/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES After renaming modulo { 0->0, 1->1, 2->2, 3->3 }, it remains to prove termination of the 30-rule system { 0 0 0 0 0 1 1 2 0 0 3 1 3 -> 2 3 3 1 1 2 3 1 2 1 1 2 2 1 0 2 3 , 0 0 0 3 1 2 2 3 2 3 1 0 1 -> 3 2 1 3 0 1 3 1 1 2 1 3 3 3 3 1 3 , 0 0 3 0 1 1 2 1 0 1 3 3 3 -> 1 3 3 1 0 2 1 1 2 2 3 2 1 2 1 1 3 , 0 0 3 2 1 3 2 2 3 2 0 0 0 -> 1 2 1 3 2 3 2 2 3 3 1 0 0 2 1 3 3 , 0 3 0 1 3 1 3 2 2 1 2 2 0 -> 2 3 3 0 3 3 3 1 3 2 0 2 2 1 3 1 2 , 0 3 2 2 0 0 3 2 3 1 1 2 1 -> 2 0 3 3 1 2 0 3 1 2 1 2 1 1 0 3 1 , 0 3 3 3 0 1 2 3 1 1 0 0 3 -> 0 2 2 0 1 2 1 2 1 3 1 3 0 3 3 0 3 , 1 0 1 3 1 1 1 1 3 2 0 3 2 -> 3 3 3 1 3 3 0 1 0 1 2 1 2 1 1 0 3 , 1 0 3 2 3 3 0 0 1 2 1 0 1 -> 2 1 1 1 1 3 2 2 2 1 3 3 1 3 2 2 1 , 1 1 0 0 0 2 3 0 1 2 0 1 3 -> 1 2 2 2 1 3 3 2 1 1 2 1 0 2 0 2 3 , 1 1 2 1 0 2 2 0 3 0 0 0 0 -> 2 2 1 3 3 3 1 2 0 1 0 2 3 1 1 0 3 , 1 3 2 3 1 1 2 0 1 2 3 1 0 -> 1 3 2 2 0 2 3 3 0 1 2 1 2 2 1 3 1 , 2 0 3 3 3 2 2 3 2 0 0 3 3 -> 3 3 2 2 0 1 1 2 1 1 2 1 2 2 1 3 3 , 2 1 2 0 2 1 0 1 1 0 1 2 0 -> 0 0 1 1 3 3 1 1 0 0 3 3 3 3 3 3 2 , 2 2 3 1 3 2 2 0 2 2 2 2 0 -> 2 1 3 0 1 3 2 2 1 0 0 2 1 1 3 0 0 , 2 3 0 3 0 2 1 2 0 3 2 0 1 -> 2 1 3 3 0 2 2 1 3 2 0 2 2 2 1 2 1 , 2 3 1 0 1 0 0 1 1 0 1 2 1 -> 1 3 1 3 3 3 3 2 2 1 3 1 2 1 1 0 3 , 2 3 3 1 2 2 3 0 2 2 0 0 1 -> 2 3 1 2 2 1 1 3 1 3 3 3 3 0 3 0 0 , 2 3 3 1 2 2 3 2 3 1 1 0 1 -> 2 2 1 0 2 1 1 1 2 2 1 1 3 3 2 1 3 , 3 0 3 0 2 3 2 3 3 3 1 2 1 -> 2 1 2 1 3 2 1 3 2 1 2 1 3 1 3 3 1 , 3 0 3 0 2 3 3 2 3 2 2 2 1 -> 2 2 2 1 3 3 3 2 1 1 2 1 1 1 1 3 1 , 3 0 3 1 3 2 0 0 1 2 1 0 0 -> 3 1 3 0 3 3 2 2 1 1 2 2 2 1 1 0 2 , 3 1 2 3 1 1 3 1 1 3 0 1 1 -> 3 3 2 1 3 1 2 3 3 3 2 1 1 2 1 0 1 , 3 2 2 1 0 2 0 3 3 3 3 2 1 -> 3 3 3 2 3 1 1 3 3 2 1 2 1 2 1 3 1 , 3 2 3 0 1 1 3 0 0 0 0 2 1 -> 3 3 2 1 1 2 3 2 1 2 0 3 1 3 2 2 1 , 3 2 3 2 3 2 3 0 3 2 0 1 1 -> 2 2 1 1 2 1 3 3 2 0 0 0 0 0 1 3 3 , 3 3 1 3 1 2 3 2 0 2 2 0 0 -> 2 1 2 1 3 0 2 2 0 2 2 1 1 3 3 3 3 , 3 3 2 1 3 1 2 0 0 3 2 3 3 -> 3 2 1 3 2 2 1 3 3 3 1 0 2 1 3 3 3 , 3 1 2 0 1 0 3 2 0 1 2 0 0 ->= 3 1 1 2 1 0 1 1 2 2 1 2 1 3 0 2 3 , 3 3 3 1 2 1 2 2 3 0 0 0 3 ->= 3 3 3 1 2 1 1 2 1 1 0 3 3 2 