] [f, g] , [f, d] [d, d] [d, d] [d, g] -> [f, g] [g, c] [c, g] , [f, f] [f, g] -> [f, a] [a, g] [g, g] , [f, c] [c, c] [c, f] -> [f, d] [d, d] [d, d] [d, f] , [f, c] [c, f] -> [f, g] [g, f] , [f, d] [d, d] [d, f] -> [f, c] [c, f] [f, f] , [f, d] [d, d] [d, d] [d, f] -> [f, g] [g, c] [c, f] , [f, f] [f, f] -> [f, a] [a, g] [g, f] , [f, g] [g, f] -> [f, d] [d, a] [a, b] [b, f] , [f, c] [c, c] [c, a] -> [f, d] [d, d] [d, d] [d, a] , [f, c] [c, a] -> [f, g] [g, a] , [f, d] [d, d] [d, a] -> [f, c] [c, f] [f, a] , [f, d] [d, d] [d, d] [d, a] -> [f, g] [g, c] [c, a] , [f, f] [f, a] -> [f, a] [a, g] [g, a] , [f, g] [g, a] -> [f, d] [d, a] [a, b] [b, a] , [a, c] [c, c] [c, b] -> [a, d] [d, d] [d, d] [d, b] , [a, d] [d, d] [d, b] -> [a, c] [c, f] [f, b] , [a, d] [d, d] [d, d] [d, b] -> [a, g] [g, c] [c, b] , [a, c] [c, c] [c, c] -> [a, d] [d, d] [d, d] [d, c] , [a, c] [c, c] -> [a, g] [g, c] , [a, d] [d, d] [d, c] -> [a, c] [c, f] [f, c] , [a, d] [d, d] [d, d] [d, c] -> [a, g] [g, c] [c, c] , [a, c] [c, c] [c, d] -> [a, d] [d, d] [d, d] [d, d] , [a, c] [c, d] -> [a, g] [g, d] , [a, d] [d, d] [d, d] -> [a, c] [c, f] [f, d] , [a, d] [d, d] [d, d] [d, d] -> [a, g] [g, c] [c, d] , [a, c] [c, c] [c, g] -> [a, d] [d, d] [d, d] [d, g] , [a, c] [c, g] -> [a, g] [g, g] , [a, d] [d, d] [d, g] -> [a, c] [c, f] [f, g] , [a, d] [d, d] [d, d] [d, g] -> [a, g] [g, c] [c, g] , [a, c] [c, c] [c, f] -> [a, d] [d, d] [d, d] [d, f] , [a, c] [c, f] -> [a, g] [g, f] , [a, d] [d, d] [d, f] -> [a, c] [c, f] [f, f] , [a, d] [d, d] [d, d] [d, f] -> [a, g] [g, c] [c, f] , [a, g] [g, f] -> [a, d] [d, a] [a, b] [b, f] , [a, c] [c, c] [c, a] -> [a, d] [d, d] [d, d] [d, a] , [a, c] [c, a] -> [a, g] [g, a] , [a, d] [d, d] [d, a] -> [a, c] [c, f] [f, a] , [a, d] [d, d] [d, d] [d, a] -> [a, g] [g, c] [c, a] , [a, g] [g, a] -> [a, d] [d, a] [a, b] [b, a] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [f, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, b] is interpreted by / \ | 1 1 | | 0 1 | \ / [c, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, b] is interpreted by / \ | 1 1 | | 0 1 | \ / [b, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, a] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 169-rule system { [b, c] [c, c] [c, b] -> [b, d] [d, d] [d, d] [d, b] , [b, d] [d, d] [d, d] [d, b] -> [b, g] [g, c] [c, b] , [b, c] [c, c] [c, c] -> [b, d] [d, d] [d, d] [d, c] , [b, c] [c, c] -> [b, g] [g, c] , [b, d] [d, d] [d, c] -> [b, c] [c, f] [f, c] , [b, d] [d, d] [d, d] [d, c] -> [b, g] [g, c] [c, c] , [b, f] [f, c] -> [b, a] [a, g] [g, c] , [b, c] [c, c] [c, d] -> [b, d] [d, d] [d, d] [d, d] , [b, c] [c, d] -> [b, g] [g, d] , [b, d] [d, d] [d, d] -> [b, c] [c, f] [f, d] , [b, d] [d, d] [d, d] [d, d] -> [b, g] [g, c] [c, d] , [b, f] [f, d] -> [b, a] [a, g] [g, d] , [b, c] [c, c] [c, g] -> [b, d] [d, d] [d, d] [d, g] , [b, c] [c, g] -> [b, g] [g, g] , [b, d] [d, d] [d, g] -> [b, c] [c, f] [f, g] , [b, d] [d, d] [d, d] [d, g] -> [b, g] [g, c] [c, g] , [b, f] [f, g] -> [b, a] [a, g] [g, g] , [b, c] [c, c] [c, f] -> [b, d] [d, d] [d, d] [d, f] , [b, c] [c, f] -> [b, g] [g, f] , [b, d] [d, d] [d, f] -> [b, c] [c, f] [f, f] , [b, d] [d, d] [d, d] [d, f] -> [b, g] [g, c] [c, f] , [b, f] [f, f] -> [b, a] [a, g] [g, f] , [b, g] [g, f] -> [b, d] [d, a] [a, b] [b, f] , [b, c] [c, c] [c, a] -> [b, d] [d, d] [d, d] [d, a] , [b, c] [c, a] -> [b, g] [g, a] , [b, d] [d, d] [d, a] -> [b, c] [c, f] [f, a] , [b, d] [d, d] [d, d] [d, a] -> [b, g] [g, c] [c, a] , [b, f] [f, a] -> [b, a] [a, g] [g, a] , [b, g] [g, a] -> [b, d] [d, a] [a, b] [b, a] , [c, c] [c, c] [c, b] -> [c, d] [d, d] [d, d] [d, b] , [c, d] [d, d] [d, d] [d, b] -> [c, g] [g, c] [c, b] , [c, c] [c, c] [c, c] -> [c, d] [d, d] [d, d] [d, c] , [c, c] [c, c] -> [c, g] [g, c] , [c, d] [d, d] [d, c] -> [c, c] [c, f] [f, c] , [c, d] [d, d] [d, d] [d, c] -> [c, g] [g, c] [c, c] , [c, f] [f, c] -> [c, a] [a, g] [g, c] , [c, c] [c, c] [c, d] -> [c, d] [d, d] [d, d] [d, d] , [c, c] [c, d] -> [c, g] [g, d] , [c, d] [d, d] [d, d] -> [c, c] [c, f] [f, d] , [c, d] [d, d] [d, d] [d, d] -> [c, g] [g, c] [c, d] , [c, f] [f, d] -> [c, a] [a, g] [g, d] , [c, c] [c, c] [c, g] -> [c, d] [d, d] [d, d] [d, g] , [c, c] [c, g] -> [c, g] [g, g] , [c, d] [d, d] [d, g] -> [c, c] [c, f] [f, g] , [c, d] [d, d] [d, d] [d, g] -> [c, g] [g, c] [c, g] , [c, f] [f, g] -> [c, a] [a, g] [g, g] , [c, c] [c, c] [c, f] -> [c, d] [d, d] [d, d] [d, f] , [c, c] [c, f] -> [c, g] [g, f] , [c, d] [d, d] [d, f] -> [c, c] [c, f] [f, f] , [c, d] [d, d] [d, d] [d, f] -> [c, g] [g, c] [c, f] , [c, f] [f, f] -> [c, a] [a, g] [g, f] , [c, g] [g, f] -> [c, d] [d, a] [a, b] [b, f] , [c, c] [c, c] [c, a] -> [c, d] [d, d] [d, d] [d, a] , [c, c] [c, a] -> [c, g] [g, a] , [c, d] [d, d] [d, a] -> [c, c] [c, f] [f, a] , [c, d] [d, d] [d, d] [d, a] -> [c, g] [g, c] [c, a] , [c, f] [f, a] -> [c, a] [a, g] [g, a] , [c, g] [g, a] -> [c, d] [d, a] [a, b] [b, a] , [d, c] [c, c] [c, b] -> [d, d] [d, d] [d, d] [d, b] , [d, d] [d, d] [d, d] [d, b] -> [d, g] [g, c] [c, b] , [d, c] [c, c] [c, c] -> [d, d] [d, d] [d, d] [d, c] , [d, c] [c, c] -> [d, g] [g, c] , [d, d] [d, d] [d, c] -> [d, c] [c, f] [f, c] , [d, d] [d, d] [d, d] [d, c] -> [d, g] [g, c] [c, c] , [d, f] [f, c] -> [d, a] [a, g] [g, c] , [d, c] [c, c] [c, d] -> [d, d] [d, d] [d, d] [d, d] , [d, c] [c, d] -> [d, g] [g, d] , [d, d] [d, d] [d, d] -> [d, c] [c, f] [f, d] , [d, d] [d, d] [d, d] [d, d] -> [d, g] [g, c] [c, d] , [d, f] [f, d] -> [d, a] [a, g] [g, d] , [d, c] [c, c] [c, g] -> [d, d] [d, d] [d, d] [d, g] , [d, c] [c, g] -> [d, g] [g, g] , [d, d] [d, d] [d, g] -> [d, c] [c, f] [f, g] , [d, d] [d, d] [d, d] [d, g] -> [d, g] [g, c] [c, g] , [d, f] [f, g] -> [d, a] [a, g] [g, g] , [d, c] [c, c] [c, f] -> [d, d] [d, d] [d, d] [d, f] , [d, c] [c, f] -> [d, g] [g, f] , [d, d] [d, d] [d, f] -> [d, c] [c, f] [f, f] , [d, d] [d, d] [d, d] [d, f] -> [d, g] [g, c] [c, f] , [d, f] [f, f] -> [d, a] [a, g] [g, f] , [d, g] [g, f] -> [d, d] [d, a] [a, b] [b, f] , [d, c] [c, c] [c, a] -> [d, d] [d, d] [d, d] [d, a] , [d, c] [c, a] -> [d, g] [g, a] , [d, d] [d, d] [d, a] -> [d, c] [c, f] [f, a] , [d, d] [d, d] [d, d] [d, a] -> [d, g] [g, c] [c, a] , [d, f] [f, a] -> [d, a] [a, g] [g, a] , [d, g] [g, a] -> [d, d] [d, a] [a, b] [b, a] , [g, c] [c, c] [c, b] -> [g, d] [d, d] [d, d] [d, b] , [g, d] [d, d] [d, d] [d, b] -> [g, g] [g, c] [c, b] , [g, c] [c, c] [c, c] -> [g, d] [d, d] [d, d] [d, c] , [g, c] [c, c] -> [g, g] [g, c] , [g, d] [d, d] [d, c] -> [g, c] [c, f] [f, c] , [g, d] [d, d] [d, d] [d, c] -> [g, g] [g, c] [c, c] , [g, f] [f, c] -> [g, a] [a, g] [g, c] , [g, c] [c, c] [c, d] -> [g, d] [d, d] [d, d] [d, d] , [g, c] [c, d] -> [g, g] [g, d] , [g, d] [d, d] [d, d] -> [g, c] [c, f] [f, d] , [g, d] [d, d] [d, d] [d, d] -> [g, g] [g, c] [c, d] , [g, f] [f, d] -> [g, a] [a, g] [g, d] , [g, c] [c, c] [c, g] -> [g, d] [d, d] [d, d] [d, g] , [g, c] [c, g] -> [g, g] [g, g] , [g, d] [d, d] [d, g] -> [g, c] [c, f] [f, g] , [g, d] [d, d] [d, d] [d, g] -> [g, g] [g, c] [c, g] , [g, f] [f, g] -> [g, a] [a, g] [g, g] , [g, c] [c, c] [c, f] -> [g, d] [d, d] [d, d] [d, f] , [g, c] [c, f] -> [g, g] [g, f] , [g, d] [d, d] [d, f] -> [g, c] [c, f] [f, f] , [g, d] [d, d] [d, d] [d, f] -> [g, g] [g, c] [c, f] , [g, f] [f, f] -> [g, a] [a, g] [g, f] , [g, g] [g, f] -> [g, d] [d, a] [a, b] [b, f] , [g, c] [c, c] [c, a] -> [g, d] [d, d] [d, d] [d, a] , [g, c] [c, a] -> [g, g] [g, a] , [g, d] [d, d] [d, a] -> [g, c] [c, f] [f, a] , [g, d] [d, d] [d, d] [d, a] -> [g, g] [g, c] [c, a] , [g, f] [f, a] -> [g, a] [a, g] [g, a] , [g, g] [g, a] -> [g, d] [d, a] [a, b] [b, a] , [f, c] [c, c] [c, b] -> [f, d] [d, d] [d, d] [d, b] , [f, d] [d, d] [d, d] [d, b] -> [f, g] [g, c] [c, b] , [f, c] [c, c] [c, c] -> [f, d] [d, d] [d, d] [d, c] , [f, c] [c, c] -> [f, g] [g, c] , [f, d] [d, d] [d, c] -> [f, c] [c, f] [f, c] , [f, d] [d, d] [d, d] [d, c] -> [f, g] [g, c] [c, c] , [f, f] [f, c] -> [f, a] [a, g] [g, c] , [f, c] [c, c] [c, d] -> [f, d] [d, d] [d, d] [d, d] , [f, c] [c, d] -> [f, g] [g, d] , [f, d] [d, d] [d, d] -> [f, c] [c, f] [f, d] , [f, d] [d, d] [d, d] [d, d] -> [f, g] [g, c] [c, d] , [f, f] [f, d] -> [f, a] [a, g] [g, d] , [f, c] [c, c] [c, g] -> [f, d] [d, d] [d, d] [d, g] , [f, c] [c, g] -> [f, g] [g, g] , [f, d] [d, d] [d, g] -> [f, c] [c, f] [f, g] , [f, d] [d, d] [d, d] [d, g] -> [f, g] [g, c] [c, g] , [f, f] [f, g] -> [f, a] [a, g] [g, g] , [f, c] [c, c] [c, f] -> [f, d] [d, d] [d, d] [d, f] , [f, c] [c, f] -> [f, g] [g, f] , [f, d] [d, d] [d, f] -> [f, c] [c, f] [f, f] , [f, d] [d, d] [d, d] [d, f] -> [f, g] [g, c] [c, f] , [f, f] [f, f] -> [f, a] [a, g] [g, f] , [f, g] [g, f] -> [f, d] [d, a] [a, b] [b, f] , [f, c] [c, c] [c, a] -> [f, d] [d, d] [d, d] [d, a] , [f, c] [c, a] -> [f, g] [g, a] , [f, d] [d, d] [d, a] -> [f, c] [c, f] [f, a] , [f, d] [d, d] [d, d] [d, a] -> [f, g] [g, c] [c, a] , [f, f] [f, a] -> [f, a] [a, g] [g, a] , [f, g] [g, a] -> [f, d] [d, a] [a, b] [b, a] , [a, c] [c, c] [c, b] -> [a, d] [d, d] [d, d] [d, b] , [a, d] [d, d] [d, d] [d, b] -> [a, g] [g, c] [c, b] , [a, c] [c, c] [c, c] -> [a, d] [d, d] [d, d] [d, c] , [a, c] [c, c] -> [a, g] [g, c] , [a, d] [d, d] [d, c] -> [a, c] [c, f] [f, c] , [a, d] [d, d] [d, d] [d, c] -> [a, g] [g, c] [c, c] , [a, c] [c, c] [c, d] -> [a, d] [d, d] [d, d] [d, d] , [a, c] [c, d] -> [a, g] [g, d] , [a, d] [d, d] [d, d] -> [a, c] [c, f] [f, d] , [a, d] [d, d] [d, d] [d, d] -> [a, g] [g, c] [c, d] , [a, c] [c, c] [c, g] -> [a, d] [d, d] [d, d] [d, g] , [a, c] [c, g] -> [a, g] [g, g] , [a, d] [d, d] [d, g] -> [a, c] [c, f] [f, g] , [a, d] [d, d] [d, d] [d, g] -> [a, g] [g, c] [c, g] , [a, c] [c, c] [c, f] -> [a, d] [d, d] [d, d] [d, f] , [a, c] [c, f] -> [a, g] [g, f] , [a, d] [d, d] [d, f] -> [a, c] [c, f] [f, f] , [a, d] [d, d] [d, d] [d, f] -> [a, g] [g, c] [c, f] , [a, g] [g, f] -> [a, d] [d, a] [a, b] [b, f] , [a, c] [c, c] [c, a] -> [a, d] [d, d] [d, d] [d, a] , [a, c] [c, a] -> [a, g] [g, a] , [a, d] [d, d] [d, a] -> [a, c] [c, f] [f, a] , [a, d] [d, d] [d, d] [d, a] -> [a, g] [g, c] [c, a] , [a, g] [g, a] -> [a, d] [d, a] [a, b] [b, a] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [f, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, d] is interpreted by / \ | 1 5 | | 0 1 | \ / [d, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, c] is interpreted by / \ | 1 5 | | 0 1 | \ / [c, b] is interpreted by / \ | 1 2 | | 0 1 | \ / [b, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, d] is interpreted by / \ | 1 3 | | 0 1 | \ / [b, g] is interpreted by / \ | 1 2 | | 0 1 | \ / [c, f] is interpreted by / \ | 1 3 | | 0 1 | \ / [g, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, f] is interpreted by / \ | 1 2 | | 0 1 | \ / [b, a] is interpreted by / \ | 1 1 | | 0 1 | \ / [a, g] is interpreted by / \ | 1 1 | | 0 1 | \ / [d, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, g] is interpreted by / \ | 1 1 | | 0 1 | \ / [d, c] is interpreted by / \ | 1 2 | | 0 1 | \ / [f, c] is interpreted by / \ | 1 2 | | 0 1 | \ / [g, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, d] is interpreted by / \ | 1 3 | | 0 1 | \ / [d, g] is interpreted by / \ | 1 4 | | 0 1 | \ / [c, g] is interpreted by / \ | 1 7 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 4 | | 0 1 | \ / [d, f] is interpreted by / \ | 1 1 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 1 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 1 | | 0 1 | \ / [c, a] is interpreted by / \ | 1 2 | | 0 1 | \ / [g, a] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 54-rule system { [b, d] [d, d] [d, c] -> [b, c] [c, f] [f, c] , [b, d] [d, d] [d, d] -> [b, c] [c, f] [f, d] , [b, d] [d, d] [d, g] -> [b, c] [c, f] [f, g] , [b, c] [c, f] -> [b, g] [g, f] , [b, d] [d, d] [d, f] -> [b, c] [c, f] [f, f] , [b, f] [f, f] -> [b, a] [a, g] [g, f] , [b, c] [c, a] -> [b, g] [g, a] , [b, d] [d, d] [d, a] -> [b, c] [c, f] [f, a] , [b, f] [f, a] -> [b, a] [a, g] [g, a] , [c, d] [d, d] [d, c] -> [c, c] [c, f] [f, c] , [c, d] [d, d] [d, d] -> [c, c] [c, f] [f, d] , [c, d] [d, d] [d, g] -> [c, c] [c, f] [f, g] , [c, c] [c, f] -> [c, g] [g, f] , [c, d] [d, d] [d, f] -> [c, c] [c, f] [f, f] , [c, f] [f, f] -> [c, a] [a, g] [g, f] , [c, c] [c, a] -> [c, g] [g, a] , [c, d] [d, d] [d, a] -> [c, c] [c, f] [f, a] , [c, f] [f, a] -> [c, a] [a, g] [g, a] , [d, c] [c, c] [c, b] -> [d, d] [d, d] [d, d] [d, b] , [d, c] [c, c] [c, d] -> [d, d] [d, d] [d, d] [d, d] , [d, c] [c, c] [c, f] -> [d, d] [d, d] [d, d] [d, f] , [d, c] [c, f] -> [d, g] [g, f] , [d, f] [f, f] -> [d, a] [a, g] [g, f] , [d, g] [g, f] -> [d, d] [d, a] [a, b] [b, f] , [d, c] [c, c] [c, a] -> [d, d] [d, d] [d, d] [d, a] , [d, c] [c, a] -> [d, g] [g, a] , [d, f] [f, a] -> [d, a] [a, g] [g, a] , [d, g] [g, a] -> [d, d] [d, a] [a, b] [b, a] , [g, d] [d, d] [d, c] -> [g, c] [c, f] [f, c] , [g, d] [d, d] [d, d] -> [g, c] [c, f] [f, d] , [g, d] [d, d] [d, g] -> [g, c] [c, f] [f, g] , [g, d] [d, d] [d, f] -> [g, c] [c, f] [f, f] , [g, f] [f, f] -> [g, a] [a, g] [g, f] , [g, g] [g, f] -> [g, d] [d, a] [a, b] [b, f] , [g, d] [d, d] [d, a] -> [g, c] [c, f] [f, a] , [g, f] [f, a] -> [g, a] [a, g] [g, a] , [g, g] [g, a] -> [g, d] [d, a] [a, b] [b, a] , [f, c] [c, c] [c, b] -> [f, d] [d, d] [d, d] [d, b] , [f, c] [c, c] [c, d] -> [f, d] [d, d] [d, d] [d, d] , [f, c] [c, c] [c, f] -> [f, d] [d, d] [d, d] [d, f] , [f, c] [c, f] -> [f, g] [g, f] , [f, f] [f, f] -> [f, a] [a, g] [g, f] , [f, g] [g, f] -> [f, d] [d, a] [a, b] [b, f] , [f, c] [c, c] [c, a] -> [f, d] [d, d] [d, d] [d, a] , [f, c] [c, a] -> [f, g] [g, a] , [f, f] [f, a] -> [f, a] [a, g] [g, a] , [f, g] [g, a] -> [f, d] [d, a] [a, b] [b, a] , [a, d] [d, d] [d, c] -> [a, c] [c, f] [f, c] , [a, d] [d, d] [d, d] -> [a, c] [c, f] [f, d] , [a, d] [d, d] [d, g] -> [a, c] [c, f] [f, g] , [a, d] [d, d] [d, f] -> [a, c] [c, f] [f, f] , [a, g] [g, f] -> [a, d] [d, a] [a, b] [b, f] , [a, d] [d, d] [d, a] -> [a, c] [c, f] [f, a] , [a, g] [g, a] -> [a, d] [d, a] [a, b] [b, a] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [f, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, d] is interpreted by / \ | 1 1 | | 0 1 | \ / [d, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, a] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 47-rule system { [b, d] [d, d] [d, c] -> [b, c] [c, f] [f, c] , [b, d] [d, d] [d, d] -> [b, c] [c, f] [f, d] , [b, d] [d, d] [d, g] -> [b, c] [c, f] [f, g] , [b, c] [c, f] -> [b, g] [g, f] , [b, d] [d, d] [d, f] -> [b, c] [c, f] [f, f] , [b, f] [f, f] -> [b, a] [a, g] [g, f] , [b, c] [c, a] -> [b, g] [g, a] , [b, d] [d, d] [d, a] -> [b, c] [c, f] [f, a] , [b, f] [f, a] -> [b, a] [a, g] [g, a] , [c, c] [c, f] -> [c, g] [g, f] , [c, f] [f, f] -> [c, a] [a, g] [g, f] , [c, c] [c, a] -> [c, g] [g, a] , [c, f] [f, a] -> [c, a] [a, g] [g, a] , [d, c] [c, c] [c, b] -> [d, d] [d, d] [d, d] [d, b] , [d, c] [c, c] [c, f] -> [d, d] [d, d] [d, d] [d, f] , [d, c] [c, f] -> [d, g] [g, f] , [d, f] [f, f] -> [d, a] [a, g] [g, f] , [d, g] [g, f] -> [d, d] [d, a] [a, b] [b, f] , [d, c] [c, c] [c, a] -> [d, d] [d, d] [d, d] [d, a] , [d, c] [c, a] -> [d, g] [g, a] , [d, f] [f, a] -> [d, a] [a, g] [g, a] , [d, g] [g, a] -> [d, d] [d, a] [a, b] [b, a] , [g, d] [d, d] [d, c] -> [g, c] [c, f] [f, c] , [g, d] [d, d] [d, d] -> [g, c] [c, f] [f, d] , [g, d] [d, d] [d, g] -> [g, c] [c, f] [f, g] , [g, d] [d, d] [d, f] -> [g, c] [c, f] [f, f] , [g, f] [f, f] -> [g, a] [a, g] [g, f] , [g, g] [g, f] -> [g, d] [d, a] [a, b] [b, f] , [g, d] [d, d] [d, a] -> [g, c] [c, f] [f, a] , [g, f] [f, a] -> [g, a] [a, g] [g, a] , [g, g] [g, a] -> [g, d] [d, a] [a, b] [b, a] , [f, c] [c, c] [c, b] -> [f, d] [d, d] [d, d] [d, b] , [f, c] [c, c] [c, f] -> [f, d] [d, d] [d, d] [d, f] , [f, c] [c, f] -> [f, g] [g, f] , [f, f] [f, f] -> [f, a] [a, g] [g, f] , [f, g] [g, f] -> [f, d] [d, a] [a, b] [b, f] , [f, c] [c, c] [c, a] -> [f, d] [d, d] [d, d] [d, a] , [f, c] [c, a] -> [f, g] [g, a] , [f, f] [f, a] -> [f, a] [a, g] [g, a] , [f, g] [g, a] -> [f, d] [d, a] [a, b] [b, a] , [a, d] [d, d] [d, c] -> [a, c] [c, f] [f, c] , [a, d] [d, d] [d, d] -> [a, c] [c, f] [f, d] , [a, d] [d, d] [d, g] -> [a, c] [c, f] [f, g] , [a, d] [d, d] [d, f] -> [a, c] [c, f] [f, f] , [a, g] [g, f] -> [a, d] [d, a] [a, b] [b, f] , [a, d] [d, d] [d, a] -> [a, c] [c, f] [f, a] , [a, g] [g, a] -> [a, d] [d, a] [a, b] [b, a] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [f, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, c] is