/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Applying context closure of depth 1 in the following form: System R over Sigma maps to { fold(xly) -> fold(xry) | l -> r in R, x,y in Sigma } over Sigma^2, where fold(a_1,...,a_n) = (a_1,a_2)...(a_{n-1}a_{n}) Remains to prove termination of the 392-rule system { [p, p] [p, 0] [0, p] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, g] [g, p] -> [p, f] [f, p] [p, p] [p, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, i] [i, p] -> [p, s] [s, p] , [p, p] [p, 0] [0, 0] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, g] [g, 0] -> [p, f] [f, p] [p, p] [p, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, i] [i, 0] -> [p, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, i] [i, s] -> [p, s] [s, s] , [p, p] [p, 0] [0, f] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, g] [g, f] -> [p, f] [f, p] [p, p] [p, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, i] [i, f] -> [p, s] [s, f] , [p, p] [p, 0] [0, g] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, g] [g, g] -> [p, f] [f, p] [p, p] [p, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, i] [i, g] -> [p, s] [s, g] , [p, p] [p, 0] [0, q] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, q] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, f] [f, s] [s, q] -> [p, g] [g, q] [q, i] [i, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, i] [i, q] -> [p, s] [s, q] , [p, p] [p, 0] [0, i] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, i] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, f] [f, s] [s, i] -> [p, g] [g, q] [q, i] [i, i] , [p, g] [g, i] -> [p, f] [f, p] [p, p] [p, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [p, i] [i, i] -> [p, s] [s, i] , [0, p] [p, 0] [0, p] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [0, p] [p, s] [s, 0] [0, p] -> [0, 0] [0, p] , [0, p] [p, s] [s, s] [s, p] -> [0, s] [s, p] [p, s] [s, p] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, g] [g, p] -> [0, f] [f, p] [p, p] [p, p] , [0, q] [q, i] [i, p] -> [0, q] [q, s] [s, p] , [0, q] [q, s] [s, p] -> [0, s] [s, s] [s, p] , [0, i] [i, p] -> [0, s] [s, p] , [0, p] [p, 0] [0, 0] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [0, p] [p, s] [s, 0] [0, 0] -> [0, 0] [0, 0] , [0, p] [p, s] [s, s] [s, 0] -> [0, s] [s, p] [p, s] [s, 0] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, g] [g, 0] -> [0, f] [f, p] [p, p] [p, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, q] [q, s] [s, 0] -> [0, s] [s, s] [s, 0] , [0, i] [i, 0] -> [0, s] [s, 0] , [0, p] [p, 0] [0, s] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [0, p] [p, s] [s, 0] [0, s] -> [0, 0] [0, s] , [0, p] [p, s] [s, s] [s, s] -> [0, s] [s, p] [p, s] [s, s] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, q] [q, s] [s, s] -> [0, s] [s, s] [s, s] , [0, i] [i, s] -> [0, s] [s, s] , [0, p] [p, 0] [0, f] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [0, p] [p, s] [s, 0] [0, f] -> [0, 0] [0, f] , [0, p] [p, s] [s, s] [s, f] -> [0, s] [s, p] [p, s] [s, f] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, g] [g, f] -> [0, f] [f, p] [p, p] [p, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, q] [q, s] [s, f] -> [0, s] [s, s] [s, f] , [0, i] [i, f] -> [0, s] [s, f] , [0, p] [p, 0] [0, g] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [0, p] [p, s] [s, 0] [0, g] -> [0, 0] [0, g] , [0, p] [p, s] [s, s] [s, g] -> [0, s] [s, p] [p, s] [s, g] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, g] [g, g] -> [0, f] [f, p] [p, p] [p, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, q] [q, s] [s, g] -> [0, s] [s, s] [s, g] , [0, i] [i, g] -> [0, s] [s, g] , [0, p] [p, 0] [0, q] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, q] , [0, p] [p, s] [s, 0] [0, q] -> [0, 0] [0, q] , [0, p] [p, s] [s, s] [s, q] -> [0, s] [s, p] [p, s] [s, q] , [0, f] [f, s] [s, q] -> [0, g] [g, q] [q, i] [i, q] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [0, q] [q, i] [i, q] -> [0, q] [q, s] [s, q] , [0, q] [q, s] [s, q] -> [0, s] [s, s] [s, q] , [0, i] [i, q] -> [0, s] [s, q] , [0, p] [p, 0] [0, i] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, i] , [0, p] [p, s] [s, 0] [0, i] -> [0, 0] [0, i] , [0, p] [p, s] [s, s] [s, i] -> [0, s] [s, p] [p, s] [s, i] , [0, f] [f, s] [s, i] -> [0, g] [g, q] [q, i] [i, i] , [0, g] [g, i] -> [0, f] [f, p] [p, p] [p, i] , [0, q] [q, i] [i, i] -> [0, q] [q, s] [s, i] , [0, q] [q, s] [s, i] -> [0, s] [s, s] [s, i] , [0, i] [i, i] -> [0, s] [s, i] , [s, p] [p, 0] [0, p] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, g] [g, p] -> [s, f] [f, p] [p, p] [p, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, q] [q, s] [s, p] -> [s, s] [s, s] [s, p] , [s, i] [i, p] -> [s, s] [s, p] , [s, p] [p, 0] [0, 0] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, g] [g, 0] -> [s, f] [f, p] [p, p] [p, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, q] [q, s] [s, 0] -> [s, s] [s, s] [s, 0] , [s, i] [i, 0] -> [s, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, q] [q, s] [s, s] -> [s, s] [s, s] [s, s] , [s, i] [i, s] -> [s, s] [s, s] , [s, p] [p, 0] [0, f] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, g] [g, f] -> [s, f] [f, p] [p, p] [p, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, q] [q, s] [s, f] -> [s, s] [s, s] [s, f] , [s, i] [i, f] -> [s, s] [s, f] , [s, p] [p, 0] [0, g] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, g] [g, g] -> [s, f] [f, p] [p, p] [p, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, q] [q, s] [s, g] -> [s, s] [s, s] [s, g] , [s, i] [i, g] -> [s, s] [s, g] , [s, p] [p, 0] [0, q] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, q] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, q] [q, s] [s, q] -> [s, s] [s, s] [s, q] , [s, i] [i, q] -> [s, s] [s, q] , [s, p] [p, 0] [0, i] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, i] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, g] [g, i] -> [s, f] [f, p] [p, p] [p, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [s, q] [q, s] [s, i] -> [s, s] [s, s] [s, i] , [s, i] [i, i] -> [s, s] [s, i] , [f, p] [p, 0] [0, p] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [f, p] [p, s] [s, 0] [0, p] -> [f, 0] [0, p] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, g] [g, p] -> [f, f] [f, p] [p, p] [p, p] , [f, q] [q, i] [i, p] -> [f, q] [q, s] [s, p] , [f, q] [q, s] [s, p] -> [f, s] [s, s] [s, p] , [f, i] [i, p] -> [f, s] [s, p] , [f, p] [p, 0] [0, 0] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [f, p] [p, s] [s, 0] [0, 0] -> [f, 0] [0, 0] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, g] [g, 0] -> [f, f] [f, p] [p, p] [p, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, q] [q, s] [s, 0] -> [f, s] [s, s] [s, 0] , [f, i] [i, 0] -> [f, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, 0] [0, s] -> [f, 0] [0, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, q] [q, s] [s, s] -> [f, s] [s, s] [s, s] , [f, i] [i, s] -> [f, s] [s, s] , [f, p] [p, 0] [0, f] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [f, p] [p, s] [s, 0] [0, f] -> [f, 0] [0, f] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, g] [g, f] -> [f, f] [f, p] [p, p] [p, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, q] [q, s] [s, f] -> [f, s] [s, s] [s, f] , [f, i] [i, f] -> [f, s] [s, f] , [f, p] [p, 0] [0, g] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [f, p] [p, s] [s, 0] [0, g] -> [f, 0] [0, g] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, g] [g, g] -> [f, f] [f, p] [p, p] [p, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, q] [q, s] [s, g] -> [f, s] [s, s] [s, g] , [f, i] [i, g] -> [f, s] [s, g] , [f, p] [p, 0] [0, q] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, q] , [f, p] [p, s] [s, 0] [0, q] -> [f, 0] [0, q] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, f] [f, s] [s, q] -> [f, g] [g, q] [q, i] [i, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, q] [q, i] [i, q] -> [f, q] [q, s] [s, q] , [f, q] [q, s] [s, q] -> [f, s] [s, s] [s, q] , [f, i] [i, q] -> [f, s] [s, q] , [f, p] [p, 0] [0, i] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, i] , [f, p] [p, s] [s, 0] [0, i] -> [f, 0] [0, i] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [f, f] [f, s] [s, i] -> [f, g] [g, q] [q, i] [i, i] , [f, g] [g, i] -> [f, f] [f, p] [p, p] [p, i] , [f, q] [q, i] [i, i] -> [f, q] [q, s] [s, i] , [f, q] [q, s] [s, i] -> [f, s] [s, s] [s, i] , [f, i] [i, i] -> [f, s] [s, i] , [g, p] [p, 0] [0, p] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [g, p] [p, s] [s, 0] [0, p] -> [g, 0] [0, p] , [g, p] [p, s] [s, s] [s, p] -> [g, s] [s, p] [p, s] [s, p] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, g] [g, p] -> [g, f] [f, p] [p, p] [p, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, i] [i, p] -> [g, s] [s, p] , [g, p] [p, 0] [0, 0] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [g, p] [p, s] [s, 0] [0, 0] -> [g, 0] [0, 0] , [g, p] [p, s] [s, s] [s, 0] -> [g, s] [s, p] [p, s] [s, 0] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, g] [g, 0] -> [g, f] [f, p] [p, p] [p, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, i] [i, 0] -> [g, s] [s, 0] , [g, p] [p, 0] [0, s] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [g, p] [p, s] [s, 0] [0, s] -> [g, 0] [0, s] , [g, p] [p, s] [s, s] [s, s] -> [g, s] [s, p] [p, s] [s, s] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, i] [i, s] -> [g, s] [s, s] , [g, p] [p, 0] [0, f] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [g, p] [p, s] [s, 0] [0, f] -> [g, 0] [0, f] , [g, p] [p, s] [s, s] [s, f] -> [g, s] [s, p] [p, s] [s, f] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, g] [g, f] -> [g, f] [f, p] [p, p] [p, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, i] [i, f] -> [g, s] [s, f] , [g, p] [p, 0] [0, g] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [g, p] [p, s] [s, 0] [0, g] -> [g, 0] [0, g] , [g, p] [p, s] [s, s] [s, g] -> [g, s] [s, p] [p, s] [s, g] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, g] [g, g] -> [g, f] [f, p] [p, p] [p, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, i] [i, g] -> [g, s] [s, g] , [g, p] [p, 0] [0, q] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, q] , [g, p] [p, s] [s, 0] [0, q] -> [g, 0] [0, q] , [g, p] [p, s] [s, s] [s, q] -> [g, s] [s, p] [p, s] [s, q] , [g, f] [f, s] [s, q] -> [g, g] [g, q] [q, i] [i, q] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, i] [i, q] -> [g, s] [s, q] , [g, p] [p, 0] [0, i] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, i] , [g, p] [p, s] [s, 0] [0, i] -> [g, 0] [0, i] , [g, p] [p, s] [s, s] [s, i] -> [g, s] [s, p] [p, s] [s, i] , [g, f] [f, s] [s, i] -> [g, g] [g, q] [q, i] [i, i] , [g, g] [g, i] -> [g, f] [f, p] [p, p] [p, i] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [g, i] [i, i] -> [g, s] [s, i] , [q, p] [p, 0] [0, p] -> [q, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [q, p] [p, s] [s, 0] [0, p] -> [q, 0] [0, p] , [q, p] [p, s] [s, s] [s, p] -> [q, s] [s, p] [p, s] [s, p] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, g] [g, p] -> [q, f] [f, p] [p, p] [p, p] , [q, q] [q, i] [i, p] -> [q, q] [q, s] [s, p] , [q, q] [q, s] [s, p] -> [q, s] [s, s] [s, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, p] [p, 0] [0, 0] -> [q, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [q, p] [p, s] [s, 0] [0, 0] -> [q, 0] [0, 0] , [q, p] [p, s] [s, s] [s, 0] -> [q, s] [s, p] [p, s] [s, 0] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, g] [g, 0] -> [q, f] [f, p] [p, p] [p, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, q] [q, s] [s, 0] -> [q, s] [s, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, p] [p, 0] [0, s] -> [q, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [q, p] [p, s] [s, 0] [0, s] -> [q, 0] [0, s] , [q, p] [p, s] [s, s] [s, s] -> [q, s] [s, p] [p, s] [s, s] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, q] [q, s] [s, s] -> [q, s] [s, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, p] [p, 0] [0, f] -> [q, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [q, p] [p, s] [s, 0] [0, f] -> [q, 0] [0, f] , [q, p] [p, s] [s, s] [s, f] -> [q, s] [s, p] [p, s] [s, f] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, g] [g, f] -> [q, f] [f, p] [p, p] [p, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, q] [q, s] [s, f] -> [q, s] [s, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, p] [p, 0] [0, g] -> [q, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [q, p] [p, s] [s, 0] [0, g] -> [q, 0] [0, g] , [q, p] [p, s] [s, s] [s, g] -> [q, s] [s, p] [p, s] [s, g] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, g] [g, g] -> [q, f] [f, p] [p, p] [p, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, q] [q, s] [s, g] -> [q, s] [s, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, p] [p, 0] [0, q] -> [q, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, q] , [q, p] [p, s] [s, 0] [0, q] -> [q, 0] [0, q] , [q, p] [p, s] [s, s] [s, q] -> [q, s] [s, p] [p, s] [s, q] , [q, f] [f, s] [s, q] -> [q, g] [g, q] [q, i] [i, q] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, q] [q, i] [i, q] -> [q, q] [q, s] [s, q] , [q, q] [q, s] [s, q] -> [q, s] [s, s] [s, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, p] [p, 0] [0, i] -> [q, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, i] , [q, p] [p, s] [s, 0] [0, i] -> [q, 0] [0, i] , [q, p] [p, s] [s, s] [s, i] -> [q, s] [s, p] [p, s] [s, i] , [q, f] [f, s] [s, i] -> [q, g] [g, q] [q, i] [i, i] , [q, g] [g, i] -> [q, f] [f, p] [p, p] [p, i] , [q, q] [q, i] [i, i] -> [q, q] [q, s] [s, i] , [q, q] [q, s] [s, i] -> [q, s] [s, s] [s, i] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, 0] [0, p] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, g] [g, p] -> [i, f] [f, p] [p, p] [p, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, q] [q, s] [s, p] -> [i, s] [s, s] [s, p] , [i, i] [i, p] -> [i, s] [s, p] , [i, p] [p, 0] [0, 0] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, g] [g, 0] -> [i, f] [f, p] [p, p] [p, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, q] [q, s] [s, 0] -> [i, s] [s, s] [s, 0] , [i, i] [i, 0] -> [i, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, q] [q, s] [s, s] -> [i, s] [s, s] [s, s] , [i, i] [i, s] -> [i, s] [s, s] , [i, p] [p, 0] [0, f] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, g] [g, f] -> [i, f] [f, p] [p, p] [p, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, q] [q, s] [s, f] -> [i, s] [s, s] [s, f] , [i, i] [i, f] -> [i, s] [s, f] , [i, p] [p, 0] [0, g] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, g] [g, g] -> [i, f] [f, p] [p, p] [p, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, q] [q, s] [s, g] -> [i, s] [s, s] [s, g] , [i, i] [i, g] -> [i, s] [s, g] , [i, p] [p, 0] [0, q] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, q] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, q] [q, s] [s, q] -> [i, s] [s, s] [s, q] , [i, i] [i, q] -> [i, s] [s, q] , [i, p] [p, 0] [0, i] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, i] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, g] [g, i] -> [i, f] [f, p] [p, p] [p, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] , [i, q] [q, s] [s, i] -> [i, s] [s, s] [s, i] , [i, i] [i, i] -> [i, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, q] is interpreted by / \ | 1 1 | | 0 1 | \ / [s, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, g] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 378-rule system { [p, p] [p, 0] [0, p] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, g] [g, p] -> [p, f] [f, p] [p, p] [p, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, i] [i, p] -> [p, s] [s, p] , [p, p] [p, 0] [0, 0] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, g] [g, 0] -> [p, f] [f, p] [p, p] [p, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, i] [i, 0] -> [p, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, i] [i, s] -> [p, s] [s, s] , [p, p] [p, 0] [0, f] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, g] [g, f] -> [p, f] [f, p] [p, p] [p, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, i] [i, f] -> [p, s] [s, f] , [p, p] [p, 0] [0, g] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, g] [g, g] -> [p, f] [f, p] [p, p] [p, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, i] [i, g] -> [p, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, f] [f, s] [s, q] -> [p, g] [g, q] [q, i] [i, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, i] [i, q] -> [p, s] [s, q] , [p, p] [p, 0] [0, i] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, i] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, f] [f, s] [s, i] -> [p, g] [g, q] [q, i] [i, i] , [p, g] [g, i] -> [p, f] [f, p] [p, p] [p, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [p, i] [i, i] -> [p, s] [s, i] , [0, p] [p, 0] [0, p] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [0, p] [p, s] [s, 0] [0, p] -> [0, 0] [0, p] , [0, p] [p, s] [s, s] [s, p] -> [0, s] [s, p] [p, s] [s, p] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, g] [g, p] -> [0, f] [f, p] [p, p] [p, p] , [0, q] [q, i] [i, p] -> [0, q] [q, s] [s, p] , [0, i] [i, p] -> [0, s] [s, p] , [0, p] [p, 0] [0, 0] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [0, p] [p, s] [s, 0] [0, 0] -> [0, 0] [0, 0] , [0, p] [p, s] [s, s] [s, 0] -> [0, s] [s, p] [p, s] [s, 0] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, g] [g, 0] -> [0, f] [f, p] [p, p] [p, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, i] [i, 0] -> [0, s] [s, 0] , [0, p] [p, 0] [0, s] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [0, p] [p, s] [s, 0] [0, s] -> [0, 0] [0, s] , [0, p] [p, s] [s, s] [s, s] -> [0, s] [s, p] [p, s] [s, s] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, i] [i, s] -> [0, s] [s, s] , [0, p] [p, 0] [0, f] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [0, p] [p, s] [s, 0] [0, f] -> [0, 0] [0, f] , [0, p] [p, s] [s, s] [s, f] -> [0, s] [s, p] [p, s] [s, f] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, g] [g, f] -> [0, f] [f, p] [p, p] [p, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, i] [i, f] -> [0, s] [s, f] , [0, p] [p, 0] [0, g] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [0, p] [p, s] [s, 0] [0, g] -> [0, 0] [0, g] , [0, p] [p, s] [s, s] [s, g] -> [0, s] [s, p] [p, s] [s, g] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, g] [g, g] -> [0, f] [f, p] [p, p] [p, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, i] [i, g] -> [0, s] [s, g] , [0, p] [p, s] [s, 0] [0, q] -> [0, 0] [0, q] , [0, p] [p, s] [s, s] [s, q] -> [0, s] [s, p] [p, s] [s, q] , [0, f] [f, s] [s, q] -> [0, g] [g, q] [q, i] [i, q] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [0, q] [q, i] [i, q] -> [0, q] [q, s] [s, q] , [0, i] [i, q] -> [0, s] [s, q] , [0, p] [p, 0] [0, i] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, i] , [0, p] [p, s] [s, 0] [0, i] -> [0, 0] [0, i] , [0, p] [p, s] [s, s] [s, i] -> [0, s] [s, p] [p, s] [s, i] , [0, f] [f, s] [s, i] -> [0, g] [g, q] [q, i] [i, i] , [0, g] [g, i] -> [0, f] [f, p] [p, p] [p, i] , [0, q] [q, i] [i, i] -> [0, q] [q, s] [s, i] , [0, i] [i, i] -> [0, s] [s, i] , [s, p] [p, 0] [0, p] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, g] [g, p] -> [s, f] [f, p] [p, p] [p, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, q] [q, s] [s, p] -> [s, s] [s, s] [s, p] , [s, i] [i, p] -> [s, s] [s, p] , [s, p] [p, 0] [0, 0] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, g] [g, 0] -> [s, f] [f, p] [p, p] [p, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, q] [q, s] [s, 0] -> [s, s] [s, s] [s, 0] , [s, i] [i, 0] -> [s, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, q] [q, s] [s, s] -> [s, s] [s, s] [s, s] , [s, i] [i, s] -> [s, s] [s, s] , [s, p] [p, 0] [0, f] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, g] [g, f] -> [s, f] [f, p] [p, p] [p, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, q] [q, s] [s, f] -> [s, s] [s, s] [s, f] , [s, i] [i, f] -> [s, s] [s, f] , [s, p] [p, 0] [0, g] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, g] [g, g] -> [s, f] [f, p] [p, p] [p, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, q] [q, s] [s, g] -> [s, s] [s, s] [s, g] , [s, i] [i, g] -> [s, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, q] [q, s] [s, q] -> [s, s] [s, s] [s, q] , [s, i] [i, q] -> [s, s] [s, q] , [s, p] [p, 0] [0, i] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, i] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, g] [g, i] -> [s, f] [f, p] [p, p] [p, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [s, q] [q, s] [s, i] -> [s, s] [s, s] [s, i] , [s, i] [i, i] -> [s, s] [s, i] , [f, p] [p, 0] [0, p] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [f, p] [p, s] [s, 0] [0, p] -> [f, 0] [0, p] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, g] [g, p] -> [f, f] [f, p] [p, p] [p, p] , [f, q] [q, i] [i, p] -> [f, q] [q, s] [s, p] , [f, q] [q, s] [s, p] -> [f, s] [s, s] [s, p] , [f, i] [i, p] -> [f, s] [s, p] , [f, p] [p, 0] [0, 0] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [f, p] [p, s] [s, 0] [0, 0] -> [f, 0] [0, 0] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, g] [g, 0] -> [f, f] [f, p] [p, p] [p, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, q] [q, s] [s, 0] -> [f, s] [s, s] [s, 0] , [f, i] [i, 0] -> [f, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, 0] [0, s] -> [f, 0] [0, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, q] [q, s] [s, s] -> [f, s] [s, s] [s, s] , [f, i] [i, s] -> [f, s] [s, s] , [f, p] [p, 0] [0, f] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [f, p] [p, s] [s, 0] [0, f] -> [f, 0] [0, f] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, g] [g, f] -> [f, f] [f, p] [p, p] [p, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, q] [q, s] [s, f] -> [f, s] [s, s] [s, f] , [f, i] [i, f] -> [f, s] [s, f] , [f, p] [p, 0] [0, g] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [f, p] [p, s] [s, 0] [0, g] -> [f, 0] [0, g] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, g] [g, g] -> [f, f] [f, p] [p, p] [p, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, q] [q, s] [s, g] -> [f, s] [s, s] [s, g] , [f, i] [i, g] -> [f, s] [s, g] , [f, p] [p, s] [s, 0] [0, q] -> [f, 0] [0, q] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, f] [f, s] [s, q] -> [f, g] [g, q] [q, i] [i, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, q] [q, i] [i, q] -> [f, q] [q, s] [s, q] , [f, q] [q, s] [s, q] -> [f, s] [s, s] [s, q] , [f, i] [i, q] -> [f, s] [s, q] , [f, p] [p, 0] [0, i] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, i] , [f, p] [p, s] [s, 0] [0, i] -> [f, 0] [0, i] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [f, f] [f, s] [s, i] -> [f, g] [g, q] [q, i] [i, i] , [f, g] [g, i] -> [f, f] [f, p] [p, p] [p, i] , [f, q] [q, i] [i, i] -> [f, q] [q, s] [s, i] , [f, q] [q, s] [s, i] -> [f, s] [s, s] [s, i] , [f, i] [i, i] -> [f, s] [s, i] , [g, p] [p, 0] [0, p] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [g, p] [p, s] [s, 0] [0, p] -> [g, 0] [0, p] , [g, p] [p, s] [s, s] [s, p] -> [g, s] [s, p] [p, s] [s, p] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, g] [g, p] -> [g, f] [f, p] [p, p] [p, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, i] [i, p] -> [g, s] [s, p] , [g, p] [p, 0] [0, 0] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [g, p] [p, s] [s, 0] [0, 0] -> [g, 0] [0, 0] , [g, p] [p, s] [s, s] [s, 0] -> [g, s] [s, p] [p, s] [s, 0] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, g] [g, 0] -> [g, f] [f, p] [p, p] [p, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, i] [i, 0] -> [g, s] [s, 0] , [g, p] [p, 0] [0, s] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [g, p] [p, s] [s, 0] [0, s] -> [g, 0] [0, s] , [g, p] [p, s] [s, s] [s, s] -> [g, s] [s, p] [p, s] [s, s] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, i] [i, s] -> [g, s] [s, s] , [g, p] [p, 0] [0, f] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [g, p] [p, s] [s, 0] [0, f] -> [g, 0] [0, f] , [g, p] [p, s] [s, s] [s, f] -> [g, s] [s, p] [p, s] [s, f] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, g] [g, f] -> [g, f] [f, p] [p, p] [p, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, i] [i, f] -> [g, s] [s, f] , [g, p] [p, 0] [0, g] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [g, p] [p, s] [s, 0] [0, g] -> [g, 0] [0, g] , [g, p] [p, s] [s, s] [s, g] -> [g, s] [s, p] [p, s] [s, g] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, g] [g, g] -> [g, f] [f, p] [p, p] [p, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, i] [i, g] -> [g, s] [s, g] , [g, p] [p, s] [s, 