/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: b is interpreted by / \ | 1 1 | | 0 1 | \ / d is interpreted by / \ | 1 0 | | 0 1 | \ / c is interpreted by / \ | 1 1 | | 0 1 | \ / a is interpreted by / \ | 1 1 | | 0 1 | \ / Remains to prove termination of the 6-rule system { b b d d b b -> c c d d b b , a a d d -> d d c c , b b b b b b -> a a b b c c , d d c c -> b b d d , d d c c -> d d b b d d , d d a a c c -> b b b b } 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 96-rule system { [b, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, b] -> [b, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, b] , [b, a] [a, a] [a, d] [d, d] [d, b] -> [b, d] [d, d] [d, c] [c, c] [c, b] , [b, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, b] -> [b, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, b] , [b, d] [d, d] [d, c] [c, c] [c, b] -> [b, b] [b, b] [b, d] [d, d] [d, b] , [b, d] [d, d] [d, c] [c, c] [c, b] -> [b, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, b] , [b, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, b] -> [b, b] [b, b] [b, b] [b, b] [b, b] , [b, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, d] -> [b, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, d] , [b, a] [a, a] [a, d] [d, d] [d, d] -> [b, d] [d, d] [d, c] [c, c] [c, d] , [b, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, d] -> [b, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, d] , [b, d] [d, d] [d, c] [c, c] [c, d] -> [b, b] [b, b] [b, d] [d, d] [d, d] , [b, d] [d, d] [d, c] [c, c] [c, d] -> [b, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, d] , [b, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, d] -> [b, b] [b, b] [b, b] [b, b] [b, d] , [b, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, c] -> [b, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, c] , [b, a] [a, a] [a, d] [d, d] [d, c] -> [b, d] [d, d] [d, c] [c, c] [c, c] , [b, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, c] -> [b, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, c] , [b, d] [d, d] [d, c] [c, c] [c, c] -> [b, b] [b, b] [b, d] [d, d] [d, c] , [b, d] [d, d] [d, c] [c, c] [c, c] -> [b, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, c] , [b, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, c] -> [b, b] [b, b] [b, b] [b, b] [b, c] , [b, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, a] -> [b, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, a] , [b, a] [a, a] [a, d] [d, d] [d, a] -> [b, d] [d, d] [d, c] [c, c] [c, a] , [b, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, a] -> [b, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, a] , [b, d] [d, d] [d, c] [c, c] [c, a] -> [b, b] [b, b] [b, d] [d, d] [d, a] , [b, d] [d, d] [d, c] [c, c] [c, a] -> [b, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, a] , [b, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, a] -> [b, b] [b, b] [b, b] [b, b] [b, a] , [d, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, b] -> [d, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, b] , [d, a] [a, a] [a, d] [d, d] [d, b] -> [d, d] [d, d] [d, c] [c, c] [c, b] , [d, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, b] -> [d, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, b] , [d, d] [d, d] [d, c] [c, c] [c, b] -> [d, b] [b, b] [b, d] [d, d] [d, b] , [d, d] [d, d] [d, c] [c, c] [c, b] -> [d, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, b] , [d, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, b] -> [d, b] [b, b] [b, b] [b, b] [b, b] , [d, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, d] -> [d, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, d] , [d, a] [a, a] [a, d] [d, d] [d, d] -> [d, d] [d, d] [d, c] [c, c] [c, d] , [d, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, d] -> [d, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, d] , [d, d] [d, d] [d, c] [c, c] [c, d] -> [d, b] [b, b] [b, d] [d, d] [d, d] , [d, d] [d, d] [d, c] [c, c] [c, d] -> [d, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, d] , [d, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, d] -> [d, b] [b, b] [b, b] [b, b] [b, d] , [d, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, c] -> [d, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, c] , [d, a] [a, a] [a, d] [d, d] [d, c] -> [d, d] [d, d] [d, c] [c, c] [c, c] , [d, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, c] -> [d, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, c] , [d, d] [d, d] [d, c] [c, c] [c, c] -> [d, b] [b, b] [b, d] [d, d] [d, c] , [d, d] [d, d] [d, c] [c, c] [c, c] -> [d, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, c] , [d, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, c] -> [d, b] [b, b] [b, b] [b, b] [b, c] , [d, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, a] -> [d, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, a] , [d, a] [a, a] [a, d] [d, d] [d, a] -> [d, d] [d, d] [d, c] [c, c] [c, a] , [d, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, a] -> [d, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, a] , [d, d] [d, d] [d, c] [c, c] [c, a] -> [d, b] [b, b] [b, d] [d, d] [d, a] , [d, d] [d, d] [d, c] [c, c] [c, a] -> [d, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, a] , [d, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, a] -> [d, b] [b, b] [b, b] [b, b] [b, a] , [c, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, b] -> [c, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, b] , [c, a] [a, a] [a, d] [d, d] [d, b] -> [c, d] [d, d] [d, c] [c, c] [c, b] , [c, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, b] -> [c, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, b] , [c, d] [d, d] [d, c] [c, c] [c, b] -> [c, b] [b, b] [b, d] [d, d] [d, b] , [c, d] [d, d] [d, c] [c, c] [c, b] -> [c, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, b] , [c, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, b] -> [c, b] [b, b] [b, b] [b, b] [b, b] , [c, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, d] -> [c, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, d] , [c, a] [a, a] [a, d] [d, d] [d, d] -> [c, d] [d, d] [d, c] [c, c] [c, d] , [c, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, d] -> [c, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, d] , [c, d] [d, d] [d, c] [c, c] [c, d] -> [c, b] [b, b] [b, d] [d, d] [d, d] , [c, d] [d, d] [d, c] [c, c] [c, d] -> [c, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, d] , [c, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, d] -> [c, b] [b, b] [b, b] [b, b] [b, d] , [c, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, c] -> [c, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, c] , [c, a] [a, a] [a, d] [d, d] [d, c] -> [c, d] [d, d] [d, c] [c, c] [c, c] , [c, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, c] -> [c, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, c] , [c, d] [d, d] [d, c] [c, c] [c, c] -> [c, b] [b, b] [b, d] [d, d] [d, c] , [c, d] [d, d] [d, c] [c, c] [c, c] -> [c, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, c] , [c, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, c] -> [c, b] [b, b] [b, b] [b, b] [b, c] , [c, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, a] -> [c, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, a] , [c, a] [a, a] [a, d] [d, d] [d, a] -> [c, d] [d, d] [d, c] [c, c] [c, a] , [c, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, a] -> [c, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, a] , [c, d] [d, d] [d, c] [c, c] [c, a] -> [c, b] [b, b] [b, d] [d, d] [d, a] , [c, d] [d, d] [d, c] [c, c] [c, a] -> [c, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, a] , [c, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, a] -> [c, b] [b, b] [b, b] [b, b] [b, a] , [a, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, b] -> [a, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, b] , [a, a] [a, a] [a, d] [d, d] [d, b] -> [a, d] [d, d] [d, c] [c, c] [c, b] , [a, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, b] -> [a, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, b] , [a, d] [d, d] [d, c] [c, c] [c, b] -> [a, b] [b, b] [b, d] [d, d] [d, b] , [a, d] [d, d] [d, c] [c, c] [c, b] -> [a, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, b] , [a, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, b] -> [a, b] [b, b] [b, b] [b, b] [b, b] , [a, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, d] -> [a, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, d] , [a, a] [a, a] [a, d] [d, d] [d, d] -> [a, d] [d, d] [d, c] [c, c] [c, d] , [a, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, d] -> [a, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, d] , [a, d] [d, d] [d, c] [c, c] [c, d] -> [a, b] [b, b] [b, d] [d, d] [d, d] , [a, d] [d, d] [d, c] [c, c] [c, d] -> [a, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, d] , [a, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, d] -> [a, b] [b, b] [b, b] [b, b] [b, d] , [a, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, c] -> [a, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, c] , [a, a] [a, a] [a, d] [d, d] [d, c] -> [a, d] [d, d] [d, c] [c, c] [c, c] , [a, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, c] -> [a, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, c] , [a, d] [d, d] [d, c] [c, c] [c, c] -> [a, b] [b, b] [b, d] [d, d] [d, c] , [a, d] [d, d] [d, c] [c, c] [c, c] -> [a, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, c] , [a, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, c] -> [a, b] [b, b] [b, b] [b, b] [b, c] , [a, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, a] -> [a, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, a] , [a, a] [a, a] [a, d] [d, d] [d, a] -> [a, d] [d, d] [d, c] [c, c] [c, a] , [a, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, a] -> [a, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, a] , [a, d] [d, d] [d, c] [c, c] [c, a] -> [a, b] [b, b] [b, d] [d, d] [d, a] , [a, d] [d, d] [d, c] [c, c] [c, a] -> [a, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, a] , [a, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, a] -> [a, b] [b, b] [b, b] [b, b] [b, a] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [b, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, d] is interpreted by / \ | 1 1 | | 0 1 | \ / [d, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, a] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 76-rule system { [b, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, b] -> [b, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, b] , [b, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, b] -> [b, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, b] , [b, d] [d, d] [d, c] [c, c] [c, b] -> [b, b] [b, b] [b, d] [d, d] [d, b] , [b, d] [d, d] [d, c] [c, c] [c, b] -> [b, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, b] , [b, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, b] -> [b, b] [b, b] [b, b] [b, b] [b, b] , [b, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, d] -> [b, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, d] , [b, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, d] -> [b, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, d] , [b, d] [d, d] [d, c] [c, c] [c, d] -> [b, b] [b, b] [b, d] [d, d] [d, d] , [b, d] [d, d] [d, c] [c, c] [c, d] -> [b, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, d] , [b, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, d] -> [b, b] [b, b] [b, b] [b, b] [b, d] , [b, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, c] -> [b, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, c] , [b, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, c] -> [b, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, c] , [b, d] [d, d] [d, c] [c, c] [c, c] -> [b, b] [b, b] [b, d] [d, d] [d, c] , [b, d] [d, d] [d, c] [c, c] [c, c] -> [b, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, c] , [b, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, c] -> [b, b] [b, b] [b, b] [b, b] [b, c] , [b, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, a] -> [b, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, a] , [b, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, a] -> [b, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, a] , [b, d] [d, d] [d, c] [c, c] [c, a] -> [b, b] [b, b] [b, d] [d, d] [d, a] , [b, d] [d, d] [d, c] [c, c] [c, a] -> [b, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, a] , [b, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, a] -> [b, b] [b, b] [b, b] [b, b] [b, a] , [d, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, b] -> [d, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, b] , [d, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, b] -> [d, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, b] , [d, d] [d, d] [d, c] [c, c] [c, b] -> [d, b] [b, b] [b, d] [d, d] [d, b] , [d, d] [d, d] [d, c] [c, c] [c, b] -> [d, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, b] , [d, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, b] -> [d, b] [b, b] [b, b] [b, b] [b, b] , [d, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, d] -> [d, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, d] , [d, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, d] -> [d, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, d] , [d, d] [d, d] [d, c] [c, c] [c, d] -> [d, b] [b, b] [b, d] [d, d] [d, d] , [d, d] [d, d] [d, c] [c, c] [c, d] -> [d, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, d] , [d, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, d] -> [d, b] [b, b] [b, b] [b, b] [b, d] , [d, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, c] -> [d, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, c] , [d, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, c] -> [d, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, c] , [d, d] [d, d] [d, c] [c, c] [c, c] -> [d, b] [b, b] [b, d] [d, d] [d, c] , [d, d] [d, d] [d, c] [c, c] [c, c] -> [d, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, c] , [d, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, c] -> [d, b] [b, b] [b, b] [b, b] [b, c] , [d, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, a] -> [d, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, a] , [d, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, a] -> [d, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, a] , [d, d] [d, d] [d, c] [c, c] [c, a] -> [d, b] [b, b] [b, d] [d, d] [d, a] , [d, d] [d, d] [d, c] [c, c] [c, a] -> [d, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, a] , [d, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, a] -> [d, b] [b, b] [b, b] [b, b] [b, a] , [c, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, b] -> [c, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, b] , [c, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, b] -> [c, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, b] , [c, d] [d, d] [d, c] [c, c] [c, b] -> [c, b] [b, b] [b, d] [d, d] [d, b] , [c, d] [d, d] [d, c] [c, c] [c, b] -> [c, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, b] , [c, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, b] -> [c, b] [b, b] [b, b] [b, b] [b, b] , [c, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, d] -> [c, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, d] , [c, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, d] -> [c, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, d] , [c, d] [d, d] [d, c] [c, c] [c, d] -> [c, b] [b, b] [b, d] [d, d] [d, d] , [c, d] [d, d] [d, c] [c, c] [c, d] -> [c, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, d] , [c, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, d] -> [c, b] [b, b] [b, b] [b, b] [b, d] , [c, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, c] -> [c, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, c] , [c, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, c] -> [c, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, c] , [c, d] [d, d] [d, c] [c, c] [c, c] -> [c, b] [b, b] [b, d] [d, d] [d, c] , [c, d] [d, d] [d, c] [c, c] [c, c] -> [c, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, c] , [c, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, c] -> [c, b] [b, b] [b, b] [b, b] [b, c] , [c, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, a] -> [c, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, a] , [c, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, a] -> [c, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, a] , [c, d] [d, d] [d, c] [c, c] [c, a] -> [c, b] [b, b] [b, d] [d, d] [d, a] , [c, d] [d, d] [d, c] [c, c] [c, a] -> [c, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, a] , [c, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, a] -> [c, b] [b, b] [b, b] [b, b] [b, a] , [a, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, b] -> [a, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, b] , [a, a] [a, a] [a, d] [d, d] [d, b] -> [a, d] [d, d] [d, c] [c, c] [c, b] , [a, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, b] -> [a, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, b] , [a, d] [d, d] [d, c] [c, c] [c, b] -> [a, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, b] , [a, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, d] -> [a, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, d] , [a, a] [a, a] [a, d] [d, d] [d, d] -> [a, d] [d, d] [d, c] [c, c] [c, d] , [a, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, d] -> [a, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, d] , [a, d] [d, d] [d, c] [c, c] [c, d] -> [a, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, d] , [a, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, c] -> [a, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, c] , [a, a] [a, a] [a, d] [d, d] [d, c] -> [a, d] [d, d] [d, c] [c, c] [c, c] , [a, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, c] -> [a, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, c] , [a, d] [d, d] [d, c] [c, c] [c, c] -> [a, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, c] , [a, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, a] -> [a, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, a] , [a, a] [a, a] [a, d] [d, d] [d, a] -> [a, d] [d, d] [d, c] [c, c] [c, a] , [a, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, a] -> [a, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, a] , [a, d] [d, d] [d, c] [c, c] [c, a] -> [a, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, a] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [b, b] is interpreted by / \ | 1 1 | | 0 1 | \ / [b, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, b] is interpreted by / \ | 1 1 | | 0 1 | \ / [b, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, c] is interpreted by / \ | 1 1 | | 0 1 | \ / [c, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, a] is interpreted by / \ | 1 1 | | 0 1 | \ / [a, a] is interpreted by / \ | 1 1 | | 0 1 | \ / [a, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, c] is interpreted by / \ | 1 1 | | 0 1 | \ / [c, b] is interpreted by / \ | 1 1 | | 0 1 | \ / [a, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, a] is interpreted by / \ | 1 2 | | 0 1 | \ / [a, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, a] is interpreted by / \ | 1 2 | | 0 1 | \ / Remains to prove termination of the 56-rule system { [b, d] [d, d] [d, c] [c, c] [c, b] -> [b, b] [b, b] [b, d] [d, d] [d, b] , [b, d] [d, d] [d, c] [c, c] [c, b] -> [b, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, b] , [b, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, b] -> [b, b] [b, b] [b, b] [b, b] [b, b] , [b, d] [d, d] [d, c] [c, c] [c, d] -> [b, b] [b, b] [b, d] [d, d] [d, d] , [b, d] [d, d] [d, c] [c, c] [c, d] -> [b, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, d] , [b, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, d] -> [b, b] [b, b] [b, b] [b, b] [b, d] , [b, d] [d, d] [d, c] [c, c] [c, c] -> [b, b] [b, b] [b, d] [d, d] [d, c] , [b, d] [d, d] [d, c] [c, c] [c, c] -> [b, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, c] , [b, d] [d, d] [d, c] [c, c] [c, a] -> [b, b] [b, b] [b, d] [d, d] [d, a] , [b, d] [d, d] [d, c] [c, c] [c, a] -> [b, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, a] , [d, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, b] -> [d, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, b] , [d, d] [d, d] [d, c] [c, c] [c, b] -> [d, b] [b, b] [b, d] [d, d] [d, b] , [d, d] [d, d] [d, c] [c, c] [c, b] -> [d, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, b] , [d, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, b] -> [d, b] [b, b] [b, b] [b, b] [b, b] , [d, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, d] -> [d, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, d] , [d, d] [d, d] [d, c] [c, c] [c, d] -> [d, b] [b, b] [b, d] [d, d] [d, d] , [d, d] [d, d] [d, c] [c, c] [c, d] -> [d, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, d] , [d, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, d] -> [d, b] [b, b] [b, b] [b, b] [b, d] , [d, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, c] -> [d, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, c] , [d, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, c] -> [d, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, c] , [d, d] [d, d] [d, c] [c, c] [c, c] -> [d, b] [b, b] [b, d] [d, d] [d, c] , [d, d] [d, d] [d, c] [c, c] [c, c] -> [d, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, c] , [d, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, a] -> [d, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, a] , [d, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, a] -> [d, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, a] , [d, d] [d, d] [d, c] [c, c] [c, a] -> [d, b] [b, b] [b, d] [d, d] [d, a] , [d, d] [d, d] [d, c] [c, c] [c, a] -> [d, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, a] , [c, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, b] -> [c, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, b] , [c, d] [d, d] [d, c] [c, c] [c, b] -> [c, b] [b, b] [b, d] [d, d] [d, b] , [c, d] [d, d] [d, c] [c, c] [c, b] -> [c, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, b] , [c, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, b] -> [c, b] [b, b] [b, b] [b, b] [b, b] , [c, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, d] -> [c, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, d] , [c, d] [d, d] [d, c] [c, c] [c, d] -> [c, b] [b, b] [b, d] [d, d] [d, d] , [c, d] [d, d] [d, c] [c, c] [c, d] -> [c, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, d] , [c, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, d] -> [c, b] [b, b] [b, b] [b, b] [b, d] , [c, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, c] -> [c, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, c] , [c, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, c] -> [c, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, c] , [c, d] [d, d] [d, c] [c, c] [c, c] -> [c, b] [b, b] [b, d] [d, d] [d, c] , [c, d] [d, d] [d, c] [c, c] [c, c] -> [c, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, c] , [c, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, a] -> [c, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, a] , [c, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, a] -> [c, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, a] , [c, d] [d, d] [d, c] [c, c] [c, a] -> [c, b] [b, b] [b, d] [d, d] [d, a] , [c, d] [d, d] [d, c] [c, c] [c, a] -> [c, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, a] , [a, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, b] -> [a, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, b] , [a, a] [a, a] [a, d] [d, d] [d, b] -> [a, d] [d, d] [d, c] [c, c] [c, b] , [a, d] [d, d] [d, c] [c, c] [c, b] -> [a, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, b] , [a, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, d] -> [a, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, d] , [a, a] [a, a] [a, d] [d, d] [d, d] -> [a, d] [d, d] [d, c] [c, c] [c, d] , [a, d] [d, d] [d, c] [c, c] [c, d] -> [a, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, d] , [a, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, c] -> [a, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, c] , [a, a] [a, a] [a, d] [d, d] [d, c] -> [a, d] [d, d] [d, c] [c, c] [c, c] , [a, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, c] -> [a, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, c] , [a, d] [d, d] [d, c] [c, c] [c, c] -> [a, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, c] , [a, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, a] -> [a, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, a] , [a, a] [a, a] [a, d] [d, d] [d, a] -> [a, d] [d, d] [d, c] [c, c] [c, a] , [a, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, a] -> [a, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, a] , [a, d] [d, d] [d, c] [c, c] [c, a] -> [a, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, a] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: [b, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [b, a] is interpreted by / \ | 1 1 | | 0 1 | \ / [a, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, d] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, b] is interpreted by / \ | 1 0 | | 0 1 | \ / [d, a] is interpreted by / \ | 1 0 | | 0 1 | \ / [a, c] is interpreted by / \ | 1 0 | | 0 1 | \ / [c, a] is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 53-rule system { [b, d] [d, d] [d, c] [c, c] [c, b] -> [b, b] [b, b] [b, d] [d, d] [d, b] , [b, d] [d, d] [d, c] [c, c] [c, b] -> [b, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, b] , [b, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, b] -> [b, b] [b, b] [b, b] [b, b] [b, b] , [b, d] [d, d] [d, c] [c, c] [c, d] -> [b, b] [b, b] [b, d] [d, d] [d, d] , [b, d] [d, d] [d, c] [c, c] [c, d] -> [b, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, d] , [b, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, d] -> [b, b] [b, b] [b, b] [b, b] [b, d] , [b, d] [d, d] [d, c] [c, c] [c, c] -> [b, b] [b, b] [b, d] [d, d] [d, c] , [b, d] [d, d] [d, c] [c, c] [c, c] -> [b, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, c] , [b, d] [d, d] [d, c] [c, c] [c, a] -> [b, b] [b, b] [b, d] [d, d] [d, a] , [b, d] [d, d] [d, c] [c, c] [c, a] -> [b, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, a] , [d, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, b] -> [d, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, b] , [d, d] [d, d] [d, c] [c, c] [c, b] -> [d, b] [b, b] [b, d] [d, d] [d, b] , [d, d] [d, d] [d, c] [c, c] [c, b] -> [d, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, b] , [d, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, b] -> [d, b] [b, b] [b, b] [b, b] [b, b] , [d, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, d] -> [d, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, d] , [d, d] [d, d] [d, c] [c, c] [c, d] -> [d, b] [b, b] [b, d] [d, d] [d, d] , [d, d] [d, d] [d, c] [c, c] [c, d] -> [d, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, d] , [d, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, d] -> [d, b] [b, b] [b, b] [b, b] [b, d] , [d, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, c] -> [d, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, c] , [d, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, c] -> [d, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, c] , [d, d] [d, d] [d, c] [c, c] [c, c] -> [d, b] [b, b] [b, d] [d, d] [d, c] , [d, d] [d, d] [d, c] [c, c] [c, c] -> [d, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, c] , [d, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, a] -> [d, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, a] , [d, d] [d, d] [d, c] [c, c] [c, a] -> [d, b] [b, b] [b, d] [d, d] [d, a] , [d, d] [d, d] [d, c] [c, c] [c, a] -> [d, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, a] , [c, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, b] -> [c, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, b] , [c, d] [d, d] [d, c] [c, c] [c, b] -> [c, b] [b, b] [b, d] [d, d] [d, b] , [c, d] [d, d] [d, c] [c, c] [c, b] -> [c, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, b] , [c, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, b] -> [c, b] [b, b] [b, b] [b, b] [b, b] , [c, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, d] -> [c, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, d] , [c, d] [d, d] [d, c] [c, c] [c, d] -> [c, b] [b, b] [b, d] [d, d] [d, d] , [c, d] [d, d] [d, c] [c, c] [c, d] -> [c, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, d] , [c, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, d] -> [c, b] [b, b] [b, b] [b, b] [b, d] , [c, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, c] -> [c, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, c] , [c, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, c] -> [c, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, c] , [c, d] [d, d] [d, c] [c, c] [c, c] -> [c, b] [b, b] [b, d] [d, d] [d, c] , [c, d] [d, d] [d, c] [c, c] [c, c] -> [c, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, c] , [c, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, a] -> [c, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, a] , [c, d] [d, d] [d, c] [c, c] [c, a] -> [c, b] [b, b] [b, d] [d, d] [d, a] , [c, d] [d, d] [d, c] [c, c] [c, a] -> [c, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, a] , [a, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, b] -> [a, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, b] , [a, a] [a, a] [a, d] [d, d] [d, b] -> [a, d] [d, d] [d, c] [c, c] [c, b] , [a, d] [d, d] [d, c] [c, c] [c, b] -> [a, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, b] , [a, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, d] -> [a, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, d] , [a, a] [a, a] [a, d] [d, d] [d, d] -> [a, d] [d, d] [d, c] [c, c] [c, d] , [a, d] [d, d] [d, c] [c, c] [c, d] -> [a, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, d] , [a, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, c] -> [a, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, c] , [a, a] [a, a] [a, d] [d, d] [d, c] -> [a, d] [d, d] [d, c] [c, c] [c, c] , [a, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, c] -> [a, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, c] , [a, d] [d, d] [d, c] [c, c] [c, c] -> [a, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, c] , [a, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, a] -> [a, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, a] , [a, a] [a, a] [a, d] [d, d] [d, a] -> [a, d] [d, d] [d, c] [c, c] [c, a] , [a, d] [d, d] [d, c] [c, c] [c, a] -> [a, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, a] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: [b, b] is interpreted by / \ | 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 | \ / [b, d] is interpreted by / \ | 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 | \ / [d, d] is interpreted by / \ | 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 1 | | 0 1 0 0 0 0 | \ / [d, b] is interpreted by / \ | 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 | \ / [b, c] is interpreted by / \ | 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 | \ / [c, c] is interpreted by / \ | 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 | \ / [c, d] is interpreted by / \ | 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 | \ / [b, a] is interpreted by / \ | 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 | \ / [a, a] is interpreted by / \ | 1 0 1 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 0 0 0 0 0 | \ / [a, d] is interpreted by / \ | 1 0 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 0 0 0 | | 0 0 0 0 0 0 | \ / [d, c] is interpreted by / \ | 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 | \ / [c, b] is interpreted by / \ | 