interpreted by / \ | 1 1 | | 0 1 | \ / [c, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, a] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 39-rule system { [b, d] [d, d] [d, c] -> [b, c] [c, f] [f, c] , [b, d] [d, d] [d, d] -> [b, c] [c, f] [f, d] , [b, d] [d, d] [d, g] -> [b, c] [c, f] [f, g] , [b, c] [c, f] -> [b, g] [g, f] , [b, d] [d, d] [d, f] -> [b, c] [c, f] [f, f] , [b, f] [f, f] -> [b, a] [a, g] [g, f] , [b, c] [c, a] -> [b, g] [g, a] , [b, d] [d, d] [d, a] -> [b, c] [c, f] [f, a] , [b, f] [f, a] -> [b, a] [a, g] [g, a] , [c, f] [f, f] -> [c, a] [a, g] [g, f] , [c, f] [f, a] -> [c, a] [a, g] [g, a] , [d, c] [c, f] -> [d, g] [g, f] , [d, f] [f, f] -> [d, a] [a, g] [g, f] , [d, g] [g, f] -> [d, d] [d, a] [a, b] [b, f] , [d, c] [c, a] -> [d, g] [g, a] , [d, f] [f, a] -> [d, a] [a, g] [g, a] , [d, g] [g, a] -> [d, d] [d, a] [a, b] [b, a] , [g, d] [d, d] [d, c] -> [g, c] [c, f] [f, c] , [g, d] [d, d] [d, d] -> [g, c] [c, f] [f, d] , [g, d] [d, d] [d, g] -> [g, c] [c, f] [f, g] , [g, d] [d, d] [d, f] -> [g, c] [c, f] [f, f] , [g, f] [f, f] -> [g, a] [a, g] [g, f] , [g, g] [g, f] -> [g, d] [d, a] [a, b] [b, f] , [g, d] [d, d] [d, a] -> [g, c] [c, f] [f, a] , [g, f] [f, a] -> [g, a] [a, g] [g, a] , [g, g] [g, a] -> [g, d] [d, a] [a, b] [b, a] , [f, c] [c, f] -> [f, g] [g, f] , [f, f] [f, f] -> [f, a] [a, g] [g, f] , [f, g] [g, f] -> [f, d] [d, a] [a, b] [b, f] , [f, c] [c, a] -> [f, g] [g, a] , [f, f] [f, a] -> [f, a] [a, g] [g, a] , [f, g] [g, a] -> [f, d] [d, a] [a, b] [b, a] , [a, d] [d, d] [d, c] -> [a, c] [c, f] [f, c] , [a, d] [d, d] [d, d] -> [a, c] [c, f] [f, d] , [a, d] [d, d] [d, g] -> [a, c] [c, f] [f, g] , [a, d] [d, d] [d, f] -> [a, c] [c, f] [f, f] , [a, g] [g, f] -> [a, d] [d, a] [a, b] [b, f] , [a, d] [d, d] [d, a] -> [a, c] [c, f] [f, a] , [a, g] [g, a] -> [a, d] [d, a] [a, b] [b, a] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [f, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, d] is interpreted by / \ | 1 1 | | 0 1 | \ / [d, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, a] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 34-rule system { [b, c] [c, f] -> [b, g] [g, f] , [b, f] [f, f] -> [b, a] [a, g] [g, f] , [b, c] [c, a] -> [b, g] [g, a] , [b, f] [f, a] -> [b, a] [a, g] [g, a] , [c, f] [f, f] -> [c, a] [a, g] [g, f] , [c, f] [f, a] -> [c, a] [a, g] [g, a] , [d, c] [c, f] -> [d, g] [g, f] , [d, f] [f, f] -> [d, a] [a, g] [g, f] , [d, g] [g, f] -> [d, d] [d, a] [a, b] [b, f] , [d, c] [c, a] -> [d, g] [g, a] , [d, f] [f, a] -> [d, a] [a, g] [g, a] , [d, g] [g, a] -> [d, d] [d, a] [a, b] [b, a] , [g, d] [d, d] [d, c] -> [g, c] [c, f] [f, c] , [g, d] [d, d] [d, d] -> [g, c] [c, f] [f, d] , [g, d] [d, d] [d, g] -> [g, c] [c, f] [f, g] , [g, d] [d, d] [d, f] -> [g, c] [c, f] [f, f] , [g, f] [f, f] -> [g, a] [a, g] [g, f] , [g, g] [g, f] -> [g, d] [d, a] [a, b] [b, f] , [g, d] [d, d] [d, a] -> [g, c] [c, f] [f, a] , [g, f] [f, a] -> [g, a] [a, g] [g, a] , [g, g] [g, a] -> [g, d] [d, a] [a, b] [b, a] , [f, c] [c, f] -> [f, g] [g, f] , [f, f] [f, f] -> [f, a] [a, g] [g, f] , [f, g] [g, f] -> [f, d] [d, a] [a, b] [b, f] , [f, c] [c, a] -> [f, g] [g, a] , [f, f] [f, a] -> [f, a] [a, g] [g, a] , [f, g] [g, a] -> [f, d] [d, a] [a, b] [b, a] , [a, d] [d, d] [d, c] -> [a, c] [c, f] [f, c] , [a, d] [d, d] [d, d] -> [a, c] [c, f] [f, d] , [a, d] [d, d] [d, g] -> [a, c] [c, f] [f, g] , [a, d] [d, d] [d, f] -> [a, c] [c, f] [f, f] , [a, g] [g, f] -> [a, d] [d, a] [a, b] [b, f] , [a, d] [d, d] [d, a] -> [a, c] [c, f] [f, a] , [a, g] [g, a] -> [a, d] [d, a] [a, b] [b, a] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [f, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, c] is