0] [0, q] -> [g, 0] [0, q] , [g, p] [p, s] [s, s] [s, q] -> [g, s] [s, p] [p, s] [s, q] , [g, f] [f, s] [s, q] -> [g, g] [g, q] [q, i] [i, q] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, i] [i, q] -> [g, s] [s, q] , [g, p] [p, 0] [0, i] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, i] , [g, p] [p, s] [s, 0] [0, i] -> [g, 0] [0, i] , [g, p] [p, s] [s, s] [s, i] -> [g, s] [s, p] [p, s] [s, i] , [g, f] [f, s] [s, i] -> [g, g] [g, q] [q, i] [i, i] , [g, g] [g, i] -> [g, f] [f, p] [p, p] [p, i] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [g, i] [i, i] -> [g, s] [s, i] , [q, p] [p, 0] [0, p] -> [q, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [q, p] [p, s] [s, 0] [0, p] -> [q, 0] [0, p] , [q, p] [p, s] [s, s] [s, p] -> [q, s] [s, p] [p, s] [s, p] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, g] [g, p] -> [q, f] [f, p] [p, p] [p, p] , [q, q] [q, i] [i, p] -> [q, q] [q, s] [s, p] , [q, q] [q, s] [s, p] -> [q, s] [s, s] [s, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, p] [p, 0] [0, 0] -> [q, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [q, p] [p, s] [s, 0] [0, 0] -> [q, 0] [0, 0] , [q, p] [p, s] [s, s] [s, 0] -> [q, s] [s, p] [p, s] [s, 0] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, g] [g, 0] -> [q, f] [f, p] [p, p] [p, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, q] [q, s] [s, 0] -> [q, s] [s, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, p] [p, 0] [0, s] -> [q, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [q, p] [p, s] [s, 0] [0, s] -> [q, 0] [0, s] , [q, p] [p, s] [s, s] [s, s] -> [q, s] [s, p] [p, s] [s, s] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, q] [q, s] [s, s] -> [q, s] [s, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, p] [p, 0] [0, f] -> [q, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [q, p] [p, s] [s, 0] [0, f] -> [q, 0] [0, f] , [q, p] [p, s] [s, s] [s, f] -> [q, s] [s, p] [p, s] [s, f] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, g] [g, f] -> [q, f] [f, p] [p, p] [p, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, q] [q, s] [s, f] -> [q, s] [s, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, p] [p, 0] [0, g] -> [q, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [q, p] [p, s] [s, 0] [0, g] -> [q, 0] [0, g] , [q, p] [p, s] [s, s] [s, g] -> [q, s] [s, p] [p, s] [s, g] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, g] [g, g] -> [q, f] [f, p] [p, p] [p, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, q] [q, s] [s, g] -> [q, s] [s, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, p] [p, s] [s, 0] [0, q] -> [q, 0] [0, q] , [q, p] [p, s] [s, s] [s, q] -> [q, s] [s, p] [p, s] [s, q] , [q, f] [f, s] [s, q] -> [q, g] [g, q] [q, i] [i, q] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, q] [q, i] [i, q] -> [q, q] [q, s] [s, q] , [q, q] [q, s] [s, q] -> [q, s] [s, s] [s, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, p] [p, 0] [0, i] -> [q, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, i] , [q, p] [p, s] [s, 0] [0, i] -> [q, 0] [0, i] , [q, p] [p, s] [s, s] [s, i] -> [q, s] [s, p] [p, s] [s, i] , [q, f] [f, s] [s, i] -> [q, g] [g, q] [q, i] [i, i] , [q, g] [g, i] -> [q, f] [f, p] [p, p] [p, i] , [q, q] [q, i] [i, i] -> [q, q] [q, s] [s, i] , [q, q] [q, s] [s, i] -> [q, s] [s, s] [s, i] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, 0] [0, p] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, g] [g, p] -> [i, f] [f, p] [p, p] [p, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, q] [q, s] [s, p] -> [i, s] [s, s] [s, p] , [i, i] [i, p] -> [i, s] [s, p] , [i, p] [p, 0] [0, 0] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, g] [g, 0] -> [i, f] [f, p] [p, p] [p, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, q] [q, s] [s, 0] -> [i, s] [s, s] [s, 0] , [i, i] [i, 0] -> [i, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, q] [q, s] [s, s] -> [i, s] [s, s] [s, s] , [i, i] [i, s] -> [i, s] [s, s] , [i, p] [p, 0] [0, f] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, g] [g, f] -> [i, f] [f, p] [p, p] [p, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, q] [q, s] [s, f] -> [i, s] [s, s] [s, f] , [i, i] [i, f] -> [i, s] [s, f] , [i, p] [p, 0] [0, g] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, g] [g, g] -> [i, f] [f, p] [p, p] [p, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, q] [q, s] [s, g] -> [i, s] [s, s] [s, g] , [i, i] [i, g] -> [i, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, q] [q, s] [s, q] -> [i, s] [s, s] [s, q] , [i, i] [i, q] -> [i, s] [s, q] , [i, p] [p, 0] [0, i] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, i] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, g] [g, i] -> [i, f] [f, p] [p, p] [p, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] , [i, q] [q, s] [s, i] -> [i, s] [s, s] [s, i] , [i, i] [i, i] -> [i, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, i] is interpreted by / \ | 1 1 | | 0 1 | \ / [s, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, g] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 364-rule system { [p, p] [p, 0] [0, p] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, g] [g, p] -> [p, f] [f, p] [p, p] [p, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, i] [i, p] -> [p, s] [s, p] , [p, p] [p, 0] [0, 0] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, g] [g, 0] -> [p, f] [f, p] [p, p] [p, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, i] [i, 0] -> [p, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, i] [i, s] -> [p, s] [s, s] , [p, p] [p, 0] [0, f] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, g] [g, f] -> [p, f] [f, p] [p, p] [p, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, i] [i, f] -> [p, s] [s, f] , [p, p] [p, 0] [0, g] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, g] [g, g] -> [p, f] [f, p] [p, p] [p, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, i] [i, g] -> [p, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, f] [f, s] [s, q] -> [p, g] [g, q] [q, i] [i, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, i] [i, q] -> [p, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, f] [f, s] [s, i] -> [p, g] [g, q] [q, i] [i, i] , [p, g] [g, i] -> [p, f] [f, p] [p, p] [p, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [p, i] [i, i] -> [p, s] [s, i] , [0, p] [p, 0] [0, p] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [0, p] [p, s] [s, 0] [0, p] -> [0, 0] [0, p] , [0, p] [p, s] [s, s] [s, p] -> [0, s] [s, p] [p, s] [s, p] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, g] [g, p] -> [0, f] [f, p] [p, p] [p, p] , [0, q] [q, i] [i, p] -> [0, q] [q, s] [s, p] , [0, p] [p, 0] [0, 0] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [0, p] [p, s] [s, 0] [0, 0] -> [0, 0] [0, 0] , [0, p] [p, s] [s, s] [s, 0] -> [0, s] [s, p] [p, s] [s, 0] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, g] [g, 0] -> [0, f] [f, p] [p, p] [p, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, p] [p, 0] [0, s] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [0, p] [p, s] [s, 0] [0, s] -> [0, 0] [0, s] , [0, p] [p, s] [s, s] [s, s] -> [0, s] [s, p] [p, s] [s, s] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, p] [p, 0] [0, f] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [0, p] [p, s] [s, 0] [0, f] -> [0, 0] [0, f] , [0, p] [p, s] [s, s] [s, f] -> [0, s] [s, p] [p, s] [s, f] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, g] [g, f] -> [0, f] [f, p] [p, p] [p, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, p] [p, 0] [0, g] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [0, p] [p, s] [s, 0] [0, g] -> [0, 0] [0, g] , [0, p] [p, s] [s, s] [s, g] -> [0, s] [s, p] [p, s] [s, g] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, g] [g, g] -> [0, f] [f, p] [p, p] [p, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, p] [p, s] [s, 0] [0, q] -> [0, 0] [0, q] , [0, p] [p, s] [s, s] [s, q] -> [0, s] [s, p] [p, s] [s, q] , [0, f] [f, s] [s, q] -> [0, g] [g, q] [q, i] [i, q] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [0, q] [q, i] [i, q] -> [0, q] [q, s] [s, q] , [0, p] [p, s] [s, 0] [0, i] -> [0, 0] [0, i] , [0, p] [p, s] [s, s] [s, i] -> [0, s] [s, p] [p, s] [s, i] , [0, f] [f, s] [s, i] -> [0, g] [g, q] [q, i] [i, i] , [0, g] [g, i] -> [0, f] [f, p] [p, p] [p, i] , [0, q] [q, i] [i, i] -> [0, q] [q, s] [s, i] , [s, p] [p, 0] [0, p] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, g] [g, p] -> [s, f] [f, p] [p, p] [p, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, q] [q, s] [s, p] -> [s, s] [s, s] [s, p] , [s, i] [i, p] -> [s, s] [s, p] , [s, p] [p, 0] [0, 0] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, g] [g, 0] -> [s, f] [f, p] [p, p] [p, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, q] [q, s] [s, 0] -> [s, s] [s, s] [s, 0] , [s, i] [i, 0] -> [s, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, q] [q, s] [s, s] -> [s, s] [s, s] [s, s] , [s, i] [i, s] -> [s, s] [s, s] , [s, p] [p, 0] [0, f] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, g] [g, f] -> [s, f] [f, p] [p, p] [p, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, q] [q, s] [s, f] -> [s, s] [s, s] [s, f] , [s, i] [i, f] -> [s, s] [s, f] , [s, p] [p, 0] [0, g] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, g] [g, g] -> [s, f] [f, p] [p, p] [p, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, q] [q, s] [s, g] -> [s, s] [s, s] [s, g] , [s, i] [i, g] -> [s, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, q] [q, s] [s, q] -> [s, s] [s, s] [s, q] , [s, i] [i, q] -> [s, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, g] [g, i] -> [s, f] [f, p] [p, p] [p, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [s, q] [q, s] [s, i] -> [s, s] [s, s] [s, i] , [s, i] [i, i] -> [s, s] [s, i] , [f, p] [p, 0] [0, p] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [f, p] [p, s] [s, 0] [0, p] -> [f, 0] [0, p] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, g] [g, p] -> [f, f] [f, p] [p, p] [p, p] , [f, q] [q, i] [i, p] -> [f, q] [q, s] [s, p] , [f, q] [q, s] [s, p] -> [f, s] [s, s] [s, p] , [f, i] [i, p] -> [f, s] [s, p] , [f, p] [p, 0] [0, 0] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [f, p] [p, s] [s, 0] [0, 0] -> [f, 0] [0, 0] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, g] [g, 0] -> [f, f] [f, p] [p, p] [p, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, q] [q, s] [s, 0] -> [f, s] [s, s] [s, 0] , [f, i] [i, 0] -> [f, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, 0] [0, s] -> [f, 0] [0, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, q] [q, s] [s, s] -> [f, s] [s, s] [s, s] , [f, i] [i, s] -> [f, s] [s, s] , [f, p] [p, 0] [0, f] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [f, p] [p, s] [s, 0] [0, f] -> [f, 0] [0, f] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, g] [g, f] -> [f, f] [f, p] [p, p] [p, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, q] [q, s] [s, f] -> [f, s] [s, s] [s, f] , [f, i] [i, f] -> [f, s] [s, f] , [f, p] [p, 0] [0, g] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [f, p] [p, s] [s, 0] [0, g] -> [f, 0] [0, g] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, g] [g, g] -> [f, f] [f, p] [p, p] [p, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, q] [q, s] [s, g] -> [f, s] [s, s] [s, g] , [f, i] [i, g] -> [f, s] [s, g] , [f, p] [p, s] [s, 0] [0, q] -> [f, 0] [0, q] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, f] [f, s] [s, q] -> [f, g] [g, q] [q, i] [i, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, q] [q, i] [i, q] -> [f, q] [q, s] [s, q] , [f, q] [q, s] [s, q] -> [f, s] [s, s] [s, q] , [f, i] [i, q] -> [f, s] [s, q] , [f, p] [p, s] [s, 0] [0, i] -> [f, 0] [0, i] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [f, f] [f, s] [s, i] -> [f, g] [g, q] [q, i] [i, i] , [f, g] [g, i] -> [f, f] [f, p] [p, p] [p, i] , [f, q] [q, i] [i, i] -> [f, q] [q, s] [s, i] , [f, q] [q, s] [s, i] -> [f, s] [s, s] [s, i] , [f, i] [i, i] -> [f, s] [s, i] , [g, p] [p, 0] [0, p] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [g, p] [p, s] [s, 0] [0, p] -> [g, 0] [0, p] , [g, p] [p, s] [s, s] [s, p] -> [g, s] [s, p] [p, s] [s, p] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, g] [g, p] -> [g, f] [f, p] [p, p] [p, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, i] [i, p] -> [g, s] [s, p] , [g, p] [p, 0] [0, 0] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [g, p] [p, s] [s, 0] [0, 0] -> [g, 0] [0, 0] , [g, p] [p, s] [s, s] [s, 0] -> [g, s] [s, p] [p, s] [s, 0] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, g] [g, 0] -> [g, f] [f, p] [p, p] [p, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, i] [i, 0] -> [g, s] [s, 0] , [g, p] [p, 0] [0, s] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [g, p] [p, s] [s, 0] [0, s] -> [g, 0] [0, s] , [g, p] [p, s] [s, s] [s, s] -> [g, s] [s, p] [p, s] [s, s] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, i] [i, s] -> [g, s] [s, s] , [g, p] [p, 0] [0, f] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [g, p] [p, s] [s, 0] [0, f] -> [g, 0] [0, f] , [g, p] [p, s] [s, s] [s, f] -> [g, s] [s, p] [p, s] [s, f] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, g] [g, f] -> [g, f] [f, p] [p, p] [p, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, i] [i, f] -> [g, s] [s, f] , [g, p] [p, 0] [0, g] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [g, p] [p, s] [s, 0] [0, g] -> [g, 0] [0, g] , [g, p] [p, s] [s, s] [s, g] -> [g, s] [s, p] [p, s] [s, g] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, g] [g, g] -> [g, f] [f, p] [p, p] [p, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, i] [i, g] -> [g, s] [s, g] , [g, p] [p, s] [s, 0] [0, q] -> [g, 0] [0, q] , [g, p] [p, s] [s, s] [s, q] -> [g, s] [s, p] [p, s] [s, q] , [g, f] [f, s] [s, q] -> [g, g] [g, q] [q, i] [i, q] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, i] [i, q] -> [g, s] [s, q] , [g, p] [p, s] [s, 0] [0, i] -> [g, 0] [0, i] , [g, p] [p, s] [s, s] [s, i] -> [g, s] [s, p] [p, s] [s, i] , [g, f] [f, s] [s, i] -> [g, g] [g, q] [q, i] [i, i] , [g, g] [g, i] -> [g, f] [f, p] [p, p] [p, i] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [g, i] [i, i] -> [g, s] [s, i] , [q, p] [p, 0] [0, p] -> [q, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [q, p] [p, s] [s, 0] [0, p] -> [q, 0] [0, p] , [q, p] [p, s] [s, s] [s, p] -> [q, s] [s, p] [p, s] [s, p] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, g] [g, p] -> [q, f] [f, p] [p, p] [p, p] , [q, q] [q, i] [i, p] -> [q, q] [q, s] [s, p] , [q, q] [q, s] [s, p] -> [q, s] [s, s] [s, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, p] [p, 0] [0, 0] -> [q, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [q, p] [p, s] [s, 0] [0, 0] -> [q, 0] [0, 0] , [q, p] [p, s] [s, s] [s, 0] -> [q, s] [s, p] [p, s] [s, 0] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, g] [g, 0] -> [q, f] [f, p] [p, p] [p, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, q] [q, s] [s, 0] -> [q, s] [s, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, p] [p, 0] [0, s] -> [q, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [q, p] [p, s] [s, 0] [0, s] -> [q, 0] [0, s] , [q, p] [p, s] [s, s] [s, s] -> [q, s] [s, p] [p, s] [s, s] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, q] [q, s] [s, s] -> [q, s] [s, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, p] [p, 0] [0, f] -> [q, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [q, p] [p, s] [s, 0] [0, f] -> [q, 0] [0, f] , [q, p] [p, s] [s, s] [s, f] -> [q, s] [s, p] [p, s] [s, f] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, g] [g, f] -> [q, f] [f, p] [p, p] [p, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, q] [q, s] [s, f] -> [q, s] [s, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, p] [p, 0] [0, g] -> [q, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [q, p] [p, s] [s, 0] [0, g] -> [q, 0] [0, g] , [q, p] [p, s] [s, s] [s, g] -> [q, s] [s, p] [p, s] [s, g] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, g] [g, g] -> [q, f] [f, p] [p, p] [p, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, q] [q, s] [s, g] -> [q, s] [s, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, p] [p, s] [s, 0] [0, q] -> [q, 0] [0, q] , [q, p] [p, s] [s, s] [s, q] -> [q, s] [s, p] [p, s] [s, q] , [q, f] [f, s] [s, q] -> [q, g] [g, q] [q, i] [i, q] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, q] [q, i] [i, q] -> [q, q] [q, s] [s, q] , [q, q] [q, s] [s, q] -> [q, s] [s, s] [s, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, p] [p, s] [s, 0] [0, i] -> [q, 0] [0, i] , [q, p] [p, s] [s, s] [s, i] -> [q, s] [s, p] [p, s] [s, i] , [q, f] [f, s] [s, i] -> [q, g] [g, q] [q, i] [i, i] , [q, g] [g, i] -> [q, f] [f, p] [p, p] [p, i] , [q, q] [q, i] [i, i] -> [q, q] [q, s] [s, i] , [q, q] [q, s] [s, i] -> [q, s] [s, s] [s, i] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, 0] [0, p] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, g] [g, p] -> [i, f] [f, p] [p, p] [p, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, q] [q, s] [s, p] -> [i, s] [s, s] [s, p] , [i, i] [i, p] -> [i, s] [s, p] , [i, p] [p, 0] [0, 0] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, g] [g, 0] -> [i, f] [f, p] [p, p] [p, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, q] [q, s] [s, 0] -> [i, s] [s, s] [s, 0] , [i, i] [i, 0] -> [i, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, q] [q, s] [s, s] -> [i, s] [s, s] [s, s] , [i, i] [i, s] -> [i, s] [s, s] , [i, p] [p, 0] [0, f] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, g] [g, f] -> [i, f] [f, p] [p, p] [p, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, q] [q, s] [s, f] -> [i, s] [s, s] [s, f] , [i, i] [i, f] -> [i, s] [s, f] , [i, p] [p, 0] [0, g] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, g] [g, g] -> [i, f] [f, p] [p, p] [p, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, q] [q, s] [s, g] -> [i, s] [s, s] [s, g] , [i, i] [i, g] -> [i, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, q] [q, s] [s, q] -> [i, s] [s, s] [s, q] , [i, i] [i, q] -> [i, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, g] [g, i] -> [i, f] [f, p] [p, p] [p, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] , [i, q] [q, s] [s, i] -> [i, s] [s, s] [s, i] , [i, i] [i, i] -> [i, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, i] is interpreted by / \ | 1 1 | | 0 1 | \ / [f, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, g] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 350-rule system { [p, p] [p, 0] [0, p] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, g] [g, p] -> [p, f] [f, p] [p, p] [p, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, i] [i, p] -> [p, s] [s, p] , [p, p] [p, 0] [0, 0] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, g] [g, 0] -> [p, f] [f, p] [p, p] [p, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, i] [i, 0] -> [p, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, i] [i, s] -> [p, s] [s, s] , [p, p] [p, 0] [0, f] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, g] [g, f] -> [p, f] [f, p] [p, p] [p, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, i] [i, f] -> [p, s] [s, f] , [p, p] [p, 0] [0, g] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, g] [g, g] -> [p, f] [f, p] [p, p] [p, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, i] [i, g] -> [p, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, f] [f, s] [s, q] -> [p, g] [g, q] [q, i] [i, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, i] [i, q] -> [p, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, f] [f, s] [s, i] -> [p, g] [g, q] [q, i] [i, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [p, i] [i, i] -> [p, s] [s, i] , [0, p] [p, 0] [0, p] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [0, p] [p, s] [s, 0] [0, p] -> [0, 0] [0, p] , [0, p] [p, s] [s, s] [s, p] -> [0, s] [s, p] [p, s] [s, p] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, g] [g, p] -> [0, f] [f, p] [p, p] [p, p] , [0, q] [q, i] [i, p] -> [0, q] [q, s] [s, p] , [0, p] [p, 0] [0, 0] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [0, p] [p, s] [s, 0] [0, 0] -> [0, 0] [0, 0] , [0, p] [p, s] [s, s] [s, 0] -> [0, s] [s, p] [p, s] [s, 0] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, g] [g, 0] -> [0, f] [f, p] [p, p] [p, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, p] [p, 0] [0, s] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [0, p] [p, s] [s, 0] [0, s] -> [0, 0] [0, s] , [0, p] [p, s] [s, s] [s, s] -> [0, s] [s, p] [p, s] [s, s] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, p] [p, 0] [0, f] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [0, p] [p, s] [s, 0] [0, f] -> [0, 0] [0, f] , [0, p] [p, s] [s, s] [s, f] -> [0, s] [s, p] [p, s] [s, f] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, g] [g, f] -> [0, f] [f, p] [p, p] [p, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, p] [p, 0] [0, g] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [0, p] [p, s] [s, 0] [0, g] -> [0, 0] [0, g] , [0, p] [p, s] [s, s] [s, g] -> [0, s] [s, p] [p, s] [s, g] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, g] [g, g] -> [0, f] [f, p] [p, p] [p, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, p] [p, s] [s, 0] [0, q] -> [0, 0] [0, q] , [0, p] [p, s] [s, s] [s, q] -> [0, s] [s, p] [p, s] [s, q] , [0, f] [f, s] [s, q] -> [0, g] [g, q] [q, i] [i, q] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [0, q] [q, i] [i, q] -> [0, q] [q, s] [s, q] , [0, p] [p, s] [s, 0] [0, i] -> [0, 0] [0, i] , [0, p] [p, s] [s, s] [s, i] -> [0, s] [s, p] [p, s] [s, i] , [0, f] [f, s] [s, i] -> [0, g] [g, q] [q, i] [i, i] , [0, q] [q, i] [i, i] -> [0, q] [q, s] [s, i] , [s, p] [p, 0] [0, p] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, g] [g, p] -> [s, f] [f, p] [p, p] [p, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, q] [q, s] [s, p] -> [s, s] [s, s] [s, p] , [s, i] [i, p] -> [s, s] [s, p] , [s, p] [p, 0] [0, 0] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, g] [g, 0] -> [s, f] [f, p] [p, p] [p, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, q] [q, s] [s, 0] -> [s, s] [s, s] [s, 0] , [s, i] [i, 0] -> [s, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, q] [q, s] [s, s] -> [s, s] [s, s] [s, s] , [s, i] [i, s] -> [s, s] [s, s] , [s, p] [p, 0] [0, f] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, g] [g, f] -> [s, f] [f, p] [p, p] [p, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, q] [q, s] [s, f] -> [s, s] [s, s] [s, f] , [s, i] [i, f] -> [s, s] [s, f] , [s, p] [p, 0] [0, g] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, g] [g, g] -> [s, f] [f, p] [p, p] [p, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, q] [q, s] [s, g] -> [s, s] [s, s] [s, g] , [s, i] [i, g] -> [s, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, q] [q, s] [s, q] -> [s, s] [s, s] [s, q] , [s, i] [i, q] -> [s, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [s, q] [q, s] [s, i] -> [s, s] [s, s] [s, i] , [s, i] [i, i] -> [s, s] [s, i] , [f, p] [p, 0] [0, p] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [f, p] [p, s] [s, 0] [0, p] -> [f, 0] [0, p] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, g] [g, p] -> [f, f] [f, p] [p, p] [p, p] , [f, q] [q, i] [i, p] -> [f, q] [q, s] [s, p] , [f, q] [q, s] [s, p] -> [f, s] [s, s] [s, p] , [f, i] [i, p] -> [f, s] [s, p] , [f, p] [p, 0] [0, 0] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [f, p] [p, s] [s, 0] [0, 0] -> [f, 0] [0, 0] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, g] [g, 0] -> [f, f] [f, p] [p, p] [p, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, q] [q, s] [s, 0] -> [f, s] [s, s] [s, 0] , [f, i] [i, 0] -> [f, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, 0] [0, s] -> [f, 0] [0, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, q] [q, s] [s, s] -> [f, s] [s, s] [s, s] , [f, i] [i, s] -> [f, s] [s, s] , [f, p] [p, 0] [0, f] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [f, p] [p, s] [s, 0] [0, f] -> [f, 0] [0, f] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, g] [g, f] -> [f, f] [f, p] [p, p] [p, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, q] [q, s] [s, f] -> [f, s] [s, s] [s, f] , [f, i] [i, f] -> [f, s] [s, f] , [f, p] [p, 0] [0, g] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [f, p] [p, s] [s, 0] [0, g] -> [f, 0] [0, g] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, g] [g, g] -> [f, f] [f, p] [p, p] [p, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, q] [q, s] [s, g] -> [f, s] [s, s] [s, g] , [f, i] [i, g] -> [f, s] [s, g] , [f, p] [p, s] [s, 0] [0, q] -> [f, 