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 | \ / [a, b] is interpreted by / \ | 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 | \ / [d, a] is interpreted by / \ | 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 | \ / [a, c] is interpreted by / \ | 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 | \ / [c, a] is interpreted by / \ | 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 | \ / Remains to prove termination of the 52-rule system { [b, d] [d, d] [d, c] [c, c] [c, b] -> [b, b] [b, b] [b, d] [d, d] [d, b] , [b, d] [d, d] [d, c] [c, c] [c, b] -> [b, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, b] , [b, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, b] -> [b, b] [b, b] [b, b] [b, b] [b, b] , [b, d] [d, d] [d, c] [c, c] [c, d] -> [b, b] [b, b] [b, d] [d, d] [d, d] , [b, d] [d, d] [d, c] [c, c] [c, d] -> [b, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, d] , [b, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, d] -> [b, b] [b, b] [b, b] [b, b] [b, d] , [b, d] [d, d] [d, c] [c, c] [c, c] -> [b, b] [b, b] [b, d] [d, d] [d, c] , [b, d] [d, d] [d, c] [c, c] [c, c] -> [b, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, c] , [b, d] [d, d] [d, c] [c, c] [c, a] -> [b, b] [b, b] [b, d] [d, d] [d, a] , [b, d] [d, d] [d, c] [c, c] [c, a] -> [b, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, a] , [d, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, b] -> [d, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, b] , [d, d] [d, d] [d, c] [c, c] [c, b] -> [d, b] [b, b] [b, d] [d, d] [d, b] , [d, d] [d, d] [d, c] [c, c] [c, b] -> [d, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, b] , [d, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, b] -> [d, b] [b, b] [b, b] [b, b] [b, b] , [d, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, d] -> [d, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, d] , [d, d] [d, d] [d, c] [c, c] [c, d] -> [d, b] [b, b] [b, d] [d, d] [d, d] , [d, d] [d, d] [d, c] [c, c] [c, d] -> [d, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, d] , [d, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, d] -> [d, b] [b, b] [b, b] [b, b] [b, d] , [d, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, c] -> [d, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, c] , [d, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, c] -> [d, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, c] , [d, d] [d, d] [d, c] [c, c] [c, c] -> [d, b] [b, b] [b, d] [d, d] [d, c] , [d, d] [d, d] [d, c] [c, c] [c, c] -> [d, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, c] , [d, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, a] -> [d, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, a] , [d, d] [d, d] [d, c] [c, c] [c, a] -> [d, b] [b, b] [b, d] [d, d] [d, a] , [d, d] [d, d] [d, c] [c, c] [c, a] -> [d, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, a] , [c, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, b] -> [c, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, b] , [c, d] [d, d] [d, c] [c, c] [c, b] -> [c, b] [b, b] [b, d] [d, d] [d, b] , [c, d] [d, d] [d, c] [c, c] [c, b] -> [c, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, b] , [c, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, b] -> [c, b] [b, b] [b, b] [b, b] [b, b] , [c, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, d] -> [c, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, d] , [c, d] [d, d] [d, c] [c, c] [c, d] -> [c, b] [b, b] [b, d] [d, d] [d, d] , [c, d] [d, d] [d, c] [c, c] [c, d] -> [c, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, d] , [c, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, d] -> [c, b] [b, b] [b, b] [b, b] [b, d] , [c, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, c] -> [c, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, c] , [c, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, c] -> [c, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, c] , [c, d] [d, d] [d, c] [c, c] [c, c] -> [c, b] [b, b] [b, d] [d, d] [d, c] , [c, d] [d, d] [d, c] [c, c] [c, c] -> [c, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, c] , [c, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, a] -> [c, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, a] , [c, d] [d, d] [d, c] [c, c] [c, a] -> [c, b] [b, b] [b, d] [d, d] [d, a] , [c, d] [d, d] [d, c] [c, c] [c, a] -> [c, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, a] , [a, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, b] -> [a, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, b] , [a, a] [a, a] [a, d] [d, d] [d, b] -> [a, d] [d, d] [d, c] [c, c] [c, b] , [a, d] [d, d] [d, c] [c, c] [c, b] -> [a, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, b] , [a, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, d] -> [a, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, d] , [a, d] [d, d] [d, c] [c, c] [c, d] -> [a, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, d] , [a, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, c] -> [a, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, c] , [a, a] [a, a] [a, d] [d, d] [d, c] -> [a, d] [d, d] [d, c] [c, c] [c, c] , [a, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, c] -> [a, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, c] , [a, d] [d, d] [d, c] [c, c] [c, c] -> [a, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, c] , [a, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, a] -> [a, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, a] , [a, a] [a, a] [a, d] [d, d] [d, a] -> [a, d] [d, d] [d, c] [c, c] [c, a] , [a, d] [d, d] [d, c] [c, c] [c, a] -> [a, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, a] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: [b, b] 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 1 | | 0 0 0 0 0 0 0 0 | \ / [b, d] 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 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [d, d] 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 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 | \ / [d, b] 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 | \ / [b, c] 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 1 0 0 0 0 0 0 | \ / [c, c] 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 | \ / [c, d] 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 | \ / [b, a] 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 | \ / [a, a] 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 | \ / [a, d] 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 | \ / [d, c] 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 | \ / [c, b] 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 | \ / [a, b] 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 | \ / [d, a] 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 | \ / [a, c] 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 | \ / [c, a] 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 51-rule system { [b, d] [d, d] [d, c] [c, c] [c, b] -> [b, b] [b, b] [b, d] [d, d] [d, b] , [b, d] [d, d] [d, c] [c, c] [c, b] -> [b, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, b] , [b, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, b] -> [b, b] [b, b] [b, b] [b, b] [b, b] , [b, d] [d, d] [d, c] [c, c] [c, d] -> [b, b] [b, b] [b, d] [d, d] [d, d] , [b, d] [d, d] [d, c] [c, c] [c, d] -> [b, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, d] , [b, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, d] -> [b, b] [b, b] [b, b] [b, b] [b, d] , [b, d] [d, d] [d, c] [c, c] [c, c] -> [b, b] [b, b] [b, d] [d, d] [d, c] , [b, d] [d, d] [d, c] [c, c] [c, c] -> [b, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, c] , [b, d] [d, d] [d, c] [c, c] [c, a] -> [b, b] [b, b] [b, d] [d, d] [d, a] , [b, d] [d, d] [d, c] [c, c] [c, a] -> [b, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, a] , [d, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, b] -> [d, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, b] , [d, d] [d, d] [d, c] [c, c] [c, b] -> [d, b] [b, b] [b, d] [d, d] [d, b] , [d, d] [d, d] [d, c] [c, c] [c, b] -> [d, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, b] , [d, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, b] -> [d, b] [b, b] [b, b] [b, b] [b, b] , [d, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, d] -> [d, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, d] , [d, d] [d, d] [d, c] [c, c] [c, d] -> [d, b] [b, b] [b, d] [d, d] [d, d] , [d, d] [d, d] [d, c] [c, c] [c, d] -> [d, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, d] , [d, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, d] -> [d, b] [b, b] [b, b] [b, b] [b, d] , [d, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, c] -> [d, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, c] , [d, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, c] -> [d, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, c] , [d, d] [d, d] [d, c] [c, c] [c, c] -> [d, b] [b, b] [b, d] [d, d] [d, c] , [d, d] [d, d] [d, c] [c, c] [c, c] -> [d, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, c] , [d, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, a] -> [d, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, a] , [d, d] [d, d] [d, c] [c, c] [c, a] -> [d, b] [b, b] [b, d] [d, d] [d, a] , [d, d] [d, d] [d, c] [c, c] [c, a] -> [d, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, a] , [c, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, b] -> [c, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, b] , [c, d] [d, d] [d, c] [c, c] [c, b] -> [c, b] [b, b] [b, d] [d, d] [d, b] , [c, d] [d, d] [d, c] [c, c] [c, b] -> [c, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, b] , [c, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, b] -> [c, b] [b, b] [b, b] [b, b] [b, b] , [c, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, d] -> [c, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, d] , [c, d] [d, d] [d, c] [c, c] [c, d] -> [c, b] [b, b] [b, d] [d, d] [d, d] , [c, d] [d, d] [d, c] [c, c] [c, d] -> [c, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, d] , [c, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, d] -> [c, b] [b, b] [b, b] [b, b] [b, d] , [c, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, c] -> [c, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, c] , [c, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, c] -> [c, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, c] , [c, d] [d, d] [d, c] [c, c] [c, c] -> [c, b] [b, b] [b, d] [d, d] [d, c] , [c, d] [d, d] [d, c] [c, c] [c, c] -> [c, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, c] , [c, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, a] -> [c, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, a] , [c, d] [d, d] [d, c] [c, c] [c, a] -> [c, b] [b, b] [b, d] [d, d] [d, a] , [c, d] [d, d] [d, c] [c, c] [c, a] -> [c, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, a] , [a, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, b] -> [a, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, b] , [a, a] [a, a] [a, d] [d, d] [d, b] -> [a, d] [d, d] [d, c] [c, c] [c, b] , [a, d] [d, d] [d, c] [c, c] [c, b] -> [a, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, b] , [a, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, d] -> [a, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, d] , [a, d] [d, d] [d, c] [c, c] [c, d] -> [a, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, d] , [a, a] [a, a] [a, d] [d, d] [d, c] -> [a, d] [d, d] [d, c] [c, c] [c, c] , [a, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, c] -> [a, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, c] , [a, d] [d, d] [d, c] [c, c] [c, c] -> [a, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, c] , [a, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, a] -> [a, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, a] , [a, a] [a, a] [a, d] [d, d] [d, a] -> [a, d] [d, d] [d, c] [c, c] [c, a] , [a, d] [d, d] [d, c] [c, c] [c, a] -> [a, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, a] } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: [b, b] 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 1 | | 0 0 0 0 0 0 0 0 | \ / [b, d] 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 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / [d, d] 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 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 | \ / [d, b] 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 | \ / [b, c] 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 | \ / [c, c] 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 | \ / [c, d] 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 | \ / [b, a] 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 1 0 0 0 0 0 0 | \ / [a, a] 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 | \ / [a, d] 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 | \ / [d, c] 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 | \ / [c, b] 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 | \ / [a, b] 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 | \ / [d, a] 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 | \ / [a, c] 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 | \ / [c, a] 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 50-rule system { [b, d] [d, d] [d, c] [c, c] [c, b] -> [b, b] [b, b] [b, d] [d, d] [d, b] , [b, d] [d, d] [d, c] [c, c] [c, b] -> [b, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, b] , [b, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, b] -> [b, b] [b, b] [b, b] [b, b] [b, b] , [b, d] [d, d] [d, c] [c, c] [c, d] -> [b, b] [b, b] [b, d] [d, d] [d, d] , [b, d] [d, d] [d, c] [c, c] [c, d] -> [b, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, d] , [b, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, d] -> [b, b] [b, b] [b, b] [b, b] [b, d] , [b, d] [d, d] [d, c] [c, c] [c, c] -> [b, b] [b, b] [b, d] [d, d] [d, c] , [b, d] [d, d] [d, c] [c, c] [c, c] -> [b, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, c] , [b, d] [d, d] [d, c] [c, c] [c, a] -> [b, b] [b, b] [b, d] [d, d] [d, a] , [b, d] [d, d] [d, c] [c, c] [c, a] -> [b, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, a] , [d, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, b] -> [d, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, b] , [d, d] [d, d] [d, c] [c, c] [c, b] -> [d, b] [b, b] [b, d] [d, d] [d, b] , [d, d] [d, d] [d, c] [c, c] [c, b] -> [d, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, b] , [d, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, b] -> [d, b] [b, b] [b, b] [b, b] [b, b] , [d, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, d] -> [d, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, d] , [d, d] [d, d] [d, c] [c, c] [c, d] -> [d, b] [b, b] [b, d] [d, d] [d, d] , [d, d] [d, d] [d, c] [c, c] [c, d] -> [d, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, d] , [d, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, d] -> [d, b] [b, b] [b, b] [b, b] [b, d] , [d, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, c] -> [d, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, c] , [d, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, c] -> [d, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, c] , [d, d] [d, d] [d, c] [c, c] [c, c] -> [d, b] [b, b] [b, d] [d, d] [d, c] , [d, d] [d, d] [d, c] [c, c] [c, c] -> [d, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, c] , [d, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, a] -> [d, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, a] , [d, d] [d, d] [d, c] [c, c] [c, a] -> [d, b] [b, b] [b, d] [d, d] [d, a] , [d, d] [d, d] [d, c] [c, c] [c, a] -> [d, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, a] , [c, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, b] -> [c, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, b] , [c, d] [d, d] [d, c] [c, c] [c, b] -> [c, b] [b, b] [b, d] [d, d] [d, b] , [c, d] [d, d] [d, c] [c, c] [c, b] -> [c, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, b] , [c, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, b] -> [c, b] [b, b] [b, b] [b, b] [b, b] , [c, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, d] -> [c, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, d] , [c, d] [d, d] [d, c] [c, c] [c, d] -> [c, b] [b, b] [b, d] [d, d] [d, d] , [c, d] [d, d] [d, c] [c, c] [c, d] -> [c, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, d] , [c, d] [d, d] [d, a] [a, a] [a, c] [c, c] [c, d] -> [c, b] [b, b] [b, b] [b, b] [b, d] , [c, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, c] -> [c, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, c] , [c, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, c] -> [c, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, c] , [c, d] [d, d] [d, c] [c, c] [c, c] -> [c, b] [b, b] [b, d] [d, d] [d, c] , [c, d] [d, d] [d, c] [c, c] [c, c] -> [c, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, c] , [c, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, a] -> [c, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, a] , [c, d] [d, d] [d, c] [c, c] [c, a] -> [c, b] [b, b] [b, d] [d, d] [d, a] , [c, d] [d, d] [d, c] [c, c] [c, a] -> [c, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, a] , [a, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, b] -> [a, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, b] , [a, a] [a, a] [a, d] [d, d] [d, b] -> [a, d] [d, d] [d, c] [c, c] [c, b] , [a, d] [d, d] [d, c] [c, c] [c, b] -> [a, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, b] , [a, b] [b, b] [b, d] [d, d] [d, b] [b, b] [b, d] -> [a, c] [c, c] [c, d] [d, d] [d, b] [b, b] [b, d] , [a, d] [d, d] [d, c] [c, c] [c, d] -> [a, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, d] , [a, a] [a, a] [a, d] [d, d] [d, c] -> [a, d] [d, d] [d, c] [c, c] [c, c] , [a, b] [b, b] [b, b] [b, b] [b, b] [b, b] [b, c] -> [a, a] [a, a] [a, b] [b, b] [b, c] [c, c] [c, c] , [a, d] [d, d] [d, c] [c, c] [c, c] -> [a, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, c] , [a, a] [a, a] [a, d] [d, d] [d, a] -> [a, d] [d, d] [d, c] [c, c] [c, a] , [a, d] [d, d] [d, c] [c, c] [c, a] -> [a, d] [d, d] [d, b] [b, b] [b, d] [d, d] [d, a] } The