interpreted by / \ | 1 1 | | 0 1 | \ / [c, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, a] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 32-rule system { [b, f] [f, f] -> [b, a] [a, g] [g, f] , [b, f] [f, a] -> [b, a] [a, g] [g, a] , [c, f] [f, f] -> [c, a] [a, g] [g, f] , [c, f] [f, a] -> [c, a] [a, g] [g, a] , [d, c] [c, f] -> [d, g] [g, f] , [d, f] [f, f] -> [d, a] [a, g] [g, f] , [d, g] [g, f] -> [d, d] [d, a] [a, b] [b, f] , [d, c] [c, a] -> [d, g] [g, a] , [d, f] [f, a] -> [d, a] [a, g] [g, a] , [d, g] [g, a] -> [d, d] [d, a] [a, b] [b, a] , [g, d] [d, d] [d, c] -> [g, c] [c, f] [f, c] , [g, d] [d, d] [d, d] -> [g, c] [c, f] [f, d] , [g, d] [d, d] [d, g] -> [g, c] [c, f] [f, g] , [g, d] [d, d] [d, f] -> [g, c] [c, f] [f, f] , [g, f] [f, f] -> [g, a] [a, g] [g, f] , [g, g] [g, f] -> [g, d] [d, a] [a, b] [b, f] , [g, d] [d, d] [d, a] -> [g, c] [c, f] [f, a] , [g, f] [f, a] -> [g, a] [a, g] [g, a] , [g, g] [g, a] -> [g, d] [d, a] [a, b] [b, a] , [f, c] [c, f] -> [f, g] [g, f] , [f, f] [f, f] -> [f, a] [a, g] [g, f] , [f, g] [g, f] -> [f, d] [d, a] [a, b] [b, f] , [f, c] [c, a] -> [f, g] [g, a] , [f, f] [f, a] -> [f, a] [a, g] [g, a] , [f, g] [g, a] -> [f, d] [d, a] [a, b] [b, a] , [a, d] [d, d] [d, c] -> [a, c] [c, f] [f, c] , [a, d] [d, d] [d, d] -> [a, c] [c, f] [f, d] , [a, d] [d, d] [d, g] -> [a, c] [c, f] [f, g] , [a, d] [d, d] [d, f] -> [a, c] [c, f] [f, f] , [a, g] [g, f] -> [a, d] [d, a] [a, b] [b, f] , [a, d] [d, d] [d, a] -> [a, c] [c, f] [f, a] , [a, g] [g, a] -> [a, d] [d, a] [a, b] [b, a] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [f, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, g] is interpreted by / \ | 1 1 | | 0 1 | \ / [d, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, a] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 30-rule system { [b, f] [f, f] -> [b, a] [a, g] [g, f] , [b, f] [f, a] -> [b, a] [a, g] [g, a] , [c, f] [f, f] -> [c, a] [a, g] [g, f] , [c, f] [f, a] -> [c, a] [a, g] [g, a] , [d, c] [c, f] -> [d, g] [g, f] , [d, f] [f, f] -> [d, a] [a, g] [g, f] , [d, g] [g, f] -> [d, d] [d, a] [a, b] [b, f] , [d, c] [c, a] -> [d, g] [g, a] , [d, f] [f, a] -> [d, a] [a, g] [g, a] , [d, g] [g, a] -> [d, d] [d, a] [a, b] [b, a] , [g, d] [d, d] [d, c] -> [g, c] [c, f] [f, c] , [g, d] [d, d] [d, d] -> [g, c] [c, f] [f, d] , [g, d] [d, d] [d, g] -> [g, c] [c, f] [f, g] , [g, d] [d, d] [d, f] -> [g, c] [c, f] [f, f] , [g, f] [f, f] -> [g, a] [a, g] [g, f] , [g, d] [d, d] [d, a] -> [g, c] [c, f] [f, a] , [g, f] [f, a] -> [g, a] [a, g] [g, a] , [f, c] [c, f] -> [f, g] [g, f] , [f, f] [f, f] -> [f, a] [a, g] [g, f] , [f, g] [g, f] -> [f, d] [d, a] [a, b] [b, f] , [f, c] [c, a] -> [f, g] [g, a] , [f, f] [f, a] -> [f, a] [a, g] [g, a] , [f, g] [g, a] -> [f, d] [d, a] [a, b] [b, a] , [a, d] [d, d] [d, c] -> [a, c] [c, f] [f, c] , [a, d] [d, d] [d, d] -> [a, c] [c, f] [f, d] , [a, d] [d, d] [d, g] -> [a, c] [c, f] [f, g] , [a, d] [d, d] [d, f] -> [a, c] [c, f] [f, f] , [a, g] [g, f] -> [a, d] [d, a] [a, b] [b, f] , [a, d] [d, d] [d, a] -> [a, c] [c, f] [f, a] , [a, g] [g, a] -> [a, d] [d, a] [a, b] [b, a] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [f, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, c] is interpreted by / \ | 1 1 | | 0 1 | \ / [f, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, a] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 26-rule system { [b, f] [f, f] -> [b, a] [a, g] [g, f] , [b, f] [f, a] -> [b, a] [a, g] [g, a] , [c, f] [f, f] -> [c, a] [a, g] [g, f] , [c, f] [f, a] -> [c, a] [a, g] [g, a] , [d, f] [f, f] -> [d, a] [a, g] [g, f] , [d, g] [g, f] -> [d, d] [d, a] [a, b] [b, f] , [d, f] [f, a] -> [d, a] [a, g] [g, a] , [d, g] [g, a] -> [d, d] [d, a] [a, b] [b, a] , [g, d] [d, d] [d, d] -> [g, c] [c, f] [f, d] , [g, d] [d, d] [d, g] -> [g, c] [c, f] [f, g] , [g, d] [d, d] [d, f] -> [g, c] [c, f] [f, f] , [g, f] [f, f] -> [g, a] [a, g] [g, f] , [g, d] [d, d] [d, a] -> [g, c] [c, f] [f, a] , [g, f] [f, a] -> [g, a] [a, g] [g, a] , [f, c] [c, f] -> [f, g] [g, f] , [f, f] [f, f] -> [f, a] [a, g] [g, f] , [f, g] [g, f] -> [f, d] [d, a] [a, b] [b, f] , [f, c] [c, a] -> [f, g] [g, a] , [f, f] [f, a] -> [f, a] [a, g] [g, a] , [f, g] [g, a] -> [f, d] [d, a] [a, b] [b, a] , [a, d] [d, d] [d, d] -> [a, c] [c, f] [f, d] , [a, d] [d, d] [d, g] -> [a, c] [c, f] [f, g] , [a, d] [d, d] [d, f] -> [a, c] [c, f] [f, f] , [a, g] [g, f] -> [a, d] [d, a] [a, b] [b, f] , [a, d] [d, d] [d, a] -> [a, c] [c, f] [f, a] , [a, g] [g, a] -> [a, d] [d, a] [a, b] [b, a] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [f, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, c] is interpreted by / \ | 1 1 | | 0 1 | \ / [g, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, a] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 24-rule system { [b, f] [f, f] -> [b, a] [a, g] [g, f] , [b, f] [f, a] -> [b, a] [a, g] [g, a] , [c, f] [f, f] -> [c, a] [a, g] [g, f] , [c, f] [f, a] -> [c, a] [a, g] [g, a] , [d, f] [f, f] -> [d, a] [a, g] [g, f] , [d, g] [g, f] -> [d, d] [d, a] [a, b] [b, f] , [d, f] [f, a] -> [d, a] [a, g] [g, a] , [d, g] [g, a] -> [d, d] [d, a] [a, b] [b, a] , [g, d] [d, d] [d, d] -> [g, c] [c, f] [f, d] , [g, d] [d, d] [d, g] -> [g, c] [c, f] [f, g] , [g, d] [d, d] [d, f] -> [g, c] [c, f] [f, f] , [g, f] [f, f] -> [g, a] [a, g] [g, f] , [g, d] [d, d] [d, a] -> [g, c] [c, f] [f, a] , [g, f] [f, a] -> [g, a] [a, g] [g, a] , [f, f] [f, f] -> [f, a] [a, g] [g, f] , [f, g] [g, f] -> [f, d] [d, a] [a, b] [b, f] , [f, f] [f, a] -> [f, a] [a, g] [g, a] , [f, g] [g, a] -> [f, d] [d, a] [a, b] [b, a] , [a, d] [d, d] [d, d] -> [a, c] [c, f] [f, d] , [a, d] [d, d] [d, g] -> [a, c] [c, f] [f, g] , [a, d] [d, d] [d, f] -> [a, c] [c, f] [f, f] , [a, g] [g, f] -> [a, d] [d, a] [a, b] [b, f] , [a, d] [d, d] [d, a] -> [a, c] [c, f] [f, a] , [a, g] [g, a] -> [a, d] [d, a] [a, b] [b, a] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [f, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, d] is interpreted by / \ | 1 1 | | 0 1 | \ / [f, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, a] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 20-rule system { [b, f] [f, f] -> [b, a] [a, g] [g, f] , [b, f] [f, a] -> [b, a] [a, g] [g, a] , [c, f] [f, f] -> [c, a] [a, g] [g, f] , [c, f] [f, a] -> [c, a] [a, g] [g, a] , [d, f] [f, f] -> [d, a] [a, g] [g, f] , [d, g] [g, f] -> [d, d] [d, a] [a, b] [b, f] , [d, f] [f, a] -> [d, a] [a, g] [g, a] , [d, g] [g, a] -> [d, d] [d, a] [a, b] [b, a] , [g, f] [f, f] -> [g, a] [a, g] [g, f] , [g, f] [f, a] -> [g, a] [a, g] [g, a] , [f, f] [f, f] -> [f, a] [a, g] [g, f] , [f, g] [g, f] -> [f, d] [d, a] [a, b] [b, f] , [f, f] [f, a] -> [f, a] [a, g] [g, a] , [f, g] [g, a] -> [f, d] [d, a] [a, b] [b, a] , [a, d] [d, d] [d, d] -> [a, c] [c, f] [f, d] , [a, d] [d, d] [d, g] -> [a, c] [c, f] [f, g] , [a, d] [d, d] [d, f] -> [a, c] [c, f] [f, f] , [a, g] [g, f] -> [a, d] [d, a] [a, b] [b, f] , [a, d] [d, d] [d, a] -> [a, c] [c, f] [f, a] , [a, g] [g, a] -> [a, d] [d, a] [a, b] [b, a] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [f, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, g] is interpreted by / \ | 1 1 | | 0 1 | \ / [c, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, a] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 17-rule system { [b, f] [f, f] -> [b, a] [a, g] [g, f] , [b, f] [f, a] -> [b, a] [a, g] [g, a] , [c, f] [f, f] -> [c, a] [a, g] [g, f] , [c, f] [f, a] -> [c, a] [a, g] [g, a] , [d, f] [f, f] -> [d, a] [a, g] [g, f] , [d, f] [f, a] -> [d, a] [a, g] [g, a] , [g, f] [f, f] -> [g, a] [a, g] [g, f] , [g, f] [f, a] -> [g, a] [a, g] [g, a] , [f, f] [f, f] -> [f, a] [a, g] [g, f] , [f, g] [g, f] -> [f, d] [d, a] [a, b] [b, f] , [f, f] [f, a] -> [f, a] [a, g] [g, a] , [f, g] [g, a] -> [f, d] [d, a] [a, b] [b, a] , [a, d] [d, d] [d, d] -> [a, c] [c, f] [f, d] , [a, d] [d, d] [d, f] -> [a, c] [c, f] [f, f] , [a, g] [g, f] -> [a, d] [d, a] [a, b] [b, f] , [a, d] [d, d] [d, a] -> [a, c] [c, f] [f, a] , [a, g] [g, a] -> [a, d] [d, a] [a, b] [b, a] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [f, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, d] is