0] [0, q] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, f] [f, s] [s, q] -> [f, g] [g, q] [q, i] [i, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, q] [q, i] [i, q] -> [f, q] [q, s] [s, q] , [f, q] [q, s] [s, q] -> [f, s] [s, s] [s, q] , [f, i] [i, q] -> [f, s] [s, q] , [f, p] [p, s] [s, 0] [0, i] -> [f, 0] [0, i] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [f, f] [f, s] [s, i] -> [f, g] [g, q] [q, i] [i, i] , [f, q] [q, i] [i, i] -> [f, q] [q, s] [s, i] , [f, q] [q, s] [s, i] -> [f, s] [s, s] [s, i] , [f, i] [i, i] -> [f, s] [s, i] , [g, p] [p, 0] [0, p] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [g, p] [p, s] [s, 0] [0, p] -> [g, 0] [0, p] , [g, p] [p, s] [s, s] [s, p] -> [g, s] [s, p] [p, s] [s, p] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, g] [g, p] -> [g, f] [f, p] [p, p] [p, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, p] [p, 0] [0, 0] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [g, p] [p, s] [s, 0] [0, 0] -> [g, 0] [0, 0] , [g, p] [p, s] [s, s] [s, 0] -> [g, s] [s, p] [p, s] [s, 0] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, g] [g, 0] -> [g, f] [f, p] [p, p] [p, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, p] [p, 0] [0, s] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [g, p] [p, s] [s, 0] [0, s] -> [g, 0] [0, s] , [g, p] [p, s] [s, s] [s, s] -> [g, s] [s, p] [p, s] [s, s] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, p] [p, 0] [0, f] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [g, p] [p, s] [s, 0] [0, f] -> [g, 0] [0, f] , [g, p] [p, s] [s, s] [s, f] -> [g, s] [s, p] [p, s] [s, f] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, g] [g, f] -> [g, f] [f, p] [p, p] [p, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, p] [p, 0] [0, g] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [g, p] [p, s] [s, 0] [0, g] -> [g, 0] [0, g] , [g, p] [p, s] [s, s] [s, g] -> [g, s] [s, p] [p, s] [s, g] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, g] [g, g] -> [g, f] [f, p] [p, p] [p, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, p] [p, s] [s, 0] [0, q] -> [g, 0] [0, q] , [g, p] [p, s] [s, s] [s, q] -> [g, s] [s, p] [p, s] [s, q] , [g, f] [f, s] [s, q] -> [g, g] [g, q] [q, i] [i, q] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, p] [p, s] [s, 0] [0, i] -> [g, 0] [0, i] , [g, p] [p, s] [s, s] [s, i] -> [g, s] [s, p] [p, s] [s, i] , [g, f] [f, s] [s, i] -> [g, g] [g, q] [q, i] [i, i] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, p] [p, 0] [0, p] -> [q, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [q, p] [p, s] [s, 0] [0, p] -> [q, 0] [0, p] , [q, p] [p, s] [s, s] [s, p] -> [q, s] [s, p] [p, s] [s, p] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, g] [g, p] -> [q, f] [f, p] [p, p] [p, p] , [q, q] [q, i] [i, p] -> [q, q] [q, s] [s, p] , [q, q] [q, s] [s, p] -> [q, s] [s, s] [s, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, p] [p, 0] [0, 0] -> [q, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [q, p] [p, s] [s, 0] [0, 0] -> [q, 0] [0, 0] , [q, p] [p, s] [s, s] [s, 0] -> [q, s] [s, p] [p, s] [s, 0] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, g] [g, 0] -> [q, f] [f, p] [p, p] [p, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, q] [q, s] [s, 0] -> [q, s] [s, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, p] [p, 0] [0, s] -> [q, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [q, p] [p, s] [s, 0] [0, s] -> [q, 0] [0, s] , [q, p] [p, s] [s, s] [s, s] -> [q, s] [s, p] [p, s] [s, s] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, q] [q, s] [s, s] -> [q, s] [s, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, p] [p, 0] [0, f] -> [q, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [q, p] [p, s] [s, 0] [0, f] -> [q, 0] [0, f] , [q, p] [p, s] [s, s] [s, f] -> [q, s] [s, p] [p, s] [s, f] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, g] [g, f] -> [q, f] [f, p] [p, p] [p, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, q] [q, s] [s, f] -> [q, s] [s, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, p] [p, 0] [0, g] -> [q, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [q, p] [p, s] [s, 0] [0, g] -> [q, 0] [0, g] , [q, p] [p, s] [s, s] [s, g] -> [q, s] [s, p] [p, s] [s, g] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, g] [g, g] -> [q, f] [f, p] [p, p] [p, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, q] [q, s] [s, g] -> [q, s] [s, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, p] [p, s] [s, 0] [0, q] -> [q, 0] [0, q] , [q, p] [p, s] [s, s] [s, q] -> [q, s] [s, p] [p, s] [s, q] , [q, f] [f, s] [s, q] -> [q, g] [g, q] [q, i] [i, q] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, q] [q, i] [i, q] -> [q, q] [q, s] [s, q] , [q, q] [q, s] [s, q] -> [q, s] [s, s] [s, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, p] [p, s] [s, 0] [0, i] -> [q, 0] [0, i] , [q, p] [p, s] [s, s] [s, i] -> [q, s] [s, p] [p, s] [s, i] , [q, f] [f, s] [s, i] -> [q, g] [g, q] [q, i] [i, i] , [q, q] [q, i] [i, i] -> [q, q] [q, s] [s, i] , [q, q] [q, s] [s, i] -> [q, s] [s, s] [s, i] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, 0] [0, p] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, g] [g, p] -> [i, f] [f, p] [p, p] [p, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, q] [q, s] [s, p] -> [i, s] [s, s] [s, p] , [i, i] [i, p] -> [i, s] [s, p] , [i, p] [p, 0] [0, 0] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, g] [g, 0] -> [i, f] [f, p] [p, p] [p, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, q] [q, s] [s, 0] -> [i, s] [s, s] [s, 0] , [i, i] [i, 0] -> [i, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, q] [q, s] [s, s] -> [i, s] [s, s] [s, s] , [i, i] [i, s] -> [i, s] [s, s] , [i, p] [p, 0] [0, f] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, g] [g, f] -> [i, f] [f, p] [p, p] [p, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, q] [q, s] [s, f] -> [i, s] [s, s] [s, f] , [i, i] [i, f] -> [i, s] [s, f] , [i, p] [p, 0] [0, g] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, g] [g, g] -> [i, f] [f, p] [p, p] [p, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, q] [q, s] [s, g] -> [i, s] [s, s] [s, g] , [i, i] [i, g] -> [i, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, q] [q, s] [s, q] -> [i, s] [s, s] [s, q] , [i, i] [i, q] -> [i, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] , [i, q] [q, s] [s, i] -> [i, s] [s, s] [s, i] , [i, i] [i, i] -> [i, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, q] is interpreted by / \ | 1 1 | | 0 1 | \ / [f, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, g] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 343-rule system { [p, p] [p, 0] [0, p] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, g] [g, p] -> [p, f] [f, p] [p, p] [p, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, i] [i, p] -> [p, s] [s, p] , [p, p] [p, 0] [0, 0] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, g] [g, 0] -> [p, f] [f, p] [p, p] [p, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, i] [i, 0] -> [p, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, i] [i, s] -> [p, s] [s, s] , [p, p] [p, 0] [0, f] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, g] [g, f] -> [p, f] [f, p] [p, p] [p, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, i] [i, f] -> [p, s] [s, f] , [p, p] [p, 0] [0, g] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, g] [g, g] -> [p, f] [f, p] [p, p] [p, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, i] [i, g] -> [p, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, f] [f, s] [s, q] -> [p, g] [g, q] [q, i] [i, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, i] [i, q] -> [p, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, f] [f, s] [s, i] -> [p, g] [g, q] [q, i] [i, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [p, i] [i, i] -> [p, s] [s, i] , [0, p] [p, 0] [0, p] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [0, p] [p, s] [s, 0] [0, p] -> [0, 0] [0, p] , [0, p] [p, s] [s, s] [s, p] -> [0, s] [s, p] [p, s] [s, p] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, g] [g, p] -> [0, f] [f, p] [p, p] [p, p] , [0, q] [q, i] [i, p] -> [0, q] [q, s] [s, p] , [0, p] [p, 0] [0, 0] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [0, p] [p, s] [s, 0] [0, 0] -> [0, 0] [0, 0] , [0, p] [p, s] [s, s] [s, 0] -> [0, s] [s, p] [p, s] [s, 0] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, g] [g, 0] -> [0, f] [f, p] [p, p] [p, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, p] [p, 0] [0, s] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [0, p] [p, s] [s, 0] [0, s] -> [0, 0] [0, s] , [0, p] [p, s] [s, s] [s, s] -> [0, s] [s, p] [p, s] [s, s] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, p] [p, 0] [0, f] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [0, p] [p, s] [s, 0] [0, f] -> [0, 0] [0, f] , [0, p] [p, s] [s, s] [s, f] -> [0, s] [s, p] [p, s] [s, f] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, g] [g, f] -> [0, f] [f, p] [p, p] [p, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, p] [p, 0] [0, g] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [0, p] [p, s] [s, 0] [0, g] -> [0, 0] [0, g] , [0, p] [p, s] [s, s] [s, g] -> [0, s] [s, p] [p, s] [s, g] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, g] [g, g] -> [0, f] [f, p] [p, p] [p, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, p] [p, s] [s, 0] [0, q] -> [0, 0] [0, q] , [0, p] [p, s] [s, s] [s, q] -> [0, s] [s, p] [p, s] [s, q] , [0, f] [f, s] [s, q] -> [0, g] [g, q] [q, i] [i, q] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [0, q] [q, i] [i, q] -> [0, q] [q, s] [s, q] , [0, p] [p, s] [s, 0] [0, i] -> [0, 0] [0, i] , [0, p] [p, s] [s, s] [s, i] -> [0, s] [s, p] [p, s] [s, i] , [0, f] [f, s] [s, i] -> [0, g] [g, q] [q, i] [i, i] , [0, q] [q, i] [i, i] -> [0, q] [q, s] [s, i] , [s, p] [p, 0] [0, p] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, g] [g, p] -> [s, f] [f, p] [p, p] [p, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, q] [q, s] [s, p] -> [s, s] [s, s] [s, p] , [s, i] [i, p] -> [s, s] [s, p] , [s, p] [p, 0] [0, 0] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, g] [g, 0] -> [s, f] [f, p] [p, p] [p, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, q] [q, s] [s, 0] -> [s, s] [s, s] [s, 0] , [s, i] [i, 0] -> [s, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, q] [q, s] [s, s] -> [s, s] [s, s] [s, s] , [s, i] [i, s] -> [s, s] [s, s] , [s, p] [p, 0] [0, f] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, g] [g, f] -> [s, f] [f, p] [p, p] [p, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, q] [q, s] [s, f] -> [s, s] [s, s] [s, f] , [s, i] [i, f] -> [s, s] [s, f] , [s, p] [p, 0] [0, g] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, g] [g, g] -> [s, f] [f, p] [p, p] [p, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, q] [q, s] [s, g] -> [s, s] [s, s] [s, g] , [s, i] [i, g] -> [s, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, q] [q, s] [s, q] -> [s, s] [s, s] [s, q] , [s, i] [i, q] -> [s, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [s, q] [q, s] [s, i] -> [s, s] [s, s] [s, i] , [s, i] [i, i] -> [s, s] [s, i] , [f, p] [p, 0] [0, p] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [f, p] [p, s] [s, 0] [0, p] -> [f, 0] [0, p] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, g] [g, p] -> [f, f] [f, p] [p, p] [p, p] , [f, q] [q, i] [i, p] -> [f, q] [q, s] [s, p] , [f, i] [i, p] -> [f, s] [s, p] , [f, p] [p, 0] [0, 0] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [f, p] [p, s] [s, 0] [0, 0] -> [f, 0] [0, 0] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, g] [g, 0] -> [f, f] [f, p] [p, p] [p, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, i] [i, 0] -> [f, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, 0] [0, s] -> [f, 0] [0, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, i] [i, s] -> [f, s] [s, s] , [f, p] [p, 0] [0, f] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [f, p] [p, s] [s, 0] [0, f] -> [f, 0] [0, f] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, g] [g, f] -> [f, f] [f, p] [p, p] [p, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, i] [i, f] -> [f, s] [s, f] , [f, p] [p, 0] [0, g] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [f, p] [p, s] [s, 0] [0, g] -> [f, 0] [0, g] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, g] [g, g] -> [f, f] [f, p] [p, p] [p, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, i] [i, g] -> [f, s] [s, g] , [f, p] [p, s] [s, 0] [0, q] -> [f, 0] [0, q] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, f] [f, s] [s, q] -> [f, g] [g, q] [q, i] [i, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, q] [q, i] [i, q] -> [f, q] [q, s] [s, q] , [f, i] [i, q] -> [f, s] [s, q] , [f, p] [p, s] [s, 0] [0, i] -> [f, 0] [0, i] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [f, f] [f, s] [s, i] -> [f, g] [g, q] [q, i] [i, i] , [f, q] [q, i] [i, i] -> [f, q] [q, s] [s, i] , [f, i] [i, i] -> [f, s] [s, i] , [g, p] [p, 0] [0, p] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [g, p] [p, s] [s, 0] [0, p] -> [g, 0] [0, p] , [g, p] [p, s] [s, s] [s, p] -> [g, s] [s, p] [p, s] [s, p] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, g] [g, p] -> [g, f] [f, p] [p, p] [p, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, p] [p, 0] [0, 0] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [g, p] [p, s] [s, 0] [0, 0] -> [g, 0] [0, 0] , [g, p] [p, s] [s, s] [s, 0] -> [g, s] [s, p] [p, s] [s, 0] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, g] [g, 0] -> [g, f] [f, p] [p, p] [p, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, p] [p, 0] [0, s] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [g, p] [p, s] [s, 0] [0, s] -> [g, 0] [0, s] , [g, p] [p, s] [s, s] [s, s] -> [g, s] [s, p] [p, s] [s, s] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, p] [p, 0] [0, f] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [g, p] [p, s] [s, 0] [0, f] -> [g, 0] [0, f] , [g, p] [p, s] [s, s] [s, f] -> [g, s] [s, p] [p, s] [s, f] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, g] [g, f] -> [g, f] [f, p] [p, p] [p, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, p] [p, 0] [0, g] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [g, p] [p, s] [s, 0] [0, g] -> [g, 0] [0, g] , [g, p] [p, s] [s, s] [s, g] -> [g, s] [s, p] [p, s] [s, g] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, g] [g, g] -> [g, f] [f, p] [p, p] [p, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, p] [p, s] [s, 0] [0, q] -> [g, 0] [0, q] , [g, p] [p, s] [s, s] [s, q] -> [g, s] [s, p] [p, s] [s, q] , [g, f] [f, s] [s, q] -> [g, g] [g, q] [q, i] [i, q] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, p] [p, s] [s, 0] [0, i] -> [g, 0] [0, i] , [g, p] [p, s] [s, s] [s, i] -> [g, s] [s, p] [p, s] [s, i] , [g, f] [f, s] [s, i] -> [g, g] [g, q] [q, i] [i, i] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, p] [p, 0] [0, p] -> [q, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [q, p] [p, s] [s, 0] [0, p] -> [q, 0] [0, p] , [q, p] [p, s] [s, s] [s, p] -> [q, s] [s, p] [p, s] [s, p] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, g] [g, p] -> [q, f] [f, p] [p, p] [p, p] , [q, q] [q, i] [i, p] -> [q, q] [q, s] [s, p] , [q, q] [q, s] [s, p] -> [q, s] [s, s] [s, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, p] [p, 0] [0, 0] -> [q, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [q, p] [p, s] [s, 0] [0, 0] -> [q, 0] [0, 0] , [q, p] [p, s] [s, s] [s, 0] -> [q, s] [s, p] [p, s] [s, 0] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, g] [g, 0] -> [q, f] [f, p] [p, p] [p, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, q] [q, s] [s, 0] -> [q, s] [s, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, p] [p, 0] [0, s] -> [q, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [q, p] [p, s] [s, 0] [0, s] -> [q, 0] [0, s] , [q, p] [p, s] [s, s] [s, s] -> [q, s] [s, p] [p, s] [s, s] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, q] [q, s] [s, s] -> [q, s] [s, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, p] [p, 0] [0, f] -> [q, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [q, p] [p, s] [s, 0] [0, f] -> [q, 0] [0, f] , [q, p] [p, s] [s, s] [s, f] -> [q, s] [s, p] [p, s] [s, f] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, g] [g, f] -> [q, f] [f, p] [p, p] [p, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, q] [q, s] [s, f] -> [q, s] [s, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, p] [p, 0] [0, g] -> [q, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [q, p] [p, s] [s, 0] [0, g] -> [q, 0] [0, g] , [q, p] [p, s] [s, s] [s, g] -> [q, s] [s, p] [p, s] [s, g] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, g] [g, g] -> [q, f] [f, p] [p, p] [p, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, q] [q, s] [s, g] -> [q, s] [s, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, p] [p, s] [s, 0] [0, q] -> [q, 0] [0, q] , [q, p] [p, s] [s, s] [s, q] -> [q, s] [s, p] [p, s] [s, q] , [q, f] [f, s] [s, q] -> [q, g] [g, q] [q, i] [i, q] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, q] [q, i] [i, q] -> [q, q] [q, s] [s, q] , [q, q] [q, s] [s, q] -> [q, s] [s, s] [s, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, p] [p, s] [s, 0] [0, i] -> [q, 0] [0, i] , [q, p] [p, s] [s, s] [s, i] -> [q, s] [s, p] [p, s] [s, i] , [q, f] [f, s] [s, i] -> [q, g] [g, q] [q, i] [i, i] , [q, q] [q, i] [i, i] -> [q, q] [q, s] [s, i] , [q, q] [q, s] [s, i] -> [q, s] [s, s] [s, i] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, 0] [0, p] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, g] [g, p] -> [i, f] [f, p] [p, p] [p, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, q] [q, s] [s, p] -> [i, s] [s, s] [s, p] , [i, i] [i, p] -> [i, s] [s, p] , [i, p] [p, 0] [0, 0] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, g] [g, 0] -> [i, f] [f, p] [p, p] [p, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, q] [q, s] [s, 0] -> [i, s] [s, s] [s, 0] , [i, i] [i, 0] -> [i, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, q] [q, s] [s, s] -> [i, s] [s, s] [s, s] , [i, i] [i, s] -> [i, s] [s, s] , [i, p] [p, 0] [0, f] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, g] [g, f] -> [i, f] [f, p] [p, p] [p, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, q] [q, s] [s, f] -> [i, s] [s, s] [s, f] , [i, i] [i, f] -> [i, s] [s, f] , [i, p] [p, 0] [0, g] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, g] [g, g] -> [i, f] [f, p] [p, p] [p, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, q] [q, s] [s, g] -> [i, s] [s, s] [s, g] , [i, i] [i, g] -> [i, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, q] [q, s] [s, q] -> [i, s] [s, s] [s, q] , [i, i] [i, q] -> [i, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] , [i, q] [q, s] [s, i] -> [i, s] [s, s] [s, i] , [i, i] [i, i] -> [i, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, i] is interpreted by / \ | 1 1 | | 0 1 | \ / [q, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, g] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 336-rule system { [p, p] [p, 0] [0, p] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, g] [g, p] -> [p, f] [f, p] [p, p] [p, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, i] [i, p] -> [p, s] [s, p] , [p, p] [p, 0] [0, 0] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, g] [g, 0] -> [p, f] [f, p] [p, p] [p, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, i] [i, 0] -> [p, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, i] [i, s] -> [p, s] [s, s] , [p, p] [p, 0] [0, f] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, g] [g, f] -> [p, f] [f, p] [p, p] [p, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, i] [i, f] -> [p, s] [s, f] , [p, p] [p, 0] [0, g] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, g] [g, g] -> [p, f] [f, p] [p, p] [p, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, i] [i, g] -> [p, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, f] [f, s] [s, q] -> [p, g] [g, q] [q, i] [i, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, i] [i, q] -> [p, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, f] [f, s] [s, i] -> [p, g] [g, q] [q, i] [i, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [p, i] [i, i] -> [p, s] [s, i] , [0, p] [p, 0] [0, p] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [0, p] [p, s] [s, 0] [0, p] -> [0, 0] [0, p] , [0, p] [p, s] [s, s] [s, p] -> [0, s] [s, p] [p, s] [s, p] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, g] [g, p] -> [0, f] [f, p] [p, p] [p, p] , [0, q] [q, i] [i, p] -> [0, q] [q, s] [s, p] , [0, p] [p, 0] [0, 0] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [0, p] [p, s] [s, 0] [0, 0] -> [0, 0] [0, 0] , [0, p] [p, s] [s, s] [s, 0] -> [0, s] [s, p] [p, s] [s, 0] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, g] [g, 0] -> [0, f] [f, p] [p, p] [p, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, p] [p, 0] [0, s] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [0, p] [p, s] [s, 0] [0, s] -> [0, 0] [0, s] , [0, p] [p, s] [s, s] [s, s] -> [0, s] [s, p] [p, s] [s, s] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, p] [p, 0] [0, f] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [0, p] [p, s] [s, 0] [0, f] -> [0, 0] [0, f] , [0, p] [p, s] [s, s] [s, f] -> [0, s] [s, p] [p, s] [s, f] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, g] [g, f] -> [0, f] [f, p] [p, p] [p, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, p] [p, 0] [0, g] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [0, p] [p, s] [s, 0] [0, g] -> [0, 0] [0, g] , [0, p] [p, s] [s, s] [s, g] -> [0, s] [s, p] [p, s] [s, g] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, g] [g, g] -> [0, f] [f, p] [p, p] [p, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, p] [p, s] [s, 0] [0, q] -> [0, 0] [0, q] , [0, p] [p, s] [s, s] [s, q] -> [0, s] [s, p] [p, s] [s, q] , [0, f] [f, s] [s, q] -> [0, g] [g, q] [q, i] [i, q] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [0, q] [q, i] [i, q] -> [0, q] [q, s] [s, q] , [0, p] [p, s] [s, 0] [0, i] -> [0, 0] [0, i] , [0, p] [p, s] [s, s] [s, i] -> [0, s] [s, p] [p, s] [s, i] , [0, f] [f, s] [s, i] -> [0, g] [g, q] [q, i] [i, i] , [0, q] [q, i] [i, i] -> [0, q] [q, s] [s, i] , [s, p] [p, 0] [0, p] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, g] [g, p] -> [s, f] [f, p] [p, p] [p, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, q] [q, s] [s, p] -> [s, s] [s, s] [s, p] , [s, i] [i, p] -> [s, s] [s, p] , [s, p] [p, 0] [0, 0] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, g] [g, 0] -> [s, f] [f, p] [p, p] [p, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, q] [q, s] [s, 0] -> [s, s] [s, s] [s, 0] , [s, i] [i, 0] -> [s, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, q] [q, s] [s, s] -> [s, s] [s, s] [s, s] , [s, i] [i, s] -> [s, s] [s, s] , [s, p] [p, 0] [0, f] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, g] [g, f] -> [s, f] [f, p] [p, p] [p, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, q] [q, s] [s, f] -> [s, s] [s, s] [s, f] , [s, i] [i, f] -> [s, s] [s, f] , [s, p] [p, 0] [0, g] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, g] [g, g] -> [s, f] [f, p] [p, p] [p, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, q] [q, s] [s, g] -> [s, s] [s, s] [s, g] , [s, i] [i, g] -> [s, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, q] [q, s] [s, q] -> [s, s] [s, s] [s, q] , [s, i] [i, q] -> [s, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [s, q] [q, s] [s, i] -> [s, s] [s, s] [s, i] , [s, i] [i, i] -> [s, s] [s, i] , [f, p] [p, 0] [0, p] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [f, p] [p, s] [s, 0] [0, p] -> [f, 0] [0, p] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, g] [g, p] -> [f, f] [f, p] [p, p] [p, p] , [f, q] [q, i] [i, p] -> [f, q] [q, s] [s, p] , [f, p] [p, 0] [0, 0] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [f, p] [p, s] [s, 0] [0, 0] -> [f, 0] [0, 0] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, g] [g, 0] -> [f, f] [f, p] [p, p] [p, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, 0] [0, s] -> [f, 0] [0, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, 0] [0, f] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [f, p] [p, s] [s, 0] [0, f] -> [f, 0] [0, f] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, g] [g, f] -> [f, f] [f, p] [p, p] [p, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, 0] [0, g] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [f, p] [p, s] [s, 0] [0, g] -> [f, 0] [0, g] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, g] [g, g] -> [f, f] [f, p] [p, p] [p, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, p] [p, s] [s, 