system was reversed. Remains to prove termination of the 50-rule system { [c, b] [c, c] [d, c] [d, d] [b, d] -> [d, b] [d, d] [b, d] [b, b] [b, b] , [c, b] [c, c] [d, c] [d, d] [b, d] -> [d, b] [d, d] [b, d] [b, b] [d, b] [d, d] [b, d] , [c, b] [c, c] [a, c] [a, a] [d, a] [d, d] [b, d] -> [b, b] [b, b] [b, b] [b, b] [b, b] , [c, d] [c, c] [d, c] [d, d] [b, d] -> [d, d] [d, d] [b, d] [b, b] [b, b] , [c, d] [c, c] [d, c] [d, d] [b, d] -> [d, d] [d, d] [b, d] [b, b] [d, b] [d, d] [b, d] , [c, d] [c, c] [a, c] [a, a] [d, a] [d, d] [b, d] -> [b, d] [b, b] [b, b] [b, b] [b, b] , [c, c] [c, c] [d, c] [d, d] [b, d] -> [d, c] [d, d] [b, d] [b, b] [b, b] , [c, c] [c, c] [d, c] [d, d] [b, d] -> [d, c] [d, d] [b, d] [b, b] [d, b] [d, d] [b, d] , [c, a] [c, c] [d, c] [d, d] [b, d] -> [d, a] [d, d] [b, d] [b, b] [b, b] , [c, a] [c, c] [d, c] [d, d] [b, d] -> [d, a] [d, d] [b, d] [b, b] [d, b] [d, d] [b, d] , [b, b] [b, b] [d, b] [d, d] [b, d] [b, b] [d, b] -> [b, b] [b, b] [d, b] [d, d] [c, d] [c, c] [d, c] , [c, b] [c, c] [d, c] [d, d] [d, d] -> [d, b] [d, d] [b, d] [b, b] [d, b] , [c, b] [c, c] [d, c] [d, d] [d, d] -> [d, b] [d, d] [b, d] [b, b] [d, b] [d, d] [d, d] , [c, b] [c, c] [a, c] [a, a] [d, a] [d, d] [d, d] -> [b, b] [b, b] [b, b] [b, b] [d, b] , [b, d] [b, b] [d, b] [d, d] [b, d] [b, b] [d, b] -> [b, d] [b, b] [d, b] [d, d] [c, d] [c, c] [d, c] , [c, d] [c, c] [d, c] [d, d] [d, d] -> [d, d] [d, d] [b, d] [b, b] [d, b] , [c, d] [c, c] [d, c] [d, d] [d, d] -> [d, d] [d, d] [b, d] [b, b] [d, b] [d, d] [d, d] , [c, d] [c, c] [a, c] [a, a] [d, a] [d, d] [d, d] -> [b, d] [b, b] [b, b] [b, b] [d, b] , [b, c] [b, b] [d, b] [d, d] [b, d] [b, b] [d, b] -> [b, c] [b, b] [d, b] [d, d] [c, d] [c, c] [d, c] , [b, c] [b, b] [b, b] [b, b] [b, b] [b, b] [d, b] -> [c, c] [c, c] [b, c] [b, b] [a, b] [a, a] [d, a] , [c, c] [c, c] [d, c] [d, d] [d, d] -> [d, c] [d, d] [b, d] [b, b] [d, b] , [c, c] [c, c] [d, c] [d, d] [d, d] -> [d, c] [d, d] [b, d] [b, b] [d, b] [d, d] [d, d] , [b, a] [b, b] [d, b] [d, d] [b, d] [b, b] [d, b] -> [b, a] [b, b] [d, b] [d, d] [c, d] [c, c] [d, c] , [c, a] [c, c] [d, c] [d, d] [d, d] -> [d, a] [d, d] [b, d] [b, b] [d, b] , [c, a] [c, c] [d, c] [d, d] [d, d] -> [d, a] [d, d] [b, d] [b, b] [d, b] [d, d] [d, d] , [b, b] [b, b] [d, b] [d, d] [b, d] [b, b] [c, b] -> [b, b] [b, b] [d, b] [d, d] [c, d] [c, c] [c, c] , [c, b] [c, c] [d, c] [d, d] [c, d] -> [d, b] [d, d] [b, d] [b, b] [c, b] , [c, b] [c, c] [d, c] [d, d] [c, d] -> [d, b] [d, d] [b, d] [b, b] [d, b] [d, d] [c, d] , [c, b] [c, c] [a, c] [a, a] [d, a] [d, d] [c, d] -> [b, b] [b, b] [b, b] [b, b] [c, b] , [b, d] [b, b] [d, b] [d, d] [b, d] [b, b] [c, b] -> [b, d] [b, b] [d, b] [d, d] [c, d] [c, c] [c, c] , [c, d] [c, c] [d, c] [d, d] [c, d] -> [d, d] [d, d] [b, d] [b, b] [c, b] , [c, d] [c, c] [d, c] [d, d] [c, d] -> [d, d] [d, d] [b, d] [b, b] [d, b] [d, d] [c, d] , [c, d] [c, c] [a, c] [a, a] [d, a] [d, d] [c, d] -> [b, d] [b, b] [b, b] [b, b] [c, b] , [b, c] [b, b] [d, b] [d, d] [b, d] [b, b] [c, b] -> [b, c] [b, b] [d, b] [d, d] [c, d] [c, c] [c, c] , [b, c] [b, b] [b, b] [b, b] [b, b] [b, b] [c, b] -> [c, c] [c, c] [b, c] [b, b] [a, b] [a, a] [c, a] , [c, c] [c, c] [d, c] [d, d] [c, d] -> [d, c] [d, d] [b, d] [b, b] [c, b] , [c, c] [c, c] [d, c] [d, d] [c, d] -> [d, c] [d, d] [b, d] [b, b] [d, b] [d, d] [c, d] , [b, a] [b, b] [d, b] [d, d] [b, d] [b, b] [c, b] -> [b, a] [b, b] [d, b] [d, d] [c, d] [c, c] [c, c] , [c, a] [c, c] [d, c] [d, d] [c, d] -> [d, a] [d, d] [b, d] [b, b] [c, b] , [c, a] [c, c] [d, c] [d, d] [c, d] -> [d, a] [d, d] [b, d] [b, b] [d, b] [d, d] [c, d] , [b, b] [b, b] [d, b] [d, d] [b, d] [b, b] [a, b] -> [b, b] [b, b] [d, b] [d, d] [c, d] [c, c] [a, c] , [d, b] [d, d] [a, d] [a, a] [a, a] -> [c, b] [c, c] [d, c] [d, d] [a, d] , [c, b] [c, c] [d, c] [d, d] [a, d] -> [d, b] [d, d] [b, d] [b, b] [d, b] [d, d] [a, d] , [b, d] [b, b] [d, b] [d, d] [b, d] [b, b] [a, b] -> [b, d] [b, b] [d, b] [d, d] [c, d] [c, c] [a, c] , [c, d] [c, c] [d, c] [d, d] [a, d] -> [d, d] [d, d] [b, d] [b, b] [d, b] [d, d] [a, d] , [d, c] [d, d] [a, d] [a, a] [a, a] -> [c, c] [c, c] [d, c] [d, d] [a, d] , [b, c] [b, b] [b, b] [b, b] [b, b] [b, b] [a, b] -> [c, c] [c, c] [b, c] [b, b] [a, b] [a, a] [a, a] , [c, c] [c, c] [d, c] [d, d] [a, d] -> [d, c] [d, d] [b, d] [b, b] [d, b] [d, d] [a, d] , [d, a] [d, d] [a, d] [a, a] [a, a] -> [c, a] [c, c] [d, c] [d, d] [a, d] , [c, a] [c, c] [d, c] [d, d] [a, d] -> [d, a] [d, d] [b, d] [b, b] [d, b] [d, d] [a, d] } The dependency pairs transformation was applied. Remains to prove termination of the 274-rule system { ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([b, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([b, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, b],true) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) , ([c, b],true) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, b],true) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, b],true) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([b, b],false) ([b, b],false) , ([c, b],true) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([b, b],false) , ([c, b],true) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) -> ([b, b],true) , ([c, d],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([b, b],false) , ([c, d],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([b, b],false) , ([c, d],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, b],true) , ([c, d],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, d],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, d],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) , ([c, d],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) , ([c, d],true) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, d],true) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, d],true) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([b, b],false) ([b, b],false) , ([c, d],true) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([b, b],false) , ([c, d],true) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) -> ([b, b],true) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([b, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([b, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, b],true) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([b, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([b, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, b],true) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, b],true) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([d, b],true) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([c, d],true) ([c, c],false) ([d, c],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([c, c],true) ([d, c],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([d, c],true) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([b, b],true) ([d, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, b],true) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([b, b],true) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, b],true) ([d, 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d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([d, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([c, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, b],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, c],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([a, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([a, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, a],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: ([c, b],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, b],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, d],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, b],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, d],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, c],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, c],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, a],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, a],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, c],true) is interpreted by / \ | 1 1 | | 0 1 | \ / ([b, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, a],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 253-rule system { ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([b, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([b, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, b],true) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) , ([c, b],true) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, b],true) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, b],true) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([b, b],false) ([b, b],false) , ([c, b],true) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([b, b],false) , ([c, b],true) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) -> ([b, b],true) , ([c, d],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([b, b],false) , ([c, d],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([b, b],false) , ([c, d],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, b],true) , ([c, d],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, d],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, d],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) , ([c, d],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) , ([c, d],true) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, d],true) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, d],true) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([b, b],false) ([b, b],false) , ([c, d],true) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([b, b],false) , ([c, d],true) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) -> ([b, b],true) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([b, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([b, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, b],true) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([b, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([b, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, b],true) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, b],true) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([d, b],true) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([c, d],true) ([c, c],false) ([d, c],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([c, c],true) ([d, c],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, 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} The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: ([c, b],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, b],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, d],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, b],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, d],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, c],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, c],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, a],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, a],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, c],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, a],true) is interpreted by / \ | 1 1 | | 0 1 | \ / ([c, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 243-rule system { ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([b, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([b, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, b],true) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) , ([c, b],true) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, b],true) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, b],true) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([b, b],false) ([b, b],false) , ([c, b],true) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([b, b],false) , ([c, b],true) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) -> ([b, b],true) , ([c, d],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([b, b],false) , ([c, d],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([b, b],false) , ([c, d],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, b],true) , ([c, d],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, d],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, d],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) , ([c, d],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) , ([c, d],true) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, d],true) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, d],true) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([b, b],false) ([b, b],false) , ([c, d],true) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([b, b],false) , ([c, d],true) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) -> ([b, b],true) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([b, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([b, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, b],true) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([b, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([b, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, b],true) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, b],true) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, b],true) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, b],true) ([b, 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([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([d, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([c, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, b],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, c],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([a, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([a, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, a],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: ([c, b],true) is interpreted by / \ | 1 1 | | 0 1 | \ / ([c, c],false) is interpreted by / \ | 1 1 | | 0 1 | \ / ([d, c],false) is interpreted by / \ | 1 1 | | 0 1 | \ / ([d, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, d],false) is interpreted by / \ | 1 1 | | 0 1 | \ / ([d, b],true) is interpreted by / \ | 1 1 | | 0 1 | \ / ([b, b],false) is interpreted by / \ | 1 1 | | 0 1 | \ / ([b, d],true) is interpreted by / \ | 1 2 | | 0 1 | \ / ([b, b],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, c],false) is interpreted by / \ | 1 1 | | 0 1 | \ / ([a, a],false) is interpreted by / \ | 1 1 | | 0 1 | \ / ([d, a],false) is interpreted by / \ | 1 1 | | 0 1 | \ / ([c, d],true) is interpreted by / \ | 1 1 | | 0 1 | \ / ([c, c],true) is interpreted by / \ | 1 1 | | 0 1 | \ / ([d, c],true) is interpreted by / \ | 1 1 | | 0 1 | \ / ([c, a],true) is interpreted by / \ | 1 1 | | 0 1 | \ / ([d, a],true) is interpreted by / \ | 1 1 | | 0 1 | \ / ([c, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, c],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, a],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, a],false) is interpreted by / \ | 1 1 | | 0 1 | \ / ([a, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 121-rule system { ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([b, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, d],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([b, b],false) , ([c, d],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, d],true) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([b, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([b, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, 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([a, a],false) ->= ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, c],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([a, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([a, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, a],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: ([c, b],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, b],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, d],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, b],true) is interpreted by / \ | 1 1 | | 0 1 | \ / ([d, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, d],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, c],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, c],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, a],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, a],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, c],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, a],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 115-rule system { ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([b, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, d],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([b, b],false) , ([c, d],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, d],true) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([b, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([b, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, d],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) , ([c, d],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, d],true) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) -> ([b, d],true) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([b, d],true) ([b, b],false) ([c, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, d],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([b, d],true) ([b, b],false) ([c, b],false) , ([c, d],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, d],true) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) -> ([b, d],true) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([b, d],true) ([b, b],false) ([c, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([b, d],true) ([b, b],false) ([c, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, b],true) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) -> ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([c, d],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, c],true) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) -> ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, a],true) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) -> ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([d, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([c, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, b],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, c],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([a, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([a, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, a],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: ([c, b],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, b],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, d],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, b],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, d],true) is interpreted by / \ | 1 1 | | 0 1 | \ / ([c, c],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, c],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, a],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, a],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, c],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, a],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 105-rule system { ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([b, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([b, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([b, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([b, d],true) ([b, b],false) ([c, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([b, d],true) ([b, b],false) ([c, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([b, d],true) ([b, b],false) ([c, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, b],true) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) -> ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, c],true) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) -> ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, a],true) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) -> ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([d, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([c, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, b],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, c],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([a, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([a, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, a],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: ([c, b],true) is interpreted by / \ | 1 1 | | 0 1 | \ / ([c, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, b],true) is interpreted by / \ | 1 1 | | 0 1 | \ / ([b, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, d],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, b],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, c],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, c],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, a],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, a],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, c],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, a],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 98-rule system { ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([b, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([b, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([b, d],true) ([b, b],false) ([c, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([b, d],true) ([b, b],false) ([c, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, b],true) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) -> ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, c],true) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) -> ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, a],true) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) -> ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([d, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([c, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, b],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, c],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([a, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([a, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, a],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: ([c, b],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, b],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, d],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, b],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, c],true) is interpreted by / \ | 1 1 | | 0 1 | \ / ([d, c],true) is interpreted by / \ | 1 1 | | 0 1 | \ / ([c, a],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, a],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, c],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, a],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 91-rule system { ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([b, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([b, d],true) ([b, b],false) ([c, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, b],true) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) -> ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, c],true) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) -> ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, a],true) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) -> ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([d, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([c, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, b],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, c],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([a, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([a, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, a],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: ([c, b],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, b],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, d],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, b],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, c],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, c],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, a],true) is interpreted by / \ | 1 1 | | 0 1 | \ / ([d, a],true) is interpreted by / \ | 1 1 | | 0 1 | \ / ([c, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, c],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, a],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 84-rule system { ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, b],true) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) -> ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, c],true) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) -> ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, a],true) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) -> ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([d, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([c, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, b],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, c],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([a, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([a, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, a],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: ([c, b],true) is interpreted by / \ | 1 0 1 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 | \ / ([c, c],false) is interpreted by / \ | 1 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 0 0 0 0 0 | \ / ([d, c],false) is interpreted by / \ | 1 0 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 0 0 0 | | 0 0 0 0 0 0 | \ / ([d, d],false) is interpreted by / \ | 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 1 | | 0 0 0 0 0 0 | \ / ([b, d],false) is interpreted by / \ | 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 | \ / ([d, b],true) is interpreted by / \ | 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 | \ / ([b, b],false) is interpreted by / \ | 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 | \ / ([b, d],true) is interpreted by / \ | 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 | \ / ([b, b],true) is interpreted by / \ | 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 | \ / ([d, b],false) is interpreted by / \ | 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 | \ / ([a, c],false) is interpreted by / \ | 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 | \ / ([a, a],false) is interpreted by / \ | 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 | \ / ([d, a],false) is interpreted by / \ | 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 | \ / ([c, d],true) is interpreted by / \ | 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 | \ / ([c, c],true) is interpreted by / \ | 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 | \ / ([d, c],true) is interpreted by / \ | 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 | \ / ([c, a],true) is interpreted by / \ | 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 | \ / ([d, a],true) is interpreted by / \ | 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 | \ / ([c, d],false) is interpreted by / \ | 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 1 0 0 0 0 | \ / ([b, c],true) is interpreted by / \ | 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 | \ / ([b, c],false) is interpreted by / \ | 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 | \ / ([a, b],false) is interpreted by / \ | 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 | \ / ([b, a],true) is interpreted by / \ | 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 | \ / ([c, b],false) is interpreted by / \ | 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 | \ / ([c, a],false) is interpreted by / \ | 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 | \ / ([a, d],false) is interpreted by / \ | 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 | \ / ([b, a],false) is interpreted by / \ | 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 | \ / Remains to prove termination of the 82-rule system { ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, b],true) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) -> ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, c],true) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) -> ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, a],true) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) -> ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([d, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([c, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, b],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, c],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([a, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([a, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, a],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: ([c, b],true) is interpreted by / \ | 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 | \ / ([c, c],false) is interpreted by / \ | 1 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 0 0 0 0 0 | \ / ([d, c],false) is interpreted by / \ | 1 0 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 0 0 0 | | 0 0 0 0 0 0 | \ / ([d, d],false) is interpreted by / \ | 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 1 | | 0 0 0 0 0 0 | \ / ([b, d],false) is interpreted by / \ | 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 | \ / ([d, b],true) is interpreted by / \ | 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 | \ / ([b, b],false) is interpreted by / \ | 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 | \ / ([b, d],true) is interpreted by / \ | 