interpreted by / \ | 1 1 | | 0 1 | \ / [b, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, a] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 14-rule system { [b, f] [f, f] -> [b, a] [a, g] [g, f] , [b, f] [f, a] -> [b, a] [a, g] [g, a] , [c, f] [f, f] -> [c, a] [a, g] [g, f] , [c, f] [f, a] -> [c, a] [a, g] [g, a] , [d, f] [f, f] -> [d, a] [a, g] [g, f] , [d, f] [f, a] -> [d, a] [a, g] [g, a] , [g, f] [f, f] -> [g, a] [a, g] [g, f] , [g, f] [f, a] -> [g, a] [a, g] [g, a] , [f, f] [f, f] -> [f, a] [a, g] [g, f] , [f, g] [g, f] -> [f, d] [d, a] [a, b] [b, f] , [f, f] [f, a] -> [f, a] [a, g] [g, a] , [f, g] [g, a] -> [f, d] [d, a] [a, b] [b, a] , [a, g] [g, f] -> [a, d] [d, a] [a, b] [b, f] , [a, g] [g, a] -> [a, d] [d, a] [a, b] [b, a] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [f, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, f] is interpreted by / \ | 1 1 | | 0 1 | \ / [f, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, a] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 12-rule system { [b, f] [f, f] -> [b, a] [a, g] [g, f] , [b, f] [f, a] -> [b, a] [a, g] [g, a] , [d, f] [f, f] -> [d, a] [a, g] [g, f] , [d, f] [f, a] -> [d, a] [a, g] [g, a] , [g, f] [f, f] -> [g, a] [a, g] [g, f] , [g, f] [f, a] -> [g, a] [a, g] [g, a] , [f, f] [f, f] -> [f, a] [a, g] [g, f] , [f, g] [g, f] -> [f, d] [d, a] [a, b] [b, f] , [f, f] [f, a] -> [f, a] [a, g] [g, a] , [f, g] [g, a] -> [f, d] [d, a] [a, b] [b, a] , [a, g] [g, f] -> [a, d] [d, a] [a, b] [b, f] , [a, g] [g, a] -> [a, d] [d, a] [a, b] [b, a] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [f, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 1 | | 0 1 | \ / [d, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, a] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 10-rule system { [b, f] [f, f] -> [b, a] [a, g] [g, f] , [b, f] [f, a] -> [b, a] [a, g] [g, a] , [d, f] [f, f] -> [d, a] [a, g] [g, f] , [d, f] [f, a] -> [d, a] [a, g] [g, a] , [g, f] [f, f] -> [g, a] [a, g] [g, f] , [g, f] [f, a] -> [g, a] [a, g] [g, a] , [f, f] [f, f] -> [f, a] [a, g] [g, f] , [f, f] [f, a] -> [f, a] [a, g] [g, a] , [a, g] [g, f] -> [a, d] [d, a] [a, b] [b, f] , [a, g] [g, a] -> [a, d] [d, a] [a, b] [b, a] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [f, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, f] is interpreted by / \ | 1 1 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, a] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 8-rule system { [b, f] [f, f] -> [b, a] [a, g] [g, f] , [b, f] [f, a] -> [b, a] [a, g] [g, a] , [g, f] [f, f] -> [g, a] [a, g] [g, f] , [g, f] [f, a] -> [g, a] [a, g] [g, a] , [f, f] [f, f] -> [f, a] [a, g] [g, f] , [f, f] [f, a] -> [f, a] [a, g] [g, a] , [a, g] [g, f] -> [a, d] [d, a] [a, b] [b, f] , [a, g] [g, a] -> [a, d] [d, a] [a, b] [b, a] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [f, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 1 | | 0 1 | \ / [c, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, a] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 4-rule system { [b, f] [f, a] -> [b, a] [a, g] [g, a] , [g, f] [f, a] -> [g, a] [a, g] [g, a] , [a, g] [g, f] -> [a, d] [d, a] [a, b] [b, f] , [a, g] [g, a] -> [a, d] [d, a] [a, b] [b, a] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [f, a] is interpreted by / \ | 1 1 | | 0 1 | \ / [a, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, a] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 2-rule system { [a, g] [g, f] -> [a, d] [d, a] [a, b] [b, f] , [a, g] [g, a] -> [a, d] [d, a] [a, b] [b, a] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [f, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, g] is interpreted by / \ | 1 1 | | 0 1 | \ / [d, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, a] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 0-rule system { } The system is trivially terminating.