0] [0, q] -> [f, 0] [0, q] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, f] [f, s] [s, q] -> [f, g] [g, q] [q, i] [i, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, q] [q, i] [i, q] -> [f, q] [q, s] [s, q] , [f, p] [p, s] [s, 0] [0, i] -> [f, 0] [0, i] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [f, f] [f, s] [s, i] -> [f, g] [g, q] [q, i] [i, i] , [f, q] [q, i] [i, i] -> [f, q] [q, s] [s, i] , [g, p] [p, 0] [0, p] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [g, p] [p, s] [s, 0] [0, p] -> [g, 0] [0, p] , [g, p] [p, s] [s, s] [s, p] -> [g, s] [s, p] [p, s] [s, p] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, g] [g, p] -> [g, f] [f, p] [p, p] [p, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, p] [p, 0] [0, 0] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [g, p] [p, s] [s, 0] [0, 0] -> [g, 0] [0, 0] , [g, p] [p, s] [s, s] [s, 0] -> [g, s] [s, p] [p, s] [s, 0] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, g] [g, 0] -> [g, f] [f, p] [p, p] [p, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, p] [p, 0] [0, s] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [g, p] [p, s] [s, 0] [0, s] -> [g, 0] [0, s] , [g, p] [p, s] [s, s] [s, s] -> [g, s] [s, p] [p, s] [s, s] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, p] [p, 0] [0, f] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [g, p] [p, s] [s, 0] [0, f] -> [g, 0] [0, f] , [g, p] [p, s] [s, s] [s, f] -> [g, s] [s, p] [p, s] [s, f] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, g] [g, f] -> [g, f] [f, p] [p, p] [p, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, p] [p, 0] [0, g] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [g, p] [p, s] [s, 0] [0, g] -> [g, 0] [0, g] , [g, p] [p, s] [s, s] [s, g] -> [g, s] [s, p] [p, s] [s, g] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, g] [g, g] -> [g, f] [f, p] [p, p] [p, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, p] [p, s] [s, 0] [0, q] -> [g, 0] [0, q] , [g, p] [p, s] [s, s] [s, q] -> [g, s] [s, p] [p, s] [s, q] , [g, f] [f, s] [s, q] -> [g, g] [g, q] [q, i] [i, q] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, p] [p, s] [s, 0] [0, i] -> [g, 0] [0, i] , [g, p] [p, s] [s, s] [s, i] -> [g, s] [s, p] [p, s] [s, i] , [g, f] [f, s] [s, i] -> [g, g] [g, q] [q, i] [i, i] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, p] [p, 0] [0, p] -> [q, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [q, p] [p, s] [s, 0] [0, p] -> [q, 0] [0, p] , [q, p] [p, s] [s, s] [s, p] -> [q, s] [s, p] [p, s] [s, p] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, g] [g, p] -> [q, f] [f, p] [p, p] [p, p] , [q, q] [q, i] [i, p] -> [q, q] [q, s] [s, p] , [q, q] [q, s] [s, p] -> [q, s] [s, s] [s, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, p] [p, 0] [0, 0] -> [q, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [q, p] [p, s] [s, 0] [0, 0] -> [q, 0] [0, 0] , [q, p] [p, s] [s, s] [s, 0] -> [q, s] [s, p] [p, s] [s, 0] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, g] [g, 0] -> [q, f] [f, p] [p, p] [p, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, q] [q, s] [s, 0] -> [q, s] [s, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, p] [p, 0] [0, s] -> [q, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [q, p] [p, s] [s, 0] [0, s] -> [q, 0] [0, s] , [q, p] [p, s] [s, s] [s, s] -> [q, s] [s, p] [p, s] [s, s] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, q] [q, s] [s, s] -> [q, s] [s, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, p] [p, 0] [0, f] -> [q, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [q, p] [p, s] [s, 0] [0, f] -> [q, 0] [0, f] , [q, p] [p, s] [s, s] [s, f] -> [q, s] [s, p] [p, s] [s, f] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, g] [g, f] -> [q, f] [f, p] [p, p] [p, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, q] [q, s] [s, f] -> [q, s] [s, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, p] [p, 0] [0, g] -> [q, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [q, p] [p, s] [s, 0] [0, g] -> [q, 0] [0, g] , [q, p] [p, s] [s, s] [s, g] -> [q, s] [s, p] [p, s] [s, g] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, g] [g, g] -> [q, f] [f, p] [p, p] [p, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, q] [q, s] [s, g] -> [q, s] [s, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, p] [p, s] [s, 0] [0, q] -> [q, 0] [0, q] , [q, p] [p, s] [s, s] [s, q] -> [q, s] [s, p] [p, s] [s, q] , [q, f] [f, s] [s, q] -> [q, g] [g, q] [q, i] [i, q] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, q] [q, i] [i, q] -> [q, q] [q, s] [s, q] , [q, q] [q, s] [s, q] -> [q, s] [s, s] [s, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, p] [p, s] [s, 0] [0, i] -> [q, 0] [0, i] , [q, p] [p, s] [s, s] [s, i] -> [q, s] [s, p] [p, s] [s, i] , [q, f] [f, s] [s, i] -> [q, g] [g, q] [q, i] [i, i] , [q, q] [q, i] [i, i] -> [q, q] [q, s] [s, i] , [q, q] [q, s] [s, i] -> [q, s] [s, s] [s, i] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, 0] [0, p] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, g] [g, p] -> [i, f] [f, p] [p, p] [p, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, q] [q, s] [s, p] -> [i, s] [s, s] [s, p] , [i, i] [i, p] -> [i, s] [s, p] , [i, p] [p, 0] [0, 0] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, g] [g, 0] -> [i, f] [f, p] [p, p] [p, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, q] [q, s] [s, 0] -> [i, s] [s, s] [s, 0] , [i, i] [i, 0] -> [i, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, q] [q, s] [s, s] -> [i, s] [s, s] [s, s] , [i, i] [i, s] -> [i, s] [s, s] , [i, p] [p, 0] [0, f] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, g] [g, f] -> [i, f] [f, p] [p, p] [p, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, q] [q, s] [s, f] -> [i, s] [s, s] [s, f] , [i, i] [i, f] -> [i, s] [s, f] , [i, p] [p, 0] [0, g] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, g] [g, g] -> [i, f] [f, p] [p, p] [p, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, q] [q, s] [s, g] -> [i, s] [s, s] [s, g] , [i, i] [i, g] -> [i, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, q] [q, s] [s, q] -> [i, s] [s, s] [s, q] , [i, i] [i, q] -> [i, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] , [i, q] [q, s] [s, i] -> [i, s] [s, s] [s, i] , [i, i] [i, i] -> [i, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, p] is interpreted by / \ | 1 1 | | 0 1 | \ / [q, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, g] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 317-rule system { [p, p] [p, 0] [0, p] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, g] [g, p] -> [p, f] [f, p] [p, p] [p, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, i] [i, p] -> [p, s] [s, p] , [p, p] [p, 0] [0, 0] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, g] [g, 0] -> [p, f] [f, p] [p, p] [p, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, i] [i, 0] -> [p, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, i] [i, s] -> [p, s] [s, s] , [p, p] [p, 0] [0, f] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, g] [g, f] -> [p, f] [f, p] [p, p] [p, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, i] [i, f] -> [p, s] [s, f] , [p, p] [p, 0] [0, g] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, g] [g, g] -> [p, f] [f, p] [p, p] [p, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, i] [i, g] -> [p, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, f] [f, s] [s, q] -> [p, g] [g, q] [q, i] [i, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, i] [i, q] -> [p, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, f] [f, s] [s, i] -> [p, g] [g, q] [q, i] [i, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [p, i] [i, i] -> [p, s] [s, i] , [0, p] [p, 0] [0, p] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [0, p] [p, s] [s, 0] [0, p] -> [0, 0] [0, p] , [0, p] [p, s] [s, s] [s, p] -> [0, s] [s, p] [p, s] [s, p] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, g] [g, p] -> [0, f] [f, p] [p, p] [p, p] , [0, q] [q, i] [i, p] -> [0, q] [q, s] [s, p] , [0, p] [p, 0] [0, 0] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [0, p] [p, s] [s, 0] [0, 0] -> [0, 0] [0, 0] , [0, p] [p, s] [s, s] [s, 0] -> [0, s] [s, p] [p, s] [s, 0] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, g] [g, 0] -> [0, f] [f, p] [p, p] [p, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, p] [p, 0] [0, s] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [0, p] [p, s] [s, 0] [0, s] -> [0, 0] [0, s] , [0, p] [p, s] [s, s] [s, s] -> [0, s] [s, p] [p, s] [s, s] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, p] [p, 0] [0, f] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [0, p] [p, s] [s, 0] [0, f] -> [0, 0] [0, f] , [0, p] [p, s] [s, s] [s, f] -> [0, s] [s, p] [p, s] [s, f] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, g] [g, f] -> [0, f] [f, p] [p, p] [p, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, p] [p, 0] [0, g] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [0, p] [p, s] [s, 0] [0, g] -> [0, 0] [0, g] , [0, p] [p, s] [s, s] [s, g] -> [0, s] [s, p] [p, s] [s, g] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, g] [g, g] -> [0, f] [f, p] [p, p] [p, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, p] [p, s] [s, 0] [0, q] -> [0, 0] [0, q] , [0, p] [p, s] [s, s] [s, q] -> [0, s] [s, p] [p, s] [s, q] , [0, f] [f, s] [s, q] -> [0, g] [g, q] [q, i] [i, q] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [0, q] [q, i] [i, q] -> [0, q] [q, s] [s, q] , [0, p] [p, s] [s, 0] [0, i] -> [0, 0] [0, i] , [0, p] [p, s] [s, s] [s, i] -> [0, s] [s, p] [p, s] [s, i] , [0, f] [f, s] [s, i] -> [0, g] [g, q] [q, i] [i, i] , [0, q] [q, i] [i, i] -> [0, q] [q, s] [s, i] , [s, p] [p, 0] [0, p] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, g] [g, p] -> [s, f] [f, p] [p, p] [p, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, q] [q, s] [s, p] -> [s, s] [s, s] [s, p] , [s, i] [i, p] -> [s, s] [s, p] , [s, p] [p, 0] [0, 0] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, g] [g, 0] -> [s, f] [f, p] [p, p] [p, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, q] [q, s] [s, 0] -> [s, s] [s, s] [s, 0] , [s, i] [i, 0] -> [s, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, q] [q, s] [s, s] -> [s, s] [s, s] [s, s] , [s, i] [i, s] -> [s, s] [s, s] , [s, p] [p, 0] [0, f] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, g] [g, f] -> [s, f] [f, p] [p, p] [p, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, q] [q, s] [s, f] -> [s, s] [s, s] [s, f] , [s, i] [i, f] -> [s, s] [s, f] , [s, p] [p, 0] [0, g] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, g] [g, g] -> [s, f] [f, p] [p, p] [p, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, q] [q, s] [s, g] -> [s, s] [s, s] [s, g] , [s, i] [i, g] -> [s, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, q] [q, s] [s, q] -> [s, s] [s, s] [s, q] , [s, i] [i, q] -> [s, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [s, q] [q, s] [s, i] -> [s, s] [s, s] [s, i] , [s, i] [i, i] -> [s, s] [s, i] , [f, p] [p, 0] [0, p] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [f, p] [p, s] [s, 0] [0, p] -> [f, 0] [0, p] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, g] [g, p] -> [f, f] [f, p] [p, p] [p, p] , [f, q] [q, i] [i, p] -> [f, q] [q, s] [s, p] , [f, p] [p, 0] [0, 0] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [f, p] [p, s] [s, 0] [0, 0] -> [f, 0] [0, 0] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, g] [g, 0] -> [f, f] [f, p] [p, p] [p, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, 0] [0, s] -> [f, 0] [0, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, 0] [0, f] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [f, p] [p, s] [s, 0] [0, f] -> [f, 0] [0, f] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, g] [g, f] -> [f, f] [f, p] [p, p] [p, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, 0] [0, g] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [f, p] [p, s] [s, 0] [0, g] -> [f, 0] [0, g] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, g] [g, g] -> [f, f] [f, p] [p, p] [p, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, p] [p, s] [s, 0] [0, q] -> [f, 0] [0, q] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, f] [f, s] [s, q] -> [f, g] [g, q] [q, i] [i, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, q] [q, i] [i, q] -> [f, q] [q, s] [s, q] , [f, p] [p, s] [s, 0] [0, i] -> [f, 0] [0, i] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [f, f] [f, s] [s, i] -> [f, g] [g, q] [q, i] [i, i] , [f, q] [q, i] [i, i] -> [f, q] [q, s] [s, i] , [g, p] [p, 0] [0, p] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [g, p] [p, s] [s, 0] [0, p] -> [g, 0] [0, p] , [g, p] [p, s] [s, s] [s, p] -> [g, s] [s, p] [p, s] [s, p] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, g] [g, p] -> [g, f] [f, p] [p, p] [p, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, p] [p, 0] [0, 0] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [g, p] [p, s] [s, 0] [0, 0] -> [g, 0] [0, 0] , [g, p] [p, s] [s, s] [s, 0] -> [g, s] [s, p] [p, s] [s, 0] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, g] [g, 0] -> [g, f] [f, p] [p, p] [p, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, p] [p, 0] [0, s] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [g, p] [p, s] [s, 0] [0, s] -> [g, 0] [0, s] , [g, p] [p, s] [s, s] [s, s] -> [g, s] [s, p] [p, s] [s, s] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, p] [p, 0] [0, f] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [g, p] [p, s] [s, 0] [0, f] -> [g, 0] [0, f] , [g, p] [p, s] [s, s] [s, f] -> [g, s] [s, p] [p, s] [s, f] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, g] [g, f] -> [g, f] [f, p] [p, p] [p, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, p] [p, 0] [0, g] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [g, p] [p, s] [s, 0] [0, g] -> [g, 0] [0, g] , [g, p] [p, s] [s, s] [s, g] -> [g, s] [s, p] [p, s] [s, g] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, g] [g, g] -> [g, f] [f, p] [p, p] [p, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, p] [p, s] [s, 0] [0, q] -> [g, 0] [0, q] , [g, p] [p, s] [s, s] [s, q] -> [g, s] [s, p] [p, s] [s, q] , [g, f] [f, s] [s, q] -> [g, g] [g, q] [q, i] [i, q] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, p] [p, s] [s, 0] [0, i] -> [g, 0] [0, i] , [g, p] [p, s] [s, s] [s, i] -> [g, s] [s, p] [p, s] [s, i] , [g, f] [f, s] [s, i] -> [g, g] [g, q] [q, i] [i, i] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, g] [g, p] -> [q, f] [f, p] [p, p] [p, p] , [q, q] [q, i] [i, p] -> [q, q] [q, s] [s, p] , [q, q] [q, s] [s, p] -> [q, s] [s, s] [s, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, g] [g, 0] -> [q, f] [f, p] [p, p] [p, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, q] [q, s] [s, 0] -> [q, s] [s, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, q] [q, s] [s, s] -> [q, s] [s, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, g] [g, f] -> [q, f] [f, p] [p, p] [p, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, q] [q, s] [s, f] -> [q, s] [s, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, g] [g, g] -> [q, f] [f, p] [p, p] [p, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, q] [q, s] [s, g] -> [q, s] [s, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, f] [f, s] [s, q] -> [q, g] [g, q] [q, i] [i, q] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, q] [q, i] [i, q] -> [q, q] [q, s] [s, q] , [q, q] [q, s] [s, q] -> [q, s] [s, s] [s, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, f] [f, s] [s, i] -> [q, g] [g, q] [q, i] [i, i] , [q, q] [q, i] [i, i] -> [q, q] [q, s] [s, i] , [q, q] [q, s] [s, i] -> [q, s] [s, s] [s, i] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, 0] [0, p] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, g] [g, p] -> [i, f] [f, p] [p, p] [p, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, q] [q, s] [s, p] -> [i, s] [s, s] [s, p] , [i, i] [i, p] -> [i, s] [s, p] , [i, p] [p, 0] [0, 0] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, g] [g, 0] -> [i, f] [f, p] [p, p] [p, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, q] [q, s] [s, 0] -> [i, s] [s, s] [s, 0] , [i, i] [i, 0] -> [i, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, q] [q, s] [s, s] -> [i, s] [s, s] [s, s] , [i, i] [i, s] -> [i, s] [s, s] , [i, p] [p, 0] [0, f] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, g] [g, f] -> [i, f] [f, p] [p, p] [p, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, q] [q, s] [s, f] -> [i, s] [s, s] [s, f] , [i, i] [i, f] -> [i, s] [s, f] , [i, p] [p, 0] [0, g] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, g] [g, g] -> [i, f] [f, p] [p, p] [p, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, q] [q, s] [s, g] -> [i, s] [s, s] [s, g] , [i, i] [i, g] -> [i, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, q] [q, s] [s, q] -> [i, s] [s, s] [s, q] , [i, i] [i, q] -> [i, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] , [i, q] [q, s] [s, i] -> [i, s] [s, s] [s, i] , [i, i] [i, i] -> [i, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, q] is interpreted by / \ | 1 1 | | 0 1 | \ / [p, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, g] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 310-rule system { [p, p] [p, 0] [0, p] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, g] [g, p] -> [p, f] [f, p] [p, p] [p, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, i] [i, p] -> [p, s] [s, p] , [p, p] [p, 0] [0, 0] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, g] [g, 0] -> [p, f] [f, p] [p, p] [p, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, i] [i, 0] -> [p, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, i] [i, s] -> [p, s] [s, s] , [p, p] [p, 0] [0, f] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, g] [g, f] -> [p, f] [f, p] [p, p] [p, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, i] [i, f] -> [p, s] [s, f] , [p, p] [p, 0] [0, g] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, g] [g, g] -> [p, f] [f, p] [p, p] [p, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, i] [i, g] -> [p, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, f] [f, s] [s, q] -> [p, g] [g, q] [q, i] [i, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, i] [i, q] -> [p, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, f] [f, s] [s, i] -> [p, g] [g, q] [q, i] [i, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [p, i] [i, i] -> [p, s] [s, i] , [0, p] [p, 0] [0, p] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [0, p] [p, s] [s, 0] [0, p] -> [0, 0] [0, p] , [0, p] [p, s] [s, s] [s, p] -> [0, s] [s, p] [p, s] [s, p] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, g] [g, p] -> [0, f] [f, p] [p, p] [p, p] , [0, q] [q, i] [i, p] -> [0, q] [q, s] [s, p] , [0, p] [p, 0] [0, 0] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [0, p] [p, s] [s, 0] [0, 0] -> [0, 0] [0, 0] , [0, p] [p, s] [s, s] [s, 0] -> [0, s] [s, p] [p, s] [s, 0] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, g] [g, 0] -> [0, f] [f, p] [p, p] [p, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, p] [p, 0] [0, s] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [0, p] [p, s] [s, 0] [0, s] -> [0, 0] [0, s] , [0, p] [p, s] [s, s] [s, s] -> [0, s] [s, p] [p, s] [s, s] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, p] [p, 0] [0, f] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [0, p] [p, s] [s, 0] [0, f] -> [0, 0] [0, f] , [0, p] [p, s] [s, s] [s, f] -> [0, s] [s, p] [p, s] [s, f] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, g] [g, f] -> [0, f] [f, p] [p, p] [p, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, p] [p, 0] [0, g] -> [0, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [0, p] [p, s] [s, 0] [0, g] -> [0, 0] [0, g] , [0, p] [p, s] [s, s] [s, g] -> [0, s] [s, p] [p, s] [s, g] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, g] [g, g] -> [0, f] [f, p] [p, p] [p, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, p] [p, s] [s, 0] [0, q] -> [0, 0] [0, q] , [0, p] [p, s] [s, s] [s, q] -> [0, s] [s, p] [p, s] [s, q] , [0, f] [f, s] [s, q] -> [0, g] [g, q] [q, i] [i, q] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [0, q] [q, i] [i, q] -> [0, q] [q, s] [s, q] , [0, p] [p, s] [s, 0] [0, i] -> [0, 0] [0, i] , [0, p] [p, s] [s, s] [s, i] -> [0, s] [s, p] [p, s] [s, i] , [0, f] [f, s] [s, i] -> [0, g] [g, q] [q, i] [i, i] , [0, q] [q, i] [i, i] -> [0, q] [q, s] [s, i] , [s, p] [p, 0] [0, p] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, g] [g, p] -> [s, f] [f, p] [p, p] [p, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, q] [q, s] [s, p] -> [s, s] [s, s] [s, p] , [s, i] [i, p] -> [s, s] [s, p] , [s, p] [p, 0] [0, 0] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, g] [g, 0] -> [s, f] [f, p] [p, p] [p, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, q] [q, s] [s, 0] -> [s, s] [s, s] [s, 0] , [s, i] [i, 0] -> [s, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, q] [q, s] [s, s] -> [s, s] [s, s] [s, s] , [s, i] [i, s] -> [s, s] [s, s] , [s, p] [p, 0] [0, f] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, g] [g, f] -> [s, f] [f, p] [p, p] [p, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, q] [q, s] [s, f] -> [s, s] [s, s] [s, f] , [s, i] [i, f] -> [s, s] [s, f] , [s, p] [p, 0] [0, g] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, g] [g, g] -> [s, f] [f, p] [p, p] [p, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, q] [q, s] [s, g] -> [s, s] [s, s] [s, g] , [s, i] [i, g] -> [s, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, q] [q, s] [s, q] -> [s, s] [s, s] [s, q] , [s, i] [i, q] -> [s, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [s, q] [q, s] [s, i] -> [s, s] [s, s] [s, i] , [s, i] [i, i] -> [s, s] [s, i] , [f, p] [p, 0] [0, p] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [f, p] [p, s] [s, 0] [0, p] -> [f, 0] [0, p] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, g] [g, p] -> [f, f] [f, p] [p, p] [p, p] , [f, q] [q, i] [i, p] -> [f, q] [q, s] [s, p] , [f, p] [p, 0] [0, 0] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [f, p] [p, s] [s, 0] [0, 0] -> [f, 0] [0, 0] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, g] [g, 0] -> [f, f] [f, p] [p, p] [p, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, 0] [0, s] -> [f, 0] [0, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, 0] [0, f] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [f, p] [p, s] [s, 0] [0, f] -> [f, 0] [0, f] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, g] [g, f] -> [f, f] [f, p] [p, p] [p, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, 0] [0, g] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [f, p] [p, s] [s, 0] [0, g] -> [f, 0] [0, g] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, g] [g, g] -> [f, f] [f, p] [p, p] [p, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, p] [p, s] [s, 0] [0, q] -> [f, 0] [0, q] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, f] 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p] [p, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, p] [p, 0] [0, s] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [g, p] [p, s] [s, 0] [0, s] -> [g, 0] [0, s] , [g, p] [p, s] [s, s] [s, s] -> [g, s] [s, p] [p, s] [s, s] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, p] [p, 0] [0, f] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [g, p] [p, s] [s, 0] [0, f] -> [g, 0] [0, f] , [g, p] [p, s] [s, s] [s, f] -> [g, s] [s, p] [p, s] [s, f] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, g] [g, f] -> [g, f] [f, p] [p, p] [p, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, p] [p, 0] [0, g] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [g, p] [p, s] [s, 0] [0, g] -> [g, 0] [0, g] , [g, p] [p, s] [s, s] [s, g] -> [g, s] [s, p] [p, s] [s, g] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, g] [g, g] -> [g, f] [f, p] [p, p] [p, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, p] [p, s] [s, 0] [0, q] -> [g, 0] [0, q] , [g, p] [p, s] [s, s] [s, q] -> [g, s] [s, p] [p, s] [s, q] , [g, f] [f, s] [s, q] -> [g, g] [g, q] [q, i] [i, q] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, p] [p, s] [s, 0] [0, i] -> [g, 0] [0, i] , [g, p] [p, s] [s, s] [s, i] -> [g, s] [s, p] [p, s] [s, i] , [g, f] [f, s] [s, i] -> [g, g] [g, q] [q, i] [i, i] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, g] [g, p] -> [q, f] [f, p] [p, p] [p, p] , [q, q] [q, i] [i, p] -> [q, q] [q, s] [s, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, g] [g, 