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 | \ / ([b, b],true) is interpreted by / \ | 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 | \ / ([d, b],false) is interpreted by / \ | 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 | \ / ([a, c],false) is interpreted by / \ | 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 | \ / ([a, a],false) is interpreted by / \ | 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 | \ / ([d, a],false) is interpreted by / \ | 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 | \ / ([c, d],true) is interpreted by / \ | 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 | \ / ([c, c],true) is interpreted by / \ | 1 0 1 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 | \ / ([d, c],true) is interpreted by / \ | 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 | \ / ([c, a],true) is interpreted by / \ | 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 | \ / ([d, a],true) is interpreted by / \ | 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 | \ / ([c, d],false) is interpreted by / \ | 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 1 0 0 0 0 | \ / ([b, c],true) is interpreted by / \ | 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 | \ / ([b, c],false) is interpreted by / \ | 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 | \ / ([a, b],false) is interpreted by / \ | 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 | \ / ([b, a],true) is interpreted by / \ | 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 | \ / ([c, b],false) is interpreted by / \ | 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 | \ / ([c, a],false) is interpreted by / \ | 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 | \ / ([a, d],false) is interpreted by / \ | 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 | \ / ([b, a],false) is interpreted by / \ | 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 | \ / Remains to prove termination of the 80-rule system { ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, b],true) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) -> ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, c],true) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) -> ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, a],true) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) -> ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([d, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([c, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, b],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, c],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([a, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([a, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, a],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: ([c, b],true) is interpreted by / \ | 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 | \ / ([c, c],false) is interpreted by / \ | 1 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 0 0 0 0 0 | \ / ([d, c],false) is interpreted by / \ | 1 0 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 0 0 0 | | 0 0 0 0 0 0 | \ / ([d, d],false) is interpreted by / \ | 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 1 | | 0 0 0 0 0 0 | \ / ([b, d],false) is interpreted by / \ | 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 | \ / ([d, b],true) is interpreted by / \ | 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 | \ / ([b, b],false) is interpreted by / \ | 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 | \ / ([b, d],true) is interpreted by / \ | 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 | \ / ([b, b],true) is interpreted by / \ | 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 | \ / ([d, b],false) is interpreted by / \ | 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 | \ / ([a, c],false) is interpreted by / \ | 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 | \ / ([a, a],false) is interpreted by / \ | 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 | \ / ([d, a],false) is interpreted by / \ | 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 | \ / ([c, d],true) is interpreted by / \ | 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 | \ / ([c, c],true) is interpreted by / \ | 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 | \ / ([d, c],true) is interpreted by / \ | 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 | \ / ([c, a],true) is interpreted by / \ | 1 0 1 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 | \ / ([d, a],true) is interpreted by / \ | 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 | \ / ([c, d],false) is interpreted by / \ | 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 1 0 0 0 0 | \ / ([b, c],true) is interpreted by / \ | 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 | \ / ([b, c],false) is interpreted by / \ | 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 | \ / ([a, b],false) is interpreted by / \ | 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 | \ / ([b, a],true) is interpreted by / \ | 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 | \ / ([c, b],false) is interpreted by / \ | 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 | \ / ([c, a],false) is interpreted by / \ | 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 | \ / ([a, d],false) is interpreted by / \ | 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 | \ / ([b, a],false) is interpreted by / \ | 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 | \ / Remains to prove termination of the 78-rule system { ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, b],true) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) -> ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, c],true) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) -> ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, a],true) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) -> ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([d, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([c, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, b],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, c],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([a, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([a, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, a],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: ([c, b],true) 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 | \ / ([c, c],false) 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 | \ / ([d, c],false) 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 | \ / ([d, d],false) 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 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 | \ / ([b, d],false) 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 | \ / ([d, b],true) 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 | \ / ([b, b],false) 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 1 | | 0 0 0 0 0 0 0 0 | \ / ([b, d],true) 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 | \ / ([b, b],true) 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 | \ / ([d, b],false) 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 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / ([a, c],false) 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 | \ / ([a, a],false) 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 | \ / ([d, a],false) 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 | \ / ([c, d],true) 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 | \ / ([c, c],true) 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 | \ / ([d, c],true) 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 | \ / ([c, a],true) 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 | \ / ([d, a],true) 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 | \ / ([c, d],false) 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 | \ / ([b, c],true) 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 | \ / ([b, c],false) 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 | \ / ([a, b],false) 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 1 0 0 0 0 0 0 | \ / ([b, a],true) 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 | \ / ([c, b],false) 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 | \ / ([c, a],false) 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 | \ / ([a, d],false) 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 | \ / ([b, a],false) 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 { ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([d, b],true) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) -> ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, c],true) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) -> ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, a],true) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) -> ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([d, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([c, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, b],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, c],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([a, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([a, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, a],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: ([c, b],true) is interpreted by / \ | 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 | \ / ([c, c],false) is interpreted by / \ | 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 | \ / ([d, c],false) is interpreted by / \ | 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 | \ / ([d, d],false) is interpreted by / \ | 1 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 0 0 0 0 0 | \ / ([b, d],false) is interpreted by / \ | 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 | \ / ([d, b],true) is interpreted by / \ | 1 0 1 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 | \ / ([b, b],false) is interpreted by / \ | 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 | \ / ([b, d],true) is interpreted by / \ | 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 | \ / ([b, b],true) is interpreted by / \ | 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 | \ / ([d, b],false) is interpreted by / \ | 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 | \ / ([a, c],false) is interpreted by / \ | 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 | \ / ([a, a],false) is interpreted by / \ | 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 1 | | 0 1 0 0 0 0 | \ / ([d, a],false) is interpreted by / \ | 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 | \ / ([c, d],true) is interpreted by / \ | 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 | \ / ([c, c],true) is interpreted by / \ | 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 | \ / ([d, c],true) is interpreted by / \ | 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 | \ / ([c, a],true) is interpreted by / \ | 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 | \ / ([d, a],true) is interpreted by / \ | 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 | \ / ([c, d],false) is interpreted by / \ | 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 | \ / ([b, c],true) is interpreted by / \ | 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 | \ / ([b, c],false) is interpreted by / \ | 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 | \ / ([a, b],false) is interpreted by / \ | 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 | \ / ([b, a],true) is interpreted by / \ | 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 | \ / ([c, b],false) is interpreted by / \ | 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 | \ / ([c, a],false) is interpreted by / \ | 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 | \ / ([a, d],false) is interpreted by / \ | 1 0 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 0 0 0 | | 0 0 0 0 0 0 | \ / ([b, a],false) is interpreted by / \ | 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 | \ / Remains to prove termination of the 76-rule system { ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, b],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, c],true) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) -> ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, a],true) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) -> ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([d, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([c, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, b],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, c],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([a, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([a, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, a],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: ([c, b],true) is interpreted by / \ | 1 1 | | 0 1 | \ / ([c, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, b],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, d],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, b],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, d],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, c],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, c],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, a],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, a],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, c],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, a],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 71-rule system { ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, c],true) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) -> ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, a],true) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) -> ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([d, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([c, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, b],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, c],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([a, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([a, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, a],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: ([c, b],true) 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 | \ / ([c, c],false) 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 | \ / ([d, c],false) 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 | \ / ([d, d],false) 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 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 | \ / ([b, d],false) 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 | \ / ([d, b],true) 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 | \ / ([b, b],false) 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 1 | | 0 0 0 0 0 0 0 0 | \ / ([b, d],true) 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 | \ / ([b, b],true) 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 | \ / ([d, b],false) 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 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / ([a, c],false) 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 | \ / ([a, a],false) 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 | \ / ([d, a],false) 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 | \ / ([c, d],true) 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 | \ / ([c, c],true) 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 | \ / ([d, c],true) 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 | \ / ([c, a],true) 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 | \ / ([d, a],true) 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 | \ / ([c, d],false) 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 | \ / ([b, c],true) 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 | \ / ([b, c],false) 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 | \ / ([a, b],false) 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 