0] -> [q, f] [f, p] [p, p] [p, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, g] [g, f] -> [q, f] [f, p] [p, p] [p, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, g] [g, g] -> [q, f] [f, p] [p, p] [p, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, f] [f, s] [s, q] -> [q, g] [g, q] [q, i] [i, q] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, q] [q, i] [i, q] -> [q, q] [q, s] [s, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, f] [f, s] [s, i] -> [q, g] [g, q] [q, i] [i, i] , [q, q] [q, i] [i, i] -> [q, q] [q, s] [s, i] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, 0] [0, p] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, p] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, g] [g, p] -> [i, f] [f, p] [p, p] [p, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, q] [q, s] [s, p] -> [i, s] [s, s] [s, p] , [i, i] [i, p] -> [i, s] [s, p] , [i, p] [p, 0] [0, 0] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, g] [g, 0] -> [i, f] [f, p] [p, p] [p, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, q] [q, s] [s, 0] -> [i, s] [s, s] [s, 0] , [i, i] [i, 0] -> [i, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, q] [q, s] [s, s] -> [i, s] [s, s] [s, s] , [i, i] [i, s] -> [i, s] [s, s] , [i, p] [p, 0] [0, f] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, g] [g, f] -> [i, f] [f, p] [p, p] [p, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, q] [q, s] [s, f] -> [i, s] [s, s] [s, f] , [i, i] [i, f] -> [i, s] [s, f] , [i, p] [p, 0] [0, g] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, g] [g, g] -> [i, f] [f, p] [p, p] [p, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, q] [q, s] [s, g] -> [i, s] [s, s] [s, g] , [i, i] [i, g] -> [i, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, q] [q, s] [s, q] -> [i, s] [s, s] [s, q] , [i, i] [i, q] -> [i, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] , [i, q] [q, s] [s, i] -> [i, s] [s, s] [s, i] , [i, i] [i, i] -> [i, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, p] is interpreted by / \ | 1 1 | | 0 1 | \ / [p, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, g] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 286-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, g] [g, p] -> [p, f] [f, p] [p, p] [p, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, i] [i, p] -> [p, s] [s, p] , [p, p] [p, 0] [0, 0] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, g] [g, 0] -> [p, f] [f, p] [p, p] [p, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, i] [i, 0] -> [p, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, i] [i, s] -> [p, s] [s, s] , [p, p] [p, 0] [0, f] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, g] [g, f] -> [p, f] [f, p] [p, p] [p, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, i] [i, f] -> [p, s] [s, f] , [p, p] [p, 0] [0, g] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, g] [g, g] -> [p, f] [f, p] [p, p] [p, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, i] [i, g] -> [p, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, f] [f, s] [s, q] -> [p, g] [g, q] [q, i] [i, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, i] [i, q] -> [p, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, f] [f, s] [s, i] -> [p, g] [g, q] [q, i] [i, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [p, i] [i, i] -> [p, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, g] [g, p] -> [0, f] [f, p] [p, p] [p, p] , [0, q] [q, i] [i, p] -> [0, q] [q, s] [s, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, g] [g, 0] -> [0, f] [f, p] [p, p] [p, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, g] [g, f] -> [0, f] [f, p] [p, p] [p, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, g] [g, g] -> [0, f] [f, p] [p, p] [p, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, f] [f, s] [s, q] -> [0, g] [g, q] [q, i] [i, q] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [0, q] [q, i] [i, q] -> [0, q] [q, s] [s, q] , [0, f] [f, s] [s, i] -> [0, g] [g, q] [q, i] [i, i] , [0, q] [q, i] [i, i] -> [0, q] [q, s] [s, i] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, g] [g, p] -> [s, f] [f, p] [p, p] [p, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, q] [q, s] [s, p] -> [s, s] [s, s] [s, p] , [s, i] [i, p] -> [s, s] [s, p] , [s, p] [p, 0] [0, 0] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, g] [g, 0] -> [s, f] [f, p] [p, p] [p, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, q] [q, s] [s, 0] -> [s, s] [s, s] [s, 0] , [s, i] [i, 0] -> [s, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, q] [q, s] [s, s] -> [s, s] [s, s] [s, s] , [s, i] [i, s] -> [s, s] [s, s] , [s, p] [p, 0] [0, f] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, g] [g, f] -> [s, f] [f, p] [p, p] [p, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, q] [q, s] [s, f] -> [s, s] [s, s] [s, f] , [s, i] [i, f] -> [s, s] [s, f] , [s, p] [p, 0] [0, g] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, g] [g, g] -> [s, f] [f, p] [p, p] [p, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, q] [q, s] [s, g] -> [s, s] [s, s] [s, g] , [s, i] [i, g] -> [s, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, q] [q, s] [s, q] -> [s, s] [s, s] [s, q] , [s, i] [i, q] -> [s, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [s, q] [q, s] [s, i] -> [s, s] [s, s] [s, i] , [s, i] [i, i] -> [s, s] [s, i] , [f, p] [p, s] [s, 0] [0, p] -> [f, 0] [0, p] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, g] [g, p] -> [f, f] [f, p] [p, p] [p, p] , [f, q] [q, i] [i, p] -> [f, q] [q, s] [s, p] , [f, p] [p, 0] [0, 0] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [f, p] [p, s] [s, 0] [0, 0] -> [f, 0] [0, 0] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, g] [g, 0] -> [f, f] [f, p] [p, p] [p, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, 0] [0, s] -> [f, 0] [0, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, 0] [0, f] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [f, p] [p, s] [s, 0] [0, f] -> [f, 0] [0, f] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, g] [g, f] -> [f, f] [f, p] [p, p] [p, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, 0] [0, g] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [f, p] [p, s] [s, 0] [0, g] -> [f, 0] [0, g] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, g] [g, g] -> [f, f] [f, p] [p, p] [p, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, p] [p, s] [s, 0] [0, q] -> [f, 0] [0, q] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, f] [f, s] [s, q] -> [f, g] [g, q] [q, i] [i, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, q] [q, i] [i, q] -> [f, q] [q, s] [s, q] , [f, p] [p, s] [s, 0] [0, i] -> [f, 0] [0, i] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [f, f] [f, s] [s, i] -> [f, g] [g, q] [q, i] [i, i] , [f, q] [q, i] [i, i] -> [f, q] [q, s] [s, i] , [g, p] [p, s] [s, 0] [0, p] -> [g, 0] [0, p] , [g, p] [p, s] [s, s] [s, p] -> [g, s] [s, p] [p, s] [s, p] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, g] [g, p] -> [g, f] [f, p] [p, p] [p, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, p] [p, 0] [0, 0] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [g, p] [p, s] [s, 0] [0, 0] -> [g, 0] [0, 0] , [g, p] [p, s] [s, s] [s, 0] -> [g, s] [s, p] [p, s] [s, 0] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, g] [g, 0] -> [g, f] [f, p] [p, p] [p, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, p] [p, 0] [0, s] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [g, p] [p, s] [s, 0] [0, s] -> [g, 0] [0, s] , [g, p] [p, s] [s, s] [s, s] -> [g, s] [s, p] [p, s] [s, s] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, p] [p, 0] [0, f] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [g, p] [p, s] [s, 0] [0, f] -> [g, 0] [0, f] , [g, p] [p, s] [s, s] [s, f] -> [g, s] [s, p] [p, s] [s, f] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, g] [g, f] -> [g, f] [f, p] [p, p] [p, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, p] [p, 0] [0, g] -> [g, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [g, p] [p, s] [s, 0] [0, g] -> [g, 0] [0, g] , [g, p] [p, s] [s, s] [s, g] -> [g, s] [s, p] [p, s] [s, g] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, g] [g, g] -> [g, f] [f, p] [p, p] [p, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, p] [p, s] [s, 0] [0, q] -> [g, 0] [0, q] , [g, p] [p, s] [s, s] [s, q] -> [g, s] [s, p] [p, s] [s, q] , [g, f] [f, s] [s, q] -> [g, g] [g, q] [q, i] [i, q] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, p] [p, s] [s, 0] [0, i] -> [g, 0] [0, i] , [g, p] [p, s] [s, s] [s, i] -> [g, s] [s, p] [p, s] [s, i] , [g, f] [f, s] [s, i] -> [g, g] [g, q] [q, i] [i, i] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, g] [g, p] -> [q, f] [f, p] [p, p] [p, p] , [q, q] [q, i] [i, p] -> [q, q] [q, s] [s, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, g] [g, 0] -> [q, f] [f, p] [p, p] [p, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, g] [g, f] -> [q, f] [f, p] [p, p] [p, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, g] [g, g] -> [q, f] [f, p] [p, p] [p, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, f] [f, s] [s, q] -> [q, g] [g, q] [q, i] [i, q] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, q] [q, i] [i, q] -> [q, q] [q, s] [s, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, f] [f, s] [s, i] -> [q, g] [g, q] [q, i] [i, i] , [q, q] [q, i] [i, i] -> [q, q] [q, s] [s, i] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, g] [g, p] -> [i, f] [f, p] [p, p] [p, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, q] [q, s] [s, p] -> [i, s] [s, s] [s, p] , [i, i] [i, p] -> [i, s] [s, p] , [i, p] [p, 0] [0, 0] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, g] [g, 0] -> [i, f] [f, p] [p, p] [p, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, q] [q, s] [s, 0] -> [i, s] [s, s] [s, 0] , [i, i] [i, 0] -> [i, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, q] [q, s] [s, s] -> [i, s] [s, s] [s, s] , [i, i] [i, s] -> [i, s] [s, s] , [i, p] [p, 0] [0, f] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, g] [g, f] -> [i, f] [f, p] [p, p] [p, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, q] [q, s] [s, f] -> [i, s] [s, s] [s, f] , [i, i] [i, f] -> [i, s] [s, f] , [i, p] [p, 0] [0, g] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, g] [g, g] -> [i, f] [f, p] [p, p] [p, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, q] [q, s] [s, g] -> [i, s] [s, s] [s, g] , [i, i] [i, g] -> [i, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, q] [q, s] [s, q] -> [i, s] [s, s] [s, q] , [i, i] [i, q] -> [i, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] , [i, q] [q, s] [s, i] -> [i, s] [s, s] [s, i] , [i, i] [i, i] -> [i, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, p] is interpreted by / \ | 1 1 | | 0 1 | \ / [f, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, g] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 261-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, i] [i, p] -> [p, s] [s, p] , [p, p] [p, 0] [0, 0] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, g] [g, 0] -> [p, f] [f, p] [p, p] [p, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, i] [i, 0] -> [p, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, i] [i, s] -> [p, s] [s, s] , [p, p] [p, 0] [0, f] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, g] [g, f] -> [p, f] [f, p] [p, p] [p, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, i] [i, f] -> [p, s] [s, f] , [p, p] [p, 0] [0, g] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, g] [g, g] -> [p, f] [f, p] [p, p] [p, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, i] [i, g] -> [p, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, f] [f, s] [s, q] -> [p, g] [g, q] [q, i] [i, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, i] [i, q] -> [p, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, f] [f, s] [s, i] -> [p, g] [g, q] [q, i] [i, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [p, i] [i, i] -> [p, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, q] [q, i] [i, p] -> [0, q] [q, s] [s, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, g] [g, 0] -> [0, f] [f, p] [p, p] [p, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, g] [g, f] -> [0, f] [f, p] [p, p] [p, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, g] [g, g] -> [0, f] [f, p] [p, p] [p, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, f] [f, s] [s, q] -> [0, g] [g, q] [q, i] [i, q] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [0, q] [q, i] [i, q] -> [0, q] [q, s] [s, q] , [0, f] [f, s] [s, i] -> [0, g] [g, q] [q, i] [i, i] , [0, q] [q, i] [i, i] -> [0, q] [q, s] [s, i] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, q] [q, s] [s, p] -> [s, s] [s, s] [s, p] , [s, i] [i, p] -> [s, s] [s, p] , [s, p] [p, 0] [0, 0] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, g] [g, 0] -> [s, f] [f, p] [p, p] [p, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, q] [q, s] [s, 0] -> [s, s] [s, s] [s, 0] , [s, i] [i, 0] -> [s, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, q] [q, s] [s, s] -> [s, s] [s, s] [s, s] , [s, i] [i, s] -> [s, s] [s, s] , [s, p] [p, 0] [0, f] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, g] [g, f] -> [s, f] [f, p] [p, p] [p, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, q] [q, s] [s, f] -> [s, s] [s, s] [s, f] , [s, i] [i, f] -> [s, s] [s, f] , [s, p] [p, 0] [0, g] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, g] [g, g] -> [s, f] [f, p] [p, p] [p, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, q] [q, s] [s, g] -> [s, s] [s, s] [s, g] , [s, i] [i, g] -> [s, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, q] [q, s] [s, q] -> [s, s] [s, s] [s, q] , [s, i] [i, q] -> [s, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [s, q] [q, s] [s, i] -> [s, s] [s, s] [s, i] , [s, i] [i, i] -> [s, s] [s, i] , [f, p] [p, s] [s, 0] [0, p] -> [f, 0] [0, p] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, q] [q, i] [i, p] -> [f, q] [q, s] [s, p] , [f, p] [p, 0] [0, 0] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [f, p] [p, s] [s, 0] [0, 0] -> [f, 0] [0, 0] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, g] [g, 0] -> [f, f] [f, p] [p, p] [p, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, 0] [0, s] -> [f, 0] [0, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, 0] [0, f] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [f, p] [p, s] [s, 0] [0, f] -> [f, 0] [0, f] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, g] [g, f] -> [f, f] [f, p] [p, p] [p, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, 0] [0, g] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [f, p] [p, s] [s, 0] [0, g] -> [f, 0] [0, g] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, g] [g, g] -> [f, f] [f, p] [p, p] [p, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, p] [p, s] [s, 0] [0, q] -> [f, 0] [0, q] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, f] [f, s] [s, q] -> [f, g] [g, q] [q, i] [i, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, q] [q, i] [i, q] -> [f, q] [q, s] [s, q] , [f, p] [p, s] [s, 0] [0, i] -> [f, 0] [0, i] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [f, f] [f, s] [s, i] -> [f, g] [g, q] [q, i] [i, i] , [f, q] [q, i] [i, i] -> [f, q] [q, s] [s, i] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, g] [g, 0] -> [g, f] [f, p] [p, p] [p, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, g] [g, f] -> [g, f] [f, p] [p, p] [p, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, g] [g, g] -> [g, f] [f, p] [p, p] [p, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, f] [f, s] [s, q] -> [g, g] [g, q] [q, i] [i, q] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, f] [f, s] [s, i] -> [g, g] [g, q] [q, i] [i, i] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, q] [q, i] [i, p] -> [q, q] [q, s] [s, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, g] [g, 0] -> [q, f] [f, p] [p, p] [p, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, g] [g, f] -> [q, f] [f, p] [p, p] [p, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, g] [g, g] -> [q, f] [f, p] [p, p] [p, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, f] [f, s] [s, q] -> [q, g] [g, q] [q, i] [i, q] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, q] [q, i] [i, q] -> [q, q] [q, s] [s, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, f] [f, s] [s, i] -> [q, g] [g, q] [q, i] [i, i] , [q, q] [q, i] [i, i] -> [q, q] [q, s] [s, i] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, q] [q, s] [s, p] -> [i, s] [s, s] [s, p] , [i, i] [i, p] -> [i, s] [s, p] , [i, p] [p, 0] [0, 0] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, g] [g, 0] -> [i, f] [f, p] [p, p] [p, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, q] [q, s] [s, 0] -> [i, s] [s, s] [s, 0] , [i, i] [i, 0] -> [i, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, q] [q, s] [s, s] -> [i, s] [s, s] [s, s] , [i, i] [i, s] -> [i, s] [s, s] , [i, p] [p, 0] [0, f] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, g] [g, f] -> [i, f] [f, p] [p, p] [p, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, q] [q, s] [s, f] -> [i, s] [s, s] [s, f] , [i, i] [i, f] -> [i, s] [s, f] , [i, p] [p, 0] [0, g] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, g] [g, g] -> [i, f] [f, p] [p, p] [p, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, q] [q, s] [s, g] -> [i, s] [s, s] [s, g] , [i, i] [i, g] -> [i, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, q] [q, s] [s, q] -> [i, s] [s, s] [s, q] , [i, i] [i, q] -> [i, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] , [i, q] [q, s] [s, i] -> [i, s] [s, s] [s, i] , [i, i] [i, i] -> [i, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, i] is interpreted by / \ | 1 1 | | 0 1 | \ / [0, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, g] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 254-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, 0] [0, 0] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, g] [g, 0] -> [p, f] [f, p] [p, p] [p, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, 0] [0, f] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, g] [g, f] -> [p, f] [f, p] [p, p] [p, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, 0] [0, g] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, g] [g, g] -> [p, f] [f, p] [p, p] [p, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, f] [f, s] [s, q] -> [p, g] [g, q] [q, i] [i, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, f] [f, s] [s, i] -> [p, g] [g, q] [q, i] [i, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, q] [q, i] [i, p] -> [0, q] [q, s] [s, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, g] [g, 0] -> [0, f] [f, p] [p, p] [p, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, g] [g, f] -> [0, f] [f, p] [p, p] [p, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, g] [g, g] -> [0, f] [f, p] [p, p] [p, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, f] [f, s] [s, q] -> [0, g] [g, q] [q, i] [i, q] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [0, q] [q, i] [i, q] -> [0, q] [q, s] [s, q] , [0, f] [f, s] [s, i] -> [0, g] [g, q] [q, i] [i, i] , [0, q] [q, i] [i, i] -> [0, q] [q, s] [s, i] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, q] [q, s] [s, p] -> [s, s] [s, s] [s, p] , [s, i] [i, p] -> [s, s] [s, p] , [s, p] [p, 0] [0, 0] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, g] [g, 0] -> [s, f] [f, p] [p, p] [p, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, q] [q, s] [s, 0] -> [s, s] [s, s] [s, 0] , [s, i] [i, 0] -> [s, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, q] [q, s] [s, s] -> [s, s] [s, s] [s, s] , [s, i] [i, s] -> [s, s] [s, s] , [s, p] [p, 0] [0, f] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, g] [g, f] -> [s, f] [f, p] [p, p] [p, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, q] [q, s] [s, f] -> [s, s] [s, s] [s, f] , [s, i] [i, f] -> [s, s] [s, f] , [s, p] [p, 0] [0, g] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, g] [g, g] -> [s, f] [f, p] [p, p] [p, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, q] [q, s] [s, g] -> [s, s] [s, s] [s, g] , [s, i] [i, g] -> [s, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, q] [q, s] [s, q] -> [s, s] [s, s] [s, q] , [s, i] [i, q] -> [s, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [s, q] [q, s] [s, i] -> [s, s] [s, s] [s, i] , [s, i] [i, i] -> [s, s] [s, i] , [f, p] [p, s] [s, 0] [0, p] -> [f, 0] [0, p] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, q] [q, i] [i, p] -> [f, q] [q, s] [s, p] , [f, p] [p, 0] [0, 0] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [f, p] [p, s] [s, 0] [0, 0] -> [f, 0] [0, 0] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, g] [g, 0] -> [f, f] [f, p] [p, p] [p, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, 0] [0, s] -> [f, 0] [0, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, 0] [0, f] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [f, p] [p, s] [s, 0] [0, f] -> [f, 0] [0, f] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, g] [g, f] -> [f, f] [f, p] [p, p] [p, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, 0] [0, g] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [f, p] [p, s] [s, 0] [0, g] -> [f, 0] [0, g] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, g] [g, g] -> [f, f] [f, p] [p, p] [p, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, p] [p, s] [s, 0] [0, q] -> [f, 0] [0, q] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, f] [f, s] [s, q] -> [f, g] [g, q] [q, i] [i, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, q] [q, i] [i, q] -> [f, q] [q, s] [s, q] , [f, p] [p, s] [s, 0] [0, i] -> [f, 0] [0, i] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [f, f] [f, s] [s, i] -> [f, g] [g, q] [q, i] [i, i] , [f, q] [q, i] [i, i] -> [f, q] [q, s] [s, i] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, g] [g, 0] -> [g, f] [f, p] [p, p] [p, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, g] [g, f] -> [g, f] [f, p] [p, p] [p, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, g] [g, g] -> [g, f] [f, p] [p, p] [p, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, f] [f, s] [s, q] -> [g, g] [g, q] [q, i] [i, q] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, f] [f, s] [s, i] -> [g, g] [g, q] [q, i] [i, i] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, q] [q, i] [i, p] -> [q, q] [q, s] [s, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, g] [g, 0] -> [q, f] [f, p] [p, p] [p, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, g] [g, f] -> [q, f] [f, p] [p, p] [p, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, g] [g, g] -> [q, f] [f, p] [p, p] [p, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, f] [f, s] [s, q] -> [q, g] [g, q] [q, i] [i, q] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, q] [q, i] [i, q] -> [q, q] [q, s] [s, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, f] [f, s] [s, i] -> [q, g] [g, q] [q, i] [i, i] , [q, q] [q, i] [i, i] -> [q, q] [q, s] [s, i] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, q] [q, s] [s, p] -> [i, s] [s, s] [s, p] , [i, i] [i, p] -> [i, s] [s, p] , [i, p] [p, 0] [0, 0] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, 0] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, g] [g, 0] -> [i, f] [f, p] [p, p] [p, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, q] [q, s] [s, 0] -> [i, s] [s, s] [s, 0] , [i, i] [i, 0] -> [i, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, q] [q, s] [s, s] -> [i, s] [s, s] [s, s] , [i, i] [i, s] -> [i, s] [s, s] , [i, p] [p, 0] [0, f] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, g] [g, f] -> [i, f] [f, p] [p, p] [p, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, q] [q, s] [s, f] -> [i, s] [s, s] [s, f] , [i, i] [i, f] -> [i, s] [s, f] , [i, p] [p, 0] [0, g] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, g] [g, g] -> [i, f] [f, p] [p, p] [p, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, q] [q, s] [s, g] -> [i, s] [s, s] [s, g] , [i, i] [i, g] -> [i, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, q] [q, s] [s, q] -> [i, s] [s, s] [s, q] , [i, i] [i, q] -> [i, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] , [i, q] [q, s] [s, i] -> [i, s] [s, s] [s, i] , [i, i] [i, i] -> [i, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 0] is interpreted by / \ | 1 1 | | 0 1 | \ / [i, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, g] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 250-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, g] [g, 0] -> [p, f] [f, p] [p, p] [p, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, 0] [0, f] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, g] [g, f] -> [p, f] [f, p] [p, p] [p, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, 0] [0, g] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, g] [g, g] -> [p, f] [f, p] [p, p] [p, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, f] [f, s] [s, q] -> [p, g] [g, q] [q, i] [i, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, f] [f, s] [s, i] -> [p, g] [g, q] [q, i] [i, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, q] [q, i] [i, p] -> [0, q] [q, s] [s, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, g] [g, 0] -> [0, f] [f, p] [p, p] [p, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, g] [g, f] -> [0, f] [f, p] [p, p] [p, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, g] [g, g] -> [0, f] [f, p] [p, p] [p, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, f] [f, s] [s, q] -> [0, g] [g, q] [q, i] [i, q] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [0, q] [q, i] [i, q] -> [0, q] [q, s] [s, q] , [0, f] [f, s] [s, i] -> [0, g] [g, q] [q, i] [i, i] , [0, q] [q, i] [i, i] -> [0, q] [q, s] [s, i] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, q] [q, s] [s, p] -> [s, s] [s, s] [s, p] , [s, i] [i, p] -> [s, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, g] [g, 0] -> [s, f] [f, p] [p, p] [p, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, q] [q, s] [s, 0] -> [s, s] [s, s] [s, 0] , [s, i] [i, 0] -> [s, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, q] [q, s] [s, s] -> [s, s] [s, s] [s, s] , [s, i] [i, s] -> [s, s] [s, s] , [s, p] [p, 0] [0, f] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, g] [g, f] -> [s, f] [f, p] [p, p] [p, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, q] [q, s] [s, f] -> [s, s] [s, s] [s, f] , [s, i] [i, f] -> [s, s] [s, f] , [s, p] [p, 0] [0, g] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, g] [g, g] -> [s, f] [f, p] [p, p] [p, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, q] [q, s] [s, g] -> [s, s] [s, s] [s, g] , [s, i] [i, g] -> [s, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, q] [q, s] [s, q] -> [s, s] [s, s] [s, q] , [s, i] [i, q] -> [s, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [s, q] [q, s] [s, i] -> [s, s] [s, s] [s, i] , [s, i] [i, i] -> [s, s] [s, i] , [f, p] [p, s] [s, 0] [0, p] -> [f, 0] [0, p] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, q] [q, i] [i, p] -> [f, q] [q, s] [s, p] , [f, p] [p, s] [s, 0] [0, 0] -> [f, 0] [0, 0] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, g] [g, 0] -> [f, f] [f, p] [p, p] [p, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, 0] [0, s] -> [f, 0] [0, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, 0] [0, f] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [f, p] [p, s] [s, 0] [0, f] -> [f, 0] [0, f] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, g] [g, f] -> [f, f] [f, p] [p, p] [p, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, 0] [0, g] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [f, p] [p, s] [s, 0] [0, g] -> [f, 0] [0, g] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, g] [g, g] -> [f, f] [f, p] [p, p] [p, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, p] [p, s] [s, 0] [0, q] -> [f, 0] [0, q] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, f] [f, s] [s, q] -> [f, g] [g, q] [q, i] [i, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, q] [q, i] [i, q] -> [f, q] [q, s] [s, q] , [f, p] [p, s] [s, 0] [0, i] -> [f, 0] [0, i] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [f, f] [f, s] [s, i] -> [f, g] [g, q] [q, i] [i, i] , [f, q] [q, i] [i, i] -> [f, q] [q, s] [s, i] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, g] [g, 0] -> [g, f] [f, p] [p, p] [p, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, g] [g, f] -> [g, f] [f, p] [p, p] [p, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, g] [g, g] -> [g, f] [f, p] [p, p] [p, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, f] [f, s] [s, q] -> [g, g] [g, q] [q, i] [i, q] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, f] [f, s] [s, i] -> [g, g] [g, q] [q, i] [i, i] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, q] [q, i] [i, p] -> [q, q] [q, s] [s, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, g] [g, 0] -> [q, f] [f, p] [p, p] [p, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, g] [g, f] -> [q, f] [f, p] [p, p] [p, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, g] [g, g] -> [q, f] [f, p] [p, p] [p, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, f] [f, s] [s, q] -> [q, g] [g, q] [q, i] [i, q] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, q] [q, i] [i, q] -> [q, q] [q, s] [s, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, f] [f, s] [s, i] -> [q, g] [g, q] [q, i] [i, i] , [q, q] [q, i] [i, i] -> [q, q] [q, s] [s, i] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, q] [q, s] [s, p] -> [i, s] [s, s] [s, p] , [i, i] [i, p] -> [i, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, g] [g, 0] -> [i, f] [f, p] [p, p] [p, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, q] [q, s] [s, 0] -> [i, s] [s, s] [s, 0] , [i, i] [i, 0] -> [i, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, q] [q, s] [s, s] -> [i, s] [s, s] [s, s] , [i, i] [i, s] -> [i, s] [s, s] , [i, p] [p, 0] [0, f] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, g] [g, f] -> [i, f] [f, p] [p, p] [p, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, q] [q, s] [s, f] -> [i, s] [s, s] [s, f] , [i, i] [i, f] -> [i, s] [s, f] , [i, p] [p, 0] [0, g] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, g] [g, g] -> [i, f] [f, p] [p, p] [p, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, q] [q, s] [s, g] -> [i, s] [s, s] [s, g] , [i, i] [i, g] -> [i, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, q] [q, s] [s, q] -> [i, s] [s, s] [s, q] , [i, i] [i, q] -> [i, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] , [i, q] [q, s] [s, i] -> [i, s] [s, s] [s, i] , [i, i] [i, i] -> [i, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, 0] is interpreted by / \ | 1 1 | | 0 1 | \ / [i, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, g] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 243-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, 0] [0, f] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, g] [g, f] -> [p, f] [f, p] [p, p] [p, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, 0] [0, g] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, g] [g, g] -> [p, f] [f, p] [p, p] [p, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, f] [f, s] [s, q] -> [p, g] [g, q] [q, i] [i, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, f] [f, s] [s, i] -> [p, g] [g, q] [q, i] [i, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, q] [q, i] [i, p] -> [0, q] [q, s] [s, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, g] [g, f] -> [0, f] [f, p] [p, p] [p, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, g] [g, g] -> [0, f] [f, p] [p, p] [p, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, f] [f, s] [s, q] -> [0, g] [g, q] [q, i] [i, q] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [0, q] [q, i] [i, q] -> [0, q] [q, s] [s, q] , [0, f] [f, s] [s, i] -> [0, g] [g, q] [q, i] [i, i] , [0, q] [q, i] [i, i] -> [0, q] [q, s] [s, i] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, q] [q, s] [s, p] -> [s, s] [s, s] [s, p] , [s, i] [i, p] -> [s, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, q] [q, s] [s, 0] -> [s, s] [s, s] [s, 0] , [s, i] [i, 0] -> [s, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, q] [q, s] [s, s] -> [s, s] [s, s] [s, s] , [s, i] [i, s] -> [s, s] [s, s] , [s, p] [p, 0] [0, f] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, g] [g, f] -> [s, f] [f, p] [p, p] [p, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, q] [q, s] [s, f] -> [s, s] [s, s] [s, f] , [s, i] [i, f] -> [s, s] [s, f] , [s, p] [p, 0] [0, g] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, g] [g, g] -> [s, f] [f, p] [p, p] [p, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, q] [q, s] [s, g] -> [s, s] [s, s] [s, g] , [s, i] [i, g] -> [s, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, q] [q, s] [s, q] -> [s, s] [s, s] [s, q] , [s, i] [i, q] -> [s, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [s, q] [q, s] [s, i] -> [s, s] [s, s] [s, i] , [s, i] [i, i] -> [s, s] [s, i] , [f, p] [p, s] [s, 0] [0, p] -> [f, 0] [0, p] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, q] [q, i] [i, p] -> [f, q] [q, s] [s, p] , [f, p] [p, s] [s, 0] [0, 0] -> [f, 0] [0, 0] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, 0] [0, s] -> [f, 0] [0, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, 0] [0, f] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [f, p] [p, s] [s, 0] [0, f] -> [f, 0] [0, f] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, g] [g, f] -> [f, f] [f, p] [p, p] [p, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, 0] [0, g] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [f, p] [p, s] [s, 0] [0, g] -> [f, 0] [0, g] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, g] [g, g] -> [f, f] [f, p] [p, p] [p, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, p] [p, s] [s, 0] [0, q] -> [f, 0] [0, q] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, f] [f, s] [s, q] -> [f, g] [g, q] [q, i] [i, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, q] [q, i] [i, q] -> [f, q] [q, s] [s, q] , [f, p] [p, s] [s, 0] [0, i] -> [f, 0] [0, i] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [f, f] [f, s] [s, i] -> [f, g] [g, q] [q, i] [i, i] , [f, q] [q, i] [i, i] -> [f, q] [q, s] [s, i] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, g] [g, f] -> [g, f] [f, p] [p, p] [p, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, g] [g, g] -> [g, f] [f, p] [p, p] [p, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, f] [f, s] [s, q] -> [g, g] [g, q] [q, i] [i, q] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, f] [f, s] [s, i] -> [g, g] [g, q] [q, i] [i, i] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, q] [q, i] [i, p] -> [q, q] [q, s] [s, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, g] [g, f] -> [q, f] [f, p] [p, p] [p, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, g] [g, g] -> [q, f] [f, p] [p, p] [p, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, f] [f, s] [s, q] -> [q, g] [g, q] [q, i] [i, q] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, q] [q, i] [i, q] -> [q, q] [q, s] [s, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, f] [f, s] [s, i] -> [q, g] [g, q] [q, i] [i, i] , [q, q] [q, i] [i, i] -> [q, q] [q, s] [s, i] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, q] [q, s] [s, p] -> [i, s] [s, s] [s, p] , [i, i] [i, p] -> [i, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, q] [q, s] [s, 0] -> [i, s] [s, s] [s, 0] , [i, i] [i, 0] -> [i, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, q] [q, s] [s, s] -> [i, s] [s, s] [s, s] , [i, i] [i, s] -> [i, s] [s, s] , [i, p] [p, 0] [0, f] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, f] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, g] [g, f] -> [i, f] [f, p] [p, p] [p, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, q] [q, s] [s, f] -> [i, s] [s, s] [s, f] , [i, i] [i, f] -> [i, s] [s, f] , [i, p] [p, 0] [0, g] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, g] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, g] [g, g] -> [i, f] [f, p] [p, p] [p, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, q] [q, s] [s, g] -> [i, s] [s, s] [s, g] , [i, i] [i, g] -> [i, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, q] [q, s] [s, q] -> [i, s] [s, s] [s, q] , [i, i] [i, q] -> [i, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] , [i, q] [q, s] [s, i] -> [i, s] [s, s] [s, i] , [i, i] [i, i] -> [i, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, f] is interpreted by / \ | 1 1 | | 0 1 | \ / [s, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, g] is interpreted by / \ | 1 1 | | 0 1 | \ / [s, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, g] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 235-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, g] [g, f] -> [p, f] [f, p] [p, p] [p, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, g] [g, g] -> [p, f] [f, p] [p, p] [p, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, f] [f, s] [s, q] -> [p, g] [g, q] [q, i] [i, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, f] [f, s] [s, i] -> [p, g] [g, q] [q, i] [i, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, q] [q, i] [i, p] -> [0, q] [q, s] [s, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, g] [g, f] -> [0, f] [f, p] [p, p] [p, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, g] [g, g] -> [0, f] [f, p] [p, p] [p, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, f] [f, s] [s, q] -> [0, g] [g, q] [q, i] [i, q] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [0, q] [q, i] [i, q] -> [0, q] [q, s] [s, q] , [0, f] [f, s] [s, i] -> [0, g] [g, q] [q, i] [i, i] , [0, q] [q, i] [i, i] -> [0, q] [q, s] [s, i] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, q] [q, s] [s, p] -> [s, s] [s, s] [s, p] , [s, i] [i, p] -> [s, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, q] [q, s] [s, 0] -> [s, s] [s, s] [s, 0] , [s, i] [i, 0] -> [s, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, q] [q, s] [s, s] -> [s, s] [s, s] [s, s] , [s, i] [i, s] -> [s, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, g] [g, f] -> [s, f] [f, p] [p, p] [p, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, q] [q, s] [s, f] -> [s, s] [s, s] [s, f] , [s, i] [i, f] -> [s, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, g] [g, g] -> [s, f] [f, p] [p, p] [p, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, q] [q, s] [s, g] -> [s, s] [s, s] [s, g] , [s, i] [i, g] -> [s, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, q] [q, s] [s, q] -> [s, s] [s, s] [s, q] , [s, i] [i, q] -> [s, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [s, q] [q, s] [s, i] -> [s, s] [s, s] [s, i] , [s, i] [i, i] -> [s, s] [s, i] , [f, p] [p, s] [s, 0] [0, p] -> [f, 0] [0, p] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, q] [q, i] [i, p] -> [f, q] [q, s] [s, p] , [f, p] [p, s] [s, 0] [0, 0] -> [f, 0] [0, 0] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, 0] [0, s] -> [f, 0] [0, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, 0] [0, f] -> [f, 0] [0, f] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, g] [g, f] -> [f, f] [f, p] [p, p] [p, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, s] [s, 0] [0, g] -> [f, 0] [0, g] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, g] [g, g] -> [f, f] [f, p] [p, p] [p, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, p] [p, s] [s, 0] [0, q] -> [f, 0] [0, q] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, f] [f, s] [s, q] -> [f, g] [g, q] [q, i] [i, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, q] [q, i] [i, q] -> [f, q] [q, s] [s, q] , [f, p] [p, s] [s, 0] [0, i] -> [f, 0] [0, i] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [f, f] [f, s] [s, i] -> [f, g] [g, q] [q, i] [i, i] , [f, q] [q, i] [i, i] -> [f, q] [q, s] [s, i] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, g] [g, f] -> [g, f] [f, p] [p, p] [p, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, g] [g, g] -> [g, f] [f, p] [p, p] [p, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, f] [f, s] [s, q] -> [g, g] [g, q] [q, i] [i, q] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, f] [f, s] [s, i] -> [g, g] [g, q] [q, i] [i, i] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, q] [q, i] [i, p] -> [q, q] [q, s] [s, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, g] [g, f] -> [q, f] [f, p] [p, p] [p, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, g] [g, g] -> [q, f] [f, p] [p, p] [p, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, f] [f, s] [s, q] -> [q, g] [g, q] [q, i] [i, q] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, q] [q, i] [i, q] -> [q, q] [q, s] [s, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, f] [f, s] [s, i] -> [q, g] [g, q] [q, i] [i, i] , [q, q] [q, i] [i, i] -> [q, q] [q, s] [s, i] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, q] [q, s] [s, p] -> [i, s] [s, s] [s, p] , [i, i] [i, p] -> [i, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, q] [q, s] [s, 0] -> [i, s] [s, s] [s, 0] , [i, i] [i, 0] -> [i, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, q] [q, s] [s, s] -> [i, s] [s, s] [s, s] , [i, i] [i, s] -> [i, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, g] [g, f] -> [i, f] [f, p] [p, p] [p, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, q] [q, s] [s, f] -> [i, s] [s, s] [s, f] , [i, i] [i, f] -> [i, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, g] [g, g] -> [i, f] [f, p] [p, p] [p, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, q] [q, s] [s, g] -> [i, s] [s, s] [s, g] , [i, i] [i, g] -> [i, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, q] [q, s] [s, q] -> [i, s] [s, s] [s, q] , [i, i] [i, q] -> [i, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] , [i, q] [q, s] [s, i] -> [i, s] [s, s] [s, i] , [i, i] [i, i] -> [i, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, q] is interpreted by / \ | 1 1 | | 0 1 | \ / [i, q] is interpreted by / \ | 1 1 | | 0 1 | \ / [0, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, g] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 221-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, g] [g, f] -> [p, f] [f, p] [p, p] [p, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, g] [g, g] -> [p, f] [f, p] [p, p] [p, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, f] [f, s] [s, q] -> [p, g] [g, q] [q, i] [i, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, f] [f, s] [s, i] -> [p, g] [g, q] [q, i] [i, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, q] [q, i] [i, p] -> [0, q] [q, s] [s, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, g] [g, f] -> [0, f] [f, p] [p, p] [p, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, g] [g, g] -> [0, f] [f, p] [p, p] [p, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, f] [f, s] [s, q] -> [0, g] [g, q] [q, i] [i, q] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [0, q] [q, i] [i, q] -> [0, q] [q, s] [s, q] , [0, f] [f, s] [s, i] -> [0, g] [g, q] [q, i] [i, i] , [0, q] [q, i] [i, i] -> [0, q] [q, s] [s, i] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, i] [i, p] -> [s, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, i] [i, 0] -> [s, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, i] [i, s] -> [s, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, g] [g, f] -> [s, f] [f, p] [p, p] [p, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, i] [i, f] -> [s, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, g] [g, g] -> [s, f] [f, p] [p, p] [p, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, i] [i, g] -> [s, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, i] [i, q] -> [s, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [s, i] [i, i] -> [s, s] [s, i] , [f, p] [p, s] [s, 0] [0, p] -> [f, 0] [0, p] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, q] [q, i] [i, p] -> [f, q] [q, s] [s, p] , [f, p] [p, s] [s, 0] [0, 0] -> [f, 0] [0, 0] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, 0] [0, s] -> [f, 0] [0, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, 0] [0, f] -> [f, 0] [0, f] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, g] [g, f] -> [f, f] [f, p] [p, p] [p, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, s] [s, 0] [0, g] -> [f, 0] [0, g] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, g] [g, g] -> [f, f] [f, p] [p, p] [p, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, p] [p, s] [s, 0] [0, q] -> [f, 0] [0, q] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, f] [f, s] [s, q] -> [f, g] [g, q] [q, i] [i, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, q] [q, i] [i, q] -> [f, q] [q, s] [s, q] , [f, p] [p, s] [s, 0] [0, i] -> [f, 0] [0, i] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [f, f] [f, s] [s, i] -> [f, g] [g, q] [q, i] [i, i] , [f, q] [q, i] [i, i] -> [f, q] [q, s] [s, i] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, g] [g, f] -> [g, f] [f, p] [p, p] [p, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, g] [g, g] -> [g, f] [f, p] [p, p] [p, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, f] [f, s] [s, q] -> [g, g] [g, q] [q, i] [i, q] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, f] [f, s] [s, i] -> [g, g] [g, q] [q, i] [i, i] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, q] [q, i] [i, p] -> [q, q] [q, s] [s, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, g] [g, f] -> [q, f] [f, p] [p, p] [p, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, g] [g, g] -> [q, f] [f, p] [p, p] [p, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, f] [f, s] [s, q] -> [q, g] [g, q] [q, i] [i, q] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, q] [q, i] [i, q] -> [q, q] [q, s] [s, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, f] [f, s] [s, i] -> [q, g] [g, q] [q, i] [i, i] , [q, q] [q, i] [i, i] -> [q, q] [q, s] [s, i] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, i] [i, p] -> [i, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, i] [i, 0] -> [i, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, i] [i, s] -> [i, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, g] [g, f] -> [i, f] [f, p] [p, p] [p, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, i] [i, f] -> [i, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, g] [g, g] -> [i, f] [f, p] [p, p] [p, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, i] [i, g] -> [i, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, i] [i, q] -> [i, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] , [i, i] [i, i] -> [i, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, i] is interpreted by / \ | 1 1 | | 0 1 | \ / [i, i] is interpreted by / \ | 1 1 | | 0 1 | \ / [f, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, g] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 207-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, g] [g, f] -> [p, f] [f, p] [p, p] [p, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, g] [g, g] -> [p, f] [f, p] [p, p] [p, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, f] [f, s] [s, q] -> [p, g] [g, q] [q, i] [i, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, f] [f, s] [s, i] -> [p, g] [g, q] [q, i] [i, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, q] [q, i] [i, p] -> [0, q] [q, s] [s, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, g] [g, f] -> [0, f] [f, p] [p, p] [p, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, g] [g, g] -> [0, f] [f, p] [p, p] [p, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, f] [f, s] [s, q] -> [0, g] [g, q] [q, i] [i, q] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [0, q] [q, i] [i, q] -> [0, q] [q, s] [s, q] , [0, f] [f, s] [s, i] -> [0, g] [g, q] [q, i] [i, i] , [0, q] [q, i] [i, i] -> [0, q] [q, s] [s, i] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, g] [g, f] -> [s, f] [f, p] [p, p] [p, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, g] [g, g] -> [s, f] [f, p] [p, p] [p, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [f, p] [p, s] [s, 0] [0, p] -> [f, 0] [0, p] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, q] [q, i] [i, p] -> [f, q] [q, s] [s, p] , [f, p] [p, s] [s, 0] [0, 0] -> [f, 0] [0, 0] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, 0] [0, s] -> [f, 0] [0, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, 0] [0, f] -> [f, 0] [0, f] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, g] [g, f] -> [f, f] [f, p] [p, p] [p, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, s] [s, 0] [0, g] -> [f, 0] [0, g] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, g] [g, g] -> [f, f] [f, p] [p, p] [p, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, p] [p, s] [s, 0] [0, q] -> [f, 0] [0, q] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, f] [f, s] [s, q] -> [f, g] [g, q] [q, i] [i, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, q] [q, i] [i, q] -> [f, q] [q, s] [s, q] , [f, p] [p, s] [s, 0] [0, i] -> [f, 