1 0 0 0 0 0 0 | \ / ([b, a],true) 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 | \ / ([c, b],false) 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 | \ / ([c, a],false) 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 | \ / ([a, d],false) 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 | \ / ([b, a],false) 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 70-rule system { ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([d, c],true) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) -> ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, a],true) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) -> ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([d, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([c, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, b],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, c],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([a, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([a, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, a],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: ([c, b],true) is interpreted by / \ | 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 | \ / ([c, c],false) is interpreted by / \ | 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 | \ / ([d, c],false) is interpreted by / \ | 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 | \ / ([d, d],false) is interpreted by / \ | 1 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 0 0 0 0 0 | \ / ([b, d],false) is interpreted by / \ | 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 | \ / ([d, b],true) is interpreted by / \ | 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 | \ / ([b, b],false) is interpreted by / \ | 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 | \ / ([b, d],true) is interpreted by / \ | 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 | \ / ([b, b],true) is interpreted by / \ | 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 | \ / ([d, b],false) is interpreted by / \ | 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 | \ / ([a, c],false) is interpreted by / \ | 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 | \ / ([a, a],false) is interpreted by / \ | 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 1 | | 0 1 0 0 0 0 | \ / ([d, a],false) is interpreted by / \ | 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 | \ / ([c, d],true) is interpreted by / \ | 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 | \ / ([c, c],true) is interpreted by / \ | 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 | \ / ([d, c],true) is interpreted by / \ | 1 0 1 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 | \ / ([c, a],true) is interpreted by / \ | 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 | \ / ([d, a],true) is interpreted by / \ | 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 | \ / ([c, d],false) is interpreted by / \ | 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 | \ / ([b, c],true) is interpreted by / \ | 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 | \ / ([b, c],false) is interpreted by / \ | 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 | \ / ([a, b],false) is interpreted by / \ | 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 | \ / ([b, a],true) is interpreted by / \ | 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 | \ / ([c, b],false) is interpreted by / \ | 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 | \ / ([c, a],false) is interpreted by / \ | 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 | \ / ([a, d],false) is interpreted by / \ | 1 0 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 0 0 0 | | 0 0 0 0 0 0 | \ / ([b, a],false) is interpreted by / \ | 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 | \ / Remains to prove termination of the 69-rule system { ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, c],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, c],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, a],true) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) -> ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([d, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([c, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, b],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, c],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([a, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([a, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, a],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: ([c, b],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, b],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, d],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, b],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, d],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, c],true) is interpreted by / \ | 1 1 | | 0 1 | \ / ([d, c],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, a],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, a],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, c],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, a],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 64-rule system { ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([d, a],true) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) -> ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([d, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([c, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, b],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, c],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([a, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([a, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, a],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: ([c, b],true) is interpreted by / \ | 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 | \ / ([c, c],false) is interpreted by / \ | 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 | \ / ([d, c],false) is interpreted by / \ | 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 | \ / ([d, d],false) is interpreted by / \ | 1 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 0 0 0 0 0 | \ / ([b, d],false) is interpreted by / \ | 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 | \ / ([d, b],true) is interpreted by / \ | 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 | \ / ([b, b],false) is interpreted by / \ | 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 | \ / ([b, d],true) is interpreted by / \ | 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 | \ / ([b, b],true) is interpreted by / \ | 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 | \ / ([d, b],false) is interpreted by / \ | 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 | \ / ([a, c],false) is interpreted by / \ | 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 | \ / ([a, a],false) is interpreted by / \ | 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 1 | | 0 1 0 0 0 0 | \ / ([d, a],false) is interpreted by / \ | 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 | \ / ([c, d],true) is interpreted by / \ | 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 | \ / ([c, c],true) is interpreted by / \ | 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 | \ / ([d, c],true) is interpreted by / \ | 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 | \ / ([c, a],true) is interpreted by / \ | 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 | \ / ([d, a],true) is interpreted by / \ | 1 0 1 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 | \ / ([c, d],false) is interpreted by / \ | 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 | \ / ([b, c],true) is interpreted by / \ | 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 | \ / ([b, c],false) is interpreted by / \ | 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 | \ / ([a, b],false) is interpreted by / \ | 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 | \ / ([b, a],true) is interpreted by / \ | 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 | \ / ([c, b],false) is interpreted by / \ | 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 | \ / ([c, a],false) is interpreted by / \ | 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 | \ / ([a, d],false) is interpreted by / \ | 1 0 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 0 0 0 | | 0 0 0 0 0 0 | \ / ([b, a],false) is interpreted by / \ | 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 | \ / Remains to prove termination of the 63-rule system { ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, a],true) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) -> ([d, a],true) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([d, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([c, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, b],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, c],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([a, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([a, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, a],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: ([c, b],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, b],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, d],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, b],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, d],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, c],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([d, c],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, a],true) is interpreted by / \ | 1 1 | | 0 1 | \ / ([d, a],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, c],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, c],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, a],true) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, b],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([c, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([a, d],false) is interpreted by / \ | 1 0 | | 0 1 | \ / ([b, a],false) is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 58-rule system { ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([d, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([c, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, b],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, c],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([a, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([a, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, a],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 14: ([c, b],true) is interpreted by / \ | 1 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 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / ([c, c],false) is interpreted by / \ | 1 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 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / ([d, c],false) is interpreted by / \ | 1 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 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / ([d, d],false) is interpreted by / \ | 1 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 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 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 | \ / ([b, d],false) is interpreted by / \ | 1 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 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 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 | \ / ([d, b],true) is interpreted by / \ | 1 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 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / ([b, b],false) is interpreted by / \ | 1 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 1 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 1 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 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 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / ([b, d],true) is interpreted by / \ | 1 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 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / ([b, b],true) is interpreted by / \ | 1 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 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / ([d, b],false) is interpreted by / \ | 1 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 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / ([a, c],false) is interpreted by / \ | 1 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 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 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 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / ([a, a],false) is interpreted by / \ | 1 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 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / ([d, a],false) is interpreted by / \ | 1 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 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 | \ / ([c, d],true) is interpreted by / \ | 1 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 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / ([c, c],true) is interpreted by / \ | 1 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 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / ([d, c],true) is interpreted by / \ | 1 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 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / ([c, a],true) is interpreted by / \ | 1 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 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / ([d, a],true) is interpreted by / \ | 1 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 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / ([c, d],false) is interpreted by / \ | 1 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 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / ([b, c],true) is interpreted by / \ | 1 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 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / ([b, c],false) is interpreted by / \ | 1 0 1 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 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / ([a, b],false) is interpreted by / \ | 1 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 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / ([b, a],true) is interpreted by / \ | 1 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 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / ([c, b],false) is interpreted by / \ | 1 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 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 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / ([c, a],false) is interpreted by / \ | 1 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 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / ([a, d],false) is interpreted by / \ | 1 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 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / ([b, a],false) is interpreted by / \ | 1 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 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 57-rule system { ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([d, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([c, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, b],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, c],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, a],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 24: ([c, b],true) is interpreted by / \ | 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / ([c, c],false) is interpreted by / \ | 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / ([d, c],false) is interpreted by / \ | 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / ([d, d],false) is interpreted by / \ | 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 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 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 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 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 