0] [0, i] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [f, f] [f, s] [s, i] -> [f, g] [g, q] [q, i] [i, i] , [f, q] [q, i] [i, i] -> [f, q] [q, s] [s, i] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, g] [g, f] -> [g, f] [f, p] [p, p] [p, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, g] [g, g] -> [g, f] [f, p] [p, p] [p, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, f] [f, s] [s, q] -> [g, g] [g, q] [q, i] [i, q] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, f] [f, s] [s, i] -> [g, g] [g, q] [q, i] [i, i] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, q] [q, i] [i, p] -> [q, q] [q, s] [s, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, g] [g, f] -> [q, f] [f, p] [p, p] [p, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, g] [g, g] -> [q, f] [f, p] [p, p] [p, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, f] [f, s] [s, q] -> [q, g] [g, q] [q, i] [i, q] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, q] [q, i] [i, q] -> [q, q] [q, s] [s, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, f] [f, s] [s, i] -> [q, g] [g, q] [q, i] [i, i] , [q, q] [q, i] [i, i] -> [q, q] [q, s] [s, i] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, g] [g, f] -> [i, f] [f, p] [p, p] [p, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, g] [g, g] -> [i, f] [f, p] [p, p] [p, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, 0] is interpreted by / \ | 1 1 | | 0 1 | \ / [0, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, 0] is interpreted by / \ | 1 1 | | 0 1 | \ / [0, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, 0] is interpreted by / \ | 1 1 | | 0 1 | \ / [i, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, g] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 200-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, g] [g, f] -> [p, f] [f, p] [p, p] [p, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, g] [g, g] -> [p, f] [f, p] [p, p] [p, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, f] [f, s] [s, q] -> [p, g] [g, q] [q, i] [i, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, f] [f, s] [s, i] -> [p, g] [g, q] [q, i] [i, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, q] [q, i] [i, p] -> [0, q] [q, s] [s, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, g] [g, f] -> [0, f] [f, p] [p, p] [p, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, g] [g, g] -> [0, f] [f, p] [p, p] [p, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, f] [f, s] [s, q] -> [0, g] [g, q] [q, i] [i, q] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [0, q] [q, i] [i, q] -> [0, q] [q, s] [s, q] , [0, f] [f, s] [s, i] -> [0, g] [g, q] [q, i] [i, i] , [0, q] [q, i] [i, i] -> [0, q] [q, s] [s, i] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, g] [g, f] -> [s, f] [f, p] [p, p] [p, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, g] [g, g] -> [s, f] [f, p] [p, p] [p, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, q] [q, i] [i, p] -> [f, q] [q, s] [s, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, g] [g, f] -> [f, f] [f, p] [p, p] [p, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, g] [g, g] -> [f, f] [f, p] [p, p] [p, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, f] [f, s] [s, q] -> [f, g] [g, q] [q, i] [i, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, q] [q, i] [i, q] -> [f, q] [q, s] [s, q] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [f, f] [f, s] [s, i] -> [f, g] [g, q] [q, i] [i, i] , [f, q] [q, i] [i, i] -> [f, q] [q, s] [s, i] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, g] [g, f] -> [g, f] [f, p] [p, p] [p, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, g] [g, g] -> [g, f] [f, p] [p, p] [p, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, f] [f, s] [s, q] -> [g, g] [g, q] [q, i] [i, q] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, f] [f, s] [s, i] -> [g, g] [g, q] [q, i] [i, i] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, q] [q, i] [i, p] -> [q, q] [q, s] [s, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, g] [g, f] -> [q, f] [f, p] [p, p] [p, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, g] [g, g] -> [q, f] [f, p] [p, p] [p, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, f] [f, s] [s, q] -> [q, g] [g, q] [q, i] [i, q] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, q] [q, i] [i, q] -> [q, q] [q, s] [s, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, f] [f, s] [s, i] -> [q, g] [g, q] [q, i] [i, i] , [q, q] [q, i] [i, i] -> [q, q] [q, s] [s, i] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, g] [g, f] -> [i, f] [f, p] [p, p] [p, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, g] [g, g] -> [i, f] [f, p] [p, p] [p, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [g, g] is interpreted by / \ | 1 1 | | 0 1 | \ / [0, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 1 | | 0 1 | \ / [0, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, g] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 186-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, f] [f, s] [s, q] -> [p, g] [g, q] [q, i] [i, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, f] [f, s] [s, i] -> [p, g] [g, q] [q, i] [i, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, q] [q, i] [i, p] -> [0, q] [q, s] [s, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, f] [f, s] [s, q] -> [0, g] [g, q] [q, i] [i, q] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [0, q] [q, i] [i, q] -> [0, q] [q, s] [s, q] , [0, f] [f, s] [s, i] -> [0, g] [g, q] [q, i] [i, i] , [0, q] [q, i] [i, i] -> [0, q] [q, s] [s, i] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, q] [q, i] [i, p] -> [f, q] [q, s] [s, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, f] [f, s] [s, q] -> [f, g] [g, q] [q, i] [i, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, q] [q, i] [i, q] -> [f, q] [q, s] [s, q] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [f, f] [f, s] [s, i] -> [f, g] [g, q] [q, i] [i, i] , [f, q] [q, i] [i, i] -> [f, q] [q, s] [s, i] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, f] [f, s] [s, q] -> [g, g] [g, q] [q, i] [i, q] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, f] [f, s] [s, i] -> [g, g] [g, q] [q, i] [i, i] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, q] [q, i] [i, p] -> [q, q] [q, s] [s, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, f] [f, s] [s, q] -> [q, g] [g, q] [q, i] [i, q] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, q] [q, i] [i, q] -> [q, q] [q, s] [s, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, f] [f, s] [s, i] -> [q, g] [g, q] [q, i] [i, i] , [q, q] [q, i] [i, i] -> [q, q] [q, s] [s, i] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 185-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, f] [f, s] [s, i] -> [p, g] [g, q] [q, i] [i, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, q] [q, i] [i, p] -> [0, q] [q, s] [s, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, f] [f, s] [s, q] -> [0, g] [g, q] [q, i] [i, q] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [0, q] [q, i] [i, q] -> [0, q] [q, s] [s, q] , [0, f] [f, s] [s, i] -> [0, g] [g, q] [q, i] [i, i] , [0, q] [q, i] [i, i] -> [0, q] [q, s] [s, i] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, q] [q, i] [i, p] -> [f, q] [q, s] [s, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, f] [f, s] [s, q] -> [f, g] [g, q] [q, i] [i, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, q] [q, i] [i, q] -> [f, q] [q, s] [s, q] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [f, f] [f, s] [s, i] -> [f, g] [g, q] [q, i] [i, i] , [f, q] [q, i] [i, i] -> [f, q] [q, s] [s, i] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, f] [f, s] [s, q] -> [g, g] [g, q] [q, i] [i, q] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, f] [f, s] [s, i] -> [g, g] [g, q] [q, i] [i, i] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, q] [q, i] [i, p] -> [q, q] [q, s] [s, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, f] [f, s] [s, q] -> [q, g] [g, q] [q, i] [i, q] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, q] [q, i] [i, q] -> [q, q] [q, s] [s, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, f] [f, s] [s, i] -> [q, g] [g, q] [q, i] [i, i] , [q, q] [q, i] [i, i] -> [q, q] [q, s] [s, i] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 184-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, q] [q, i] [i, p] -> [0, q] [q, s] [s, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, f] [f, s] [s, q] -> [0, g] [g, q] [q, i] [i, q] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [0, q] [q, i] [i, q] -> [0, q] [q, s] [s, q] , [0, f] [f, s] [s, i] -> [0, g] [g, q] [q, i] [i, i] , [0, q] [q, i] [i, i] -> [0, q] [q, s] [s, i] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, q] [q, i] [i, p] -> [f, q] [q, s] [s, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, f] [f, s] [s, q] -> [f, g] [g, q] [q, i] [i, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, q] [q, i] [i, q] -> [f, q] [q, s] [s, q] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [f, f] [f, s] [s, i] -> [f, g] [g, q] [q, i] [i, i] , [f, q] [q, i] [i, i] -> [f, q] [q, s] [s, i] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, f] [f, s] [s, q] -> [g, g] [g, q] [q, i] [i, q] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, f] [f, s] [s, i] -> [g, g] [g, q] [q, i] [i, i] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, q] [q, i] [i, p] -> [q, q] [q, s] [s, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, f] [f, s] [s, q] -> [q, g] [g, q] [q, i] [i, q] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, q] [q, i] [i, q] -> [q, q] [q, s] [s, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, f] [f, s] [s, i] -> [q, g] [g, q] [q, i] [i, i] , [q, q] [q, i] [i, i] -> [q, q] [q, s] [s, i] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 183-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, f] [f, s] [s, q] -> [0, g] [g, q] [q, i] [i, q] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [0, q] [q, i] [i, q] -> [0, q] [q, s] [s, q] , [0, f] [f, s] [s, i] -> [0, g] [g, q] [q, i] [i, i] , [0, q] [q, i] [i, i] -> [0, q] [q, s] [s, i] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, q] [q, i] [i, p] -> [f, q] [q, s] [s, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, f] [f, s] [s, q] -> [f, g] [g, q] [q, i] [i, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, q] [q, i] [i, q] -> [f, q] [q, s] [s, q] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [f, f] [f, s] [s, i] -> [f, g] [g, q] [q, i] [i, i] , [f, q] [q, i] [i, i] -> [f, q] [q, s] [s, i] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, f] [f, s] [s, q] -> [g, g] [g, q] [q, i] [i, q] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, f] [f, s] [s, i] -> [g, g] [g, q] [q, i] [i, i] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, q] [q, i] [i, p] -> [q, q] [q, s] [s, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, f] [f, s] [s, q] -> [q, g] [g, q] [q, i] [i, q] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, q] [q, i] [i, q] -> [q, q] [q, s] [s, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, f] [f, s] [s, i] -> [q, g] [g, q] [q, i] [i, i] , [q, q] [q, i] [i, i] -> [q, q] [q, s] [s, i] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 182-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [0, q] [q, i] [i, q] -> [0, q] [q, s] [s, q] , [0, f] [f, s] [s, i] -> [0, g] [g, q] [q, i] [i, i] , [0, q] [q, i] [i, i] -> [0, q] [q, s] [s, i] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, q] [q, i] [i, p] -> [f, q] [q, s] [s, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, f] [f, s] [s, q] -> [f, g] [g, q] [q, i] [i, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, q] [q, i] [i, q] -> [f, q] [q, s] [s, q] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [f, f] [f, s] [s, i] -> [f, g] [g, q] [q, i] [i, i] , [f, q] [q, i] [i, i] -> [f, q] [q, s] [s, i] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, f] [f, s] [s, q] -> [g, g] [g, q] [q, i] [i, q] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, f] [f, s] [s, i] -> [g, g] [g, q] [q, i] [i, i] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, q] [q, i] [i, p] -> [q, q] [q, s] [s, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, f] [f, s] [s, q] -> [q, g] [g, q] [q, i] [i, q] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, q] [q, i] [i, q] -> [q, q] [q, s] [s, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, f] [f, s] [s, i] -> [q, g] [g, q] [q, i] [i, i] , [q, q] [q, i] [i, i] -> [q, q] [q, s] [s, i] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 181-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [0, f] [f, s] [s, i] -> [0, g] [g, q] [q, i] [i, i] , [0, q] [q, i] [i, i] -> [0, q] [q, s] [s, i] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, q] [q, i] [i, p] -> [f, q] [q, s] [s, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, f] [f, s] [s, q] -> [f, g] [g, q] [q, i] [i, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, q] [q, i] [i, q] -> [f, q] [q, s] [s, q] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [f, f] [f, s] [s, i] -> [f, g] [g, q] [q, i] [i, i] , [f, q] [q, i] [i, i] -> [f, q] [q, s] [s, i] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, f] [f, s] [s, q] -> [g, g] [g, q] [q, i] [i, q] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, f] [f, s] [s, i] -> [g, g] [g, q] [q, i] [i, i] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, q] [q, i] [i, p] -> [q, q] [q, s] [s, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, f] [f, s] [s, q] -> [q, g] [g, q] [q, i] [i, q] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, q] [q, i] [i, q] -> [q, q] [q, s] [s, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, f] [f, s] [s, i] -> [q, g] [g, q] [q, i] [i, i] , [q, q] [q, i] [i, i] -> [q, q] [q, s] [s, i] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 180-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [0, q] [q, i] [i, i] -> [0, q] [q, s] [s, i] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, q] [q, i] [i, p] -> [f, q] [q, s] [s, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, f] [f, s] [s, q] -> [f, g] [g, q] [q, i] [i, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, q] [q, i] [i, q] -> [f, q] [q, s] [s, q] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [f, f] [f, s] [s, i] -> [f, g] [g, q] [q, i] [i, i] , [f, q] [q, i] [i, i] -> [f, q] [q, s] [s, i] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, f] [f, s] [s, q] -> [g, g] [g, q] [q, i] [i, q] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, f] [f, s] [s, i] -> [g, g] [g, q] [q, i] [i, i] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, q] [q, i] [i, p] -> [q, q] [q, s] [s, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, f] [f, s] [s, q] -> [q, g] [g, q] [q, i] [i, q] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, q] [q, i] [i, q] -> [q, q] [q, s] [s, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, f] [f, s] [s, i] -> [q, g] [g, q] [q, i] [i, i] , [q, q] [q, i] [i, i] -> [q, q] [q, s] [s, i] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 179-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, q] [q, i] [i, p] -> [f, q] [q, s] [s, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, f] [f, s] [s, q] -> [f, g] [g, q] [q, i] [i, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, q] [q, i] [i, q] -> [f, q] [q, s] [s, q] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [f, f] [f, s] [s, i] -> [f, g] [g, q] [q, i] [i, i] , [f, q] [q, i] [i, i] -> [f, q] [q, s] [s, i] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, f] [f, s] [s, q] -> [g, g] [g, q] [q, i] [i, q] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, f] [f, s] [s, i] -> [g, g] [g, q] [q, i] [i, i] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, q] [q, i] [i, p] -> [q, q] [q, s] [s, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, f] [f, s] [s, q] -> [q, g] [g, q] [q, i] [i, q] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, q] [q, i] [i, q] -> [q, q] [q, s] [s, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, f] [f, s] [s, i] -> [q, g] [g, q] [q, i] [i, i] , [q, q] [q, i] [i, i] -> [q, q] [q, s] [s, i] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 178-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, f] [f, s] [s, q] -> [f, g] [g, q] [q, i] [i, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, q] [q, i] [i, q] -> [f, q] [q, s] [s, q] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [f, f] [f, s] [s, i] -> [f, g] [g, q] [q, i] [i, i] , [f, q] [q, i] [i, i] -> [f, q] [q, s] [s, i] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, f] [f, s] [s, q] -> [g, g] [g, q] [q, i] [i, q] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, f] [f, s] [s, i] -> [g, g] [g, q] [q, i] [i, i] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, q] [q, i] [i, p] -> [q, q] [q, s] [s, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, f] [f, s] [s, q] -> [q, g] [g, q] [q, i] [i, q] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, q] [q, i] [i, q] -> [q, q] [q, s] [s, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, f] [f, s] [s, i] -> [q, g] [g, q] [q, i] [i, i] , [q, q] [q, i] [i, i] -> [q, q] [q, s] [s, i] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 177-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, q] [q, i] [i, q] -> [f, q] [q, s] [s, q] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [f, f] [f, s] [s, i] -> [f, g] [g, q] [q, i] [i, i] , [f, q] [q, i] [i, i] -> [f, q] [q, s] [s, i] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, f] [f, s] [s, q] -> [g, g] [g, q] [q, i] [i, q] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, f] [f, s] [s, i] -> [g, g] [g, q] [q, i] [i, i] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, q] [q, i] [i, p] -> [q, q] [q, s] [s, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, f] [f, s] [s, q] -> [q, g] [g, q] [q, i] [i, q] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, q] [q, i] [i, q] -> [q, q] [q, s] [s, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, f] [f, s] [s, i] -> [q, g] [g, q] [q, i] [i, i] , [q, q] [q, i] [i, i] -> [q, q] [q, s] [s, i] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 176-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [f, f] [f, s] [s, i] -> [f, g] [g, q] [q, i] [i, i] , [f, q] [q, i] [i, i] -> [f, q] [q, s] [s, i] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, f] [f, s] [s, q] -> [g, g] [g, q] [q, i] [i, q] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, f] [f, s] [s, i] -> [g, g] [g, q] [q, i] [i, i] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, q] [q, i] [i, p] -> [q, q] [q, s] [s, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, f] [f, s] [s, q] -> [q, g] [g, q] [q, i] [i, q] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, q] [q, i] [i, q] -> [q, q] [q, s] [s, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, f] [f, s] [s, i] -> [q, g] [g, q] [q, i] [i, i] , [q, q] [q, i] [i, i] -> [q, q] [q, s] [s, i] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 175-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [f, q] [q, i] [i, i] -> [f, q] [q, s] [s, i] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, f] [f, s] [s, q] -> [g, g] [g, q] [q, i] [i, q] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, f] [f, s] [s, i] -> [g, g] [g, q] [q, i] [i, i] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, q] [q, i] [i, p] -> [q, q] [q, s] [s, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, f] [f, s] [s, q] -> [q, g] [g, q] [q, i] [i, q] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, q] [q, i] [i, q] -> [q, q] [q, s] [s, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, f] [f, s] [s, i] -> [q, g] [g, q] [q, i] [i, i] , [q, q] [q, i] [i, i] -> [q, q] [q, s] [s, i] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 174-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, f] [f, s] [s, q] -> [g, g] [g, q] [q, i] [i, q] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, f] [f, s] [s, i] -> [g, g] [g, q] [q, i] [i, i] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, q] [q, i] [i, p] -> [q, q] [q, s] [s, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, f] [f, s] [s, q] -> [q, g] [g, q] [q, i] [i, q] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, q] [q, i] [i, q] -> [q, q] [q, s] [s, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, f] [f, s] [s, i] -> [q, g] [g, q] [q, i] [i, i] , [q, q] [q, i] [i, i] -> [q, q] [q, s] [s, i] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 173-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, f] [f, s] [s, i] -> [g, g] [g, q] [q, i] [i, i] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, q] [q, i] [i, p] -> [q, q] [q, s] [s, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, f] [f, s] [s, q] -> [q, g] [g, q] [q, i] [i, q] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, q] [q, i] [i, q] -> [q, q] [q, s] [s, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, f] [f, s] [s, i] -> [q, g] [g, q] [q, i] [i, i] , [q, q] [q, i] [i, i] -> [q, q] [q, s] [s, i] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 172-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, q] [q, i] [i, p] -> [q, q] [q, s] [s, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, f] [f, s] [s, q] -> [q, g] [g, q] [q, i] [i, q] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, q] [q, i] [i, q] -> [q, q] [q, s] [s, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, f] [f, s] [s, i] -> [q, g] [g, q] [q, i] [i, i] , [q, q] [q, i] [i, i] -> [q, q] [q, s] [s, i] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 171-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, f] [f, s] [s, q] -> [q, g] [g, q] [q, i] [i, q] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, q] [q, i] [i, q] -> [q, q] [q, s] [s, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, f] [f, s] [s, i] -> [q, g] [g, q] [q, i] [i, i] , [q, q] [q, i] [i, i] -> [q, q] [q, s] [s, i] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 170-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, q] [q, i] [i, q] -> [q, q] [q, s] [s, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, f] [f, s] [s, i] -> [q, g] [g, q] [q, i] [i, i] , [q, q] [q, i] [i, i] -> [q, q] [q, s] [s, i] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 169-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, f] [f, s] [s, i] -> [q, g] [g, q] [q, i] [i, i] , [q, q] [q, i] [i, i] -> [q, q] [q, s] [s, i] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 168-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, q] [q, i] [i, i] -> [q, q] [q, s] [s, i] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 167-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, 0] [0, s] -> [p, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 1 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 166-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, p] [p, s] [s, s] [s, q] -> [f, s] [s, p] [p, s] [s, q] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: [g, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / Remains to prove termination of the 165-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [f, p] [p, s] [s, s] [s, i] -> [f, s] [s, p] [p, s] [s, i] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: [g, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / Remains to prove termination of the 164-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, f] [f, s] [s, f] -> [p, g] [g, q] [q, i] [i, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, f] [f, s] [s, g] -> [p, g] [g, q] [q, i] [i, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 162-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, f] [f, s] [s, f] -> [0, g] [g, q] [q, i] [i, f] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, f] [f, s] [s, g] -> [0, g] [g, q] [q, i] [i, g] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 160-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, q] [q, i] [i, f] -> [0, q] [q, s] [s, f] , [0, q] [q, i] [i, g] -> [0, q] [q, s] [s, g] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / Remains to prove termination of the 158-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, f] [f, s] [s, f] -> [f, g] [g, q] [q, i] [i, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, f] [f, s] [s, g] -> [f, g] [g, q] [q, i] [i, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 156-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, q] [q, i] [i, f] -> [f, q] [q, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, q] [q, i] [i, g] -> [f, q] [q, s] [s, g] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / Remains to prove termination of the 154-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, q] [q, i] [i, q] -> [s, q] [q, s] [s, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, q] [q, i] [i, q] -> [i, q] [q, s] [s, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 152-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [s, q] [q, i] [i, i] -> [s, q] [q, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] , [i, q] [q, i] [i, i] -> [i, q] [q, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 150-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, f] [f, s] [s, f] -> [g, g] [g, q] [q, i] [i, f] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, f] [f, s] [s, g] -> [g, g] [g, q] [q, i] [i, g] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 148-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, f] [f, s] [s, f] -> [q, g] [g, q] [q, i] [i, f] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, f] [f, s] [s, g] -> [q, g] [g, q] [q, i] [i, g] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 146-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, f] [f, s] [s, q] -> [s, g] [g, q] [q, i] [i, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, f] [f, s] [s, q] -> [i, g] [g, q] [q, i] [i, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 144-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, i] [i, q] -> [p, q] [q, s] [s, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, q] -> [g, q] [q, s] [s, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, i] [i, q] -> [q, s] [s, q] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, q] is interpreted by / \ | 1 1 | | 0 1 | \ / [0, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, g] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 141-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, q] [q, i] [i, p] -> [s, q] [q, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 140-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, s] [s, q] -> [g, s] [s, s] [s, q] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 139-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, q] [q, i] [i, p] -> [i, q] [q, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 138-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, q] [q, i] [i, f] -> [s, q] [q, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, q] [q, i] [i, g] -> [s, q] [q, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / Remains to prove termination of the 136-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [s, f] [f, s] [s, i] -> [s, g] [g, q] [q, i] [i, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] , [i, f] [f, s] [s, i] -> [i, g] [g, q] [q, i] [i, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 134-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, i] [i, i] -> [p, q] [q, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, i] -> [g, q] [q, s] [s, i] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [q, i] [i, i] -> [q, s] [s, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, i] is interpreted by / \ | 1 1 | | 0 1 | \ / [g, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, g] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 131-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [g, q] [q, s] [s, i] -> [g, s] [s, s] [s, i] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 130-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, q] [q, i] [i, f] -> [q, q] [q, s] [s, f] , [q, i] [i, f] -> [q, s] [s, f] , [q, q] [q, i] [i, g] -> [q, q] [q, s] [s, g] , [q, i] [i, g] -> [q, s] [s, g] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / Remains to prove termination of the 128-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, i] [i, f] -> [q, s] [s, f] , [q, i] [i, g] -> [q, s] [s, g] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, q] [q, i] [i, f] -> [i, q] [q, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, q] [q, i] [i, g] -> [i, q] [q, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / Remains to prove termination of the 126-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, p] [p, s] [s, s] [s, f] -> [f, s] [s, p] [p, s] [s, f] , [f, p] [p, s] [s, s] [s, g] -> [f, s] [s, p] [p, s] [s, g] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, i] [i, f] -> [q, s] [s, f] , [q, i] [i, g] -> [q, s] [s, g] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: [g, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / Remains to prove termination of the 124-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, 0] [0, s] -> [s, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, i] [i, f] -> [q, s] [s, f] , [q, i] [i, g] -> [q, s] [s, g] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, 0] [0, s] -> [i, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 1 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [s, p] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 122-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, f] [f, s] [s, f] -> [s, g] [g, q] [q, i] [i, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, f] [f, s] [s, g] -> [s, g] [g, q] [q, i] [i, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, i] [i, f] -> [q, s] [s, f] , [q, i] [i, g] -> [q, s] [s, g] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, f] [f, s] [s, f] -> [i, g] [g, q] [q, i] [i, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, f] [f, s] [s, g] -> [i, g] [g, q] [q, i] [i, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [i, f] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 118-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, i] [i, f] -> [p, q] [q, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, i] [i, g] -> [p, q] [q, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, q] [q, i] [i, f] -> [g, q] [q, s] [s, f] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, q] [q, i] [i, g] -> [g, q] [q, s] [s, g] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, i] [i, f] -> [q, s] [s, f] , [q, i] [i, g] -> [q, s] [s, g] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, f] is interpreted by / \ | 1 2 | | 0 1 | \ / [i, f] is interpreted by / \ | 1 3 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, g] is interpreted by / \ | 1 2 | | 0 1 | \ / [i, g] is interpreted by / \ | 1 3 | | 0 1 | \ / Remains to prove termination of the 112-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, q] [q, s] [s, f] -> [g, s] [s, s] [s, f] , [g, q] [q, s] [s, g] -> [g, s] [s, s] [s, g] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 110-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, q] [q, i] [i, s] -> [f, q] [q, s] [s, s] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 109-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, q] [q, i] [i, s] -> [0, q] [q, s] [s, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 108-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, q] [q, i] [i, s] -> [q, q] [q, s] [s, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 107-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, q] [q, i] [i, 0] -> [0, q] [q, s] [s, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 106-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, q] [q, i] [i, 0] -> [s, q] [q, s] [s, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 105-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, q] [q, i] [i, 0] -> [i, q] [q, s] [s, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 104-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, q] [q, i] [i, 0] -> [q, q] [q, s] [s, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 103-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, q] [q, i] [i, s] -> [i, q] [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 102-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, q] [q, s] [s, q] -> [p, s] [s, s] [s, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 101-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, q] [q, i] [i, s] -> [s, q] [q, s] [s, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 100-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, p] [p, s] [s, s] [s, q] -> [p, s] [s, p] [p, s] [s, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: [g, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 1 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / Remains to prove termination of the 99-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [p, q] [q, s] [s, i] -> [p, s] [s, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 98-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [p, p] [p, s] [s, s] [s, i] -> [p, s] [s, p] [p, s] [s, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: [g, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 1 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / Remains to prove termination of the 97-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, q] [q, i] [i, 0] -> [f, q] [q, s] [s, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 96-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, q] [q, s] [s, f] -> [p, s] [s, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, q] [q, s] [s, g] -> [p, s] [s, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 94-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, s] [s, f] -> [p, s] [s, p] [p, s] [s, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, s] [s, g] -> [p, s] [s, p] [p, s] [s, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: [g, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 1 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / Remains to prove termination of the 92-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, 0] [0, s] -> [p, 0] [0, s] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: [g, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 1 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / Remains to prove termination of the 91-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, p] [p, 0] [0, s] -> [f, s] [s, s] [s, 0] [0, s] [s, s] [s, p] [p, s] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: [g, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 90-rule system { [p, p] [p, s] [s, 0] [0, p] -> [p, 0] [0, p] , [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, 0] [0, 0] -> [p, 0] [0, 0] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, p] [p, s] [s, 0] [0, f] -> [p, 0] [0, f] , [p, p] [p, s] [s, 0] [0, g] -> [p, 0] [0, g] , [p, p] [p, s] [s, 0] [0, q] -> [p, 0] [0, q] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [p, p] [p, s] [s, 0] [0, i] -> [p, 0] [0, i] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, 0] is interpreted by / \ | 1 1 | | 0 1 | \ / [0, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, 0] is interpreted by / \ | 1 1 | | 0 1 | \ / [i, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, g] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 84-rule system { [p, p] [p, s] [s, s] [s, p] -> [p, s] [s, p] [p, s] [s, p] , [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, p] [p, s] [s, s] [s, 0] -> [p, s] [s, p] [p, s] [s, 0] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, p] [p, s] [s, s] [s, s] -> [p, s] [s, p] [p, s] [s, s] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, s] is interpreted by / \ | 1 1 | | 0 1 | \ / [s, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, s] is interpreted by / \ | 1 1 | | 0 1 | \ / [p, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, q] is interpreted by / \ | 1 1 | | 0 1 | \ / [q, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, q] is interpreted by / \ | 1 1 | | 0 1 | \ / [q, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, s] is interpreted by / \ | 1 1 | | 0 1 | \ / [g, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, g] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 81-rule system { [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, s] [s, q] -> [s, s] [s, p] [p, s] [s, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, s] [s, q] -> [i, s] [s, p] [p, s] [s, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: [g, g] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 | | 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / Remains to prove termination of the 79-rule system { [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [s, p] [p, s] [s, s] [s, i] -> [s, s] [s, p] [p, s] [s, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] , [i, p] [p, s] [s, s] [s, i] -> [i, s] [s, p] [p, s] [s, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: [g, g] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 | | 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / Remains to prove termination of the 77-rule system { [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [f, p] [p, s] [s, s] [s, p] -> [f, s] [s, p] [p, s] [s, p] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: [g, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | | 0 1 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / Remains to prove termination of the 76-rule system { [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, s] [s, f] -> [s, s] [s, p] [p, s] [s, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, s] [s, g] -> [s, s] [s, p] [p, s] [s, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, s] [s, f] -> [i, s] [s, p] [p, s] [s, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, s] [s, g] -> [i, s] [s, p] [p, s] [s, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: [g, g] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 | | 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / Remains to prove termination of the 72-rule system { [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, p] [p, s] [s, s] [s, s] -> [f, s] [s, p] [p, s] [s, s] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: [g, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 1 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | | 0 1 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / Remains to prove termination of the 71-rule system { [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, p] [p, s] [s, s] [s, 0] -> [f, s] [s, p] [p, s] [s, 0] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: [g, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | | 0 1 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / Remains to prove termination of the 70-rule system { [p, f] [f, s] [s, p] -> [p, g] [g, q] [q, i] [i, p] , [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, f] [f, s] [s, 0] -> [p, g] [g, q] [q, i] [i, 0] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, f] [f, s] [s, s] -> [p, g] [g, q] [q, i] [i, s] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [0, f] [f, s] [s, p] -> [0, g] [g, q] [q, i] [i, p] , [0, f] [f, s] [s, 0] -> [0, g] [g, q] [q, i] [i, 0] , [0, f] [f, s] [s, s] -> [0, g] [g, q] [q, i] [i, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, f] [f, s] [s, p] -> [s, g] [g, q] [q, i] [i, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, f] [f, s] [s, 0] -> [s, g] [g, q] [q, i] [i, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, f] [f, s] [s, s] -> [s, g] [g, q] [q, i] [i, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [f, f] [f, s] [s, p] -> [f, g] [g, q] [q, i] [i, p] , [f, f] [f, s] [s, 0] -> [f, g] [g, q] [q, i] [i, 0] , [f, f] [f, s] [s, s] -> [f, g] [g, q] [q, i] [i, s] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, f] [f, s] [s, p] -> [g, g] [g, q] [q, i] [i, p] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, f] [f, s] [s, 0] -> [g, g] [g, q] [q, i] [i, 0] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, f] [f, s] [s, s] -> [g, g] [g, q] [q, i] [i, s] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [q, f] [f, s] [s, p] -> [q, g] [g, q] [q, i] [i, p] , [q, i] [i, p] -> [q, s] [s, p] , [q, f] [f, s] [s, 0] -> [q, g] [g, q] [q, i] [i, 0] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, f] [f, s] [s, s] -> [q, g] [g, q] [q, i] [i, s] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, f] [f, s] [s, p] -> [i, g] [g, q] [q, i] [i, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, f] [f, s] [s, 0] -> [i, g] [g, q] [q, i] [i, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, f] [f, s] [s, s] -> [i, g] [g, q] [q, i] [i, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, s] is interpreted by / \ | 1 1 | | 0 1 | \ / [p, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, g] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 49-rule system { [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, g] [g, s] -> [g, f] [f, p] [p, p] [p, s] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [g, g] [g, q] -> [g, f] [f, p] [p, p] [p, q] , [q, i] [i, p] -> [q, s] [s, p] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [g, g] is interpreted by / \ | 1 1 | | 0 1 | \ / [0, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, g] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 47-rule system { [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [f, g] [g, s] -> [f, f] [f, p] [p, p] [p, s] , [f, g] [g, q] -> [f, f] [f, p] [p, p] [p, q] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [q, i] [i, p] -> [q, s] [s, p] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 1 | | 0 1 | \ / [f, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, g] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 45-rule system { [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [q, i] [i, p] -> [q, s] [s, p] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, g] [g, s] -> [q, f] [f, p] [p, p] [p, s] , [q, i] [i, s] -> [q, s] [s, s] , [q, g] [g, q] -> [q, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, g] is interpreted by / \ | 1 1 | | 0 1 | \ / [q, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, g] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 43-rule system { [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, g] [g, s] -> [p, f] [f, p] [p, p] [p, s] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [p, g] [g, q] -> [p, f] [f, p] [p, p] [p, q] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [q, i] [i, p] -> [q, s] [s, p] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, i] [i, s] -> [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, g] is interpreted by / \ | 1 1 | | 0 1 | \ / [g, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, g] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 41-rule system { [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [0, g] [g, q] -> [0, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, g] [g, q] -> [s, f] [f, p] [p, p] [p, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, s] [s, p] -> [g, s] [s, s] [s, p] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, s] [s, 0] -> [g, s] [s, s] [s, 0] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [g, q] [q, s] [s, s] -> [g, s] [s, s] [s, s] , [q, i] [i, p] -> [q, s] [s, p] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, i] [i, s] -> [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, g] [g, q] -> [i, f] [f, p] [p, p] [p, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, q] is interpreted by / \ | 1 1 | | 0 1 | \ / [q, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, g] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 35-rule system { [p, q] [q, i] [i, p] -> [p, q] [q, s] [s, p] , [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, q] [q, i] [i, 0] -> [p, q] [q, s] [s, 0] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, q] [q, i] [i, s] -> [p, q] [q, s] [s, s] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [g, q] [q, i] [i, p] -> [g, q] [q, s] [s, p] , [g, q] [q, i] [i, 0] -> [g, q] [q, s] [s, 0] , [g, q] [q, i] [i, s] -> [g, q] [q, s] [s, s] , [q, i] [i, p] -> [q, s] [s, p] , [q, i] [i, 0] -> [q, s] [s, 0] , [q, i] [i, s] -> [q, s] [s, s] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, i] is interpreted by / \ | 1 1 | | 0 1 | \ / [i, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, g] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 26-rule system { [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [i, p] [p, s] [s, 0] [0, p] -> [i, 0] [0, p] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, p] [p, s] [s, 0] [0, 0] -> [i, 0] [0, 0] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, p] [p, s] [s, 0] [0, s] -> [i, 0] [0, s] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] , [i, p] [p, s] [s, 0] [0, f] -> [i, 0] [0, f] , [i, p] [p, s] [s, 0] [0, g] -> [i, 0] [0, g] , [i, p] [p, s] [s, 0] [0, q] -> [i, 0] [0, q] , [i, p] [p, s] [s, 0] [0, i] -> [i, 0] [0, i] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, 0] is interpreted by / \ | 1 1 | | 0 1 | \ / [0, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, g] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 19-rule system { [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [i, p] [p, s] [s, s] [s, p] -> [i, s] [s, p] [p, s] [s, p] , [i, p] [p, s] [s, s] [s, 0] -> [i, s] [s, p] [p, s] [s, 0] , [i, p] [p, s] [s, s] [s, s] -> [i, s] [s, p] [p, s] [s, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, p] is interpreted by / \ | 1 1 | | 0 1 | \ / [g, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, g] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 16-rule system { [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [s, p] [p, s] [s, 0] [0, p] -> [s, 0] [0, p] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, p] [p, s] [s, 0] [0, 0] -> [s, 0] [0, 0] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, p] [p, s] [s, 0] [0, s] -> [s, 0] [0, s] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [s, p] [p, s] [s, 0] [0, f] -> [s, 0] [0, f] , [s, p] [p, s] [s, 0] [0, g] -> [s, 0] [0, g] , [s, p] [p, s] [s, 0] [0, q] -> [s, 0] [0, q] , [s, p] [p, s] [s, 0] [0, i] -> [s, 0] [0, i] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, p] is interpreted by / \ | 1 1 | | 0 1 | \ / [p, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, g] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 9-rule system { [p, q] [q, s] [s, p] -> [p, s] [s, s] [s, p] , [p, q] [q, s] [s, 0] -> [p, s] [s, s] [s, 0] , [p, q] [q, s] [s, s] -> [p, s] [s, s] [s, s] , [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, q] is interpreted by / \ | 1 1 | | 0 1 | \ / [q, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, g] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 6-rule system { [0, g] [g, s] -> [0, f] [f, p] [p, p] [p, s] , [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] , [s, g] [g, s] -> [s, f] [f, p] [p, p] [p, s] , [i, g] [g, s] -> [i, f] [f, p] [p, p] [p, s] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [g, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [f, p] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, q] is interpreted by / \ | 1 0 | | 0 1 | \ / [q, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [p, i] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, 0] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, s] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, s] is interpreted by / \ | 1 1 | | 0 1 | \ / [0, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [g, f] is interpreted by / \ | 1 0 | | 0 1 | \ / [0, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [s, g] is interpreted by / \ | 1 0 | | 0 1 | \ / [i, g] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 3-rule system { [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, p] [p, s] [s, s] [s, 0] -> [s, s] [s, p] [p, s] [s, 0] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: [g, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 1 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / Remains to prove termination of the 2-rule system { [s, p] [p, s] [s, s] [s, p] -> [s, s] [s, p] [p, s] [s, p] , [s, p] [p, s] [s, s] [s, s] -> [s, s] [s, p] [p, s] [s, s] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: [g, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 1 1 | | 0 1 0 0 0 | \ / [s, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, p] is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 1 0 0 | | 0 1 0 0 0 | \ / [p, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [f, p] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, q] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [q, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [p, i] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, 0] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, s] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [g, f] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [0, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [s, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / [i, g] is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / Remains to prove termination of the 0-rule system { } The system is trivially terminating.