56-rule system { ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, c],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([d, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([c, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, b],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, c],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: ([c, b],true) 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 | \ / ([c, c],false) 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 | \ / ([d, c],false) 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 | \ / ([d, d],false) 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 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 | \ / ([b, d],false) 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 | \ / ([d, b],true) 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 | \ / ([b, b],false) 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 1 | | 0 0 0 0 0 0 0 0 | \ / ([b, d],true) 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 | \ / ([b, b],true) 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 | \ / ([d, b],false) 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 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 | \ / ([a, c],false) 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 | \ / ([a, a],false) 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 | \ / ([d, a],false) 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 | \ / ([c, d],true) 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 | \ / ([c, c],true) 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 | \ / ([d, c],true) 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 | \ / ([c, a],true) 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 | \ / ([d, a],true) 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 | \ / ([c, d],false) 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 | \ / ([b, c],true) 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 | \ / ([b, c],false) 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 | \ / ([a, b],false) 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 | \ / ([b, a],true) 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 | \ / ([c, b],false) 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 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 1 0 0 0 0 0 0 | \ / ([c, a],false) 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 | \ / ([a, d],false) 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 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / ([b, a],false) 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 54-rule system { ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([d, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([c, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, b],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, c],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 24: ([c, b],true) is interpreted by / \ | 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / ([a, d],false) is interpreted by / \ | 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / ([b, a],false) is interpreted by / \ | 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 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 52-rule system { ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([d, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([c, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, a],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, b],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, c],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: ([c, b],true) 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 | \ / ([c, c],false) 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 | \ / ([d, c],false) 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 | \ / ([d, d],false) 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 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 | \ / ([b, d],false) 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 | \ / ([d, b],true) 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 | \ / ([b, b],false) 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 1 | | 0 0 0 0 0 0 0 0 | \ / ([b, d],true) 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 | \ / ([b, b],true) 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 | \ / ([d, b],false) 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 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 | \ / ([a, c],false) 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 | \ / ([a, a],false) 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 | \ / ([d, a],false) 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 | \ / ([c, d],true) 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 | \ / ([c, c],true) 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 | \ / ([d, c],true) 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 | \ / ([c, a],true) 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 | \ / ([d, a],true) 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 | \ / ([c, d],false) 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 | \ / ([b, c],true) 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 | \ / ([b, c],false) 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 | \ / ([a, b],false) 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 | \ / ([b, a],true) 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 | \ / ([c, b],false) 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 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 1 0 0 0 0 0 0 | \ / ([c, a],false) 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 | \ / ([a, d],false) 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 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / ([b, a],false) 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 | \ / Remains to prove termination of the 50-rule system { ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, d],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([d, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([c, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, b],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, c],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: ([c, b],true) 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 | \ / ([c, c],false) 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 | \ / ([d, c],false) 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 | \ / ([d, d],false) 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 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 | \ / ([b, d],false) 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 | \ / ([d, b],true) 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 | \ / ([b, b],false) 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 1 | | 0 0 0 0 0 0 0 0 | \ / ([b, d],true) 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 | \ / ([b, b],true) 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 | \ / ([d, b],false) 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 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 | \ / ([a, c],false) 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 | \ / ([a, a],false) 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 | \ / ([d, a],false) 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 | \ / ([c, d],true) 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 | \ / ([c, c],true) 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 | \ / ([d, c],true) 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 | \ / ([c, a],true) 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 | \ / ([d, a],true) 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 | \ / ([c, d],false) 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 | \ / ([b, c],true) 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 | \ / ([b, c],false) 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 | \ / ([a, b],false) 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 | \ / ([b, a],true) 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 | \ / ([c, b],false) 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 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 1 0 0 0 0 0 0 | \ / ([c, a],false) 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 | \ / ([a, d],false) 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 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / ([b, a],false) 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 48-rule system { ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, a],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([d, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([c, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, b],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, c],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: ([c, b],true) 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 | \ / ([c, c],false) 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 | \ / ([d, c],false) 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 | \ / ([d, d],false) 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 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 | \ / ([b, d],false) 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 | \ / ([d, b],true) 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 | \ / ([b, b],false) 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 1 | | 0 0 0 0 0 0 0 0 | \ / ([b, d],true) 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 | \ / ([b, b],true) 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 | \ / ([d, b],false) 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 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 | \ / ([a, c],false) 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 | \ / ([a, a],false) 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 | \ / ([d, a],false) 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 | \ / ([c, d],true) 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 | \ / ([c, c],true) 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 | \ / ([d, c],true) 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 | \ / ([c, a],true) 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 | \ / ([d, a],true) 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 | \ / ([c, d],false) 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 | \ / ([b, c],true) 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 | \ / ([b, c],false) 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 | \ / ([a, b],false) 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 | \ / ([b, a],true) 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 | \ / ([c, b],false) 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 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 1 0 0 0 0 0 0 | \ / ([c, a],false) 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 | \ / ([a, d],false) 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 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / ([b, a],false) 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 46-rule system { ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) -> ([b, b],true) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([d, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([c, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, b],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, c],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: ([c, b],true) 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 | \ / ([c, c],false) 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 | \ / ([d, c],false) 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 | \ / ([d, d],false) 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 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 | \ / ([b, d],false) 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 | \ / ([d, b],true) 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 | \ / ([b, b],false) 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 1 | | 0 0 0 0 0 0 0 0 | \ / ([b, d],true) 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 | \ / ([b, b],true) 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 | \ / ([d, b],false) 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 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 | \ / ([a, c],false) 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 | \ / ([a, a],false) 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 | \ / ([d, a],false) 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 | \ / ([c, d],true) 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 | \ / ([c, c],true) 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 | \ / ([d, c],true) 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 | \ / ([c, a],true) 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 | \ / ([d, a],true) 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 | \ / ([c, d],false) 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 | \ / ([b, c],true) 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 | \ / ([b, c],false) 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 | \ / ([a, b],false) 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 | \ / ([b, a],true) 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 | \ / ([c, b],false) 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 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 1 0 0 0 0 0 0 | \ / ([c, a],false) 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 | \ / ([a, d],false) 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 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / ([b, a],false) 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 44-rule system { ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([b, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([b, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([b, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([d, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([d, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([d, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([d, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([d, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([d, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, b],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([c, d],false) ([c, c],false) ([a, c],false) ([a, a],false) ([d, a],false) ([d, d],false) ([c, d],false) ->= ([b, d],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) , ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) ->= ([b, c],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([c, c],false) , ([b, c],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ([c, b],false) ->= ([c, c],false) ([c, c],false) ([b, c],false) ([b, b],false) ([a, b],false) ([a, a],false) ([c, a],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([c, b],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([c, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) , ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, b],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([d, b],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, b],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([b, d],false) ([b, b],false) ([a, b],false) ->= ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([c, d],false) ([c, c],false) ([a, c],false) , ([c, d],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, d],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([d, c],false) ([d, d],false) ([a, d],false) ([a, a],false) ([a, a],false) ->= ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) , ([c, c],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, c],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) , ([c, a],false) ([c, c],false) ([d, c],false) ([d, d],false) ([a, d],false) ->= ([d, a],false) ([d, d],false) ([b, d],false) ([b, b],false) ([d, b],false) ([d, d],false) ([a, d],false) } The system is trivially terminating.