2 0 3 } 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}) After renaming modulo { [0, 0]->0, [0, 1]->1, [1, 1]->2, [1, 2]->3, [2, 0]->4, [0, 3]->5, [3, 1]->6, [1, 3]->7, [3, 0]->8, [0, 2]->9, [2, 3]->10, [3, 3]->11, [2, 1]->12, [2, 2]->13, [1, 0]->14, [3, 2]->15 }, it remains to prove termination of the 480-rule system { 0 0 0 0 0 1 2 3 4 0 5 6 7 8 -> 9 10 11 6 2 3 10 6 3 12 2 3 13 12 14 9 10 8 , 0 0 0 5 6 3 13 10 15 10 6 14 1 14 -> 5 15 12 7 8 1 7 6 2 3 12 7 11 11 11 6 7 8 , 0 0 5 8 1 2 3 12 14 1 7 11 11 8 -> 1 7 11 6 14 9 12 2 3 13 10 15 12 3 12 2 7 8 , 0 0 5 15 12 7 15 13 10 15 4 0 0 0 -> 1 3 12 7 15 10 15 13 10 11 6 14 0 9 12 7 11 8 , 0 5 8 1 7 6 7 15 13 12 3 13 4 0 -> 9 10 11 8 5 11 11 6 7 15 4 9 13 12 7 6 3 4 , 0 5 15 13 4 0 5 15 10 6 2 3 12 14 -> 9 4 5 11 6 3 4 5 6 3 12 3 12 2 14 5 6 14 , 0 5 11 11 8 1 3 10 6 2 14 0 5 8 -> 0 9 13 4 1 3 12 3 12 7 6 7 8 5 11 8 5 8 , 1 14 1 7 6 2 2 2 7 15 4 5 15 4 -> 5 11 11 6 7 11 8 1 14 1 3 12 3 12 2 14 5 8 , 1 14 5 15 10 11 8 0 1 3 12 14 1 14 -> 9 12 2 2 2 7 15 13 13 12 7 11 6 7 15 13 12 14 , 1 2 14 0 0 9 10 8 1 3 4 1 7 8 -> 1 3 13 13 12 7 11 15 12 2 3 12 14 9 4 9 10 8 , 1 2 3 12 14 9 13 4 5 8 0 0 0 0 -> 9 13 12 7 11 11 6 3 4 1 14 9 10 6 2 14 5 8 , 1 7 15 10 6 2 3 4 1 3 10 6 14 0 -> 1 7 15 13 4 9 10 11 8 1 3 12 3 13 12 7 6 14 , 9 4 5 11 11 15 13 10 15 4 0 5 11 8 -> 5 11 15 13 4 1 2 3 12 2 3 12 3 13 12 7 11 8 , 9 12 3 4 9 12 14 1 2 14 1 3 4 0 -> 0 0 1 2 7 11 6 2 14 0 5 11 11 11 11 11 15 4 , 9 13 10 6 7 15 13 4 9 13 13 13 4 0 -> 9 12 7 8 1 7 15 13 12 14 0 9 12 2 7 8 0 0 , 9 10 8 5 8 9 12 3 4 5 15 4 1 14 -> 9 12 7 11 8 9 13 12 7 15 4 9 13 13 12 3 12 14 , 9 10 6 14 1 14 0 1 2 14 1 3 12 14 -> 1 7 6 7 11 11 11 15 13 12 7 6 3 12 2 14 5 8 , 9 10 11 6 3 13 10 8 9 13 4 0 1 14 -> 9 10 6 3 13 12 2 7 6 7 11 11 11 8 5 8 0 0 , 9 10 11 6 3 13 10 15 10 6 2 14 1 14 -> 9 13 12 14 9 12 2 2 3 13 12 2 7 11 15 12 7 8 , 5 8 5 8 9 10 15 10 11 11 6 3 12 14 -> 9 12 3 12 7 15 12 7 15 12 3 12 7 6 7 11 6 14 , 5 8 5 8 9 10 11 15 10 15 13 13 12 14 -> 9 13 13 12 7 11 11 15 12 2 3 12 2 2 2 7 6 14 , 5 8 5 6 7 15 4 0 1 3 12 14 0 0 -> 5 6 7 8 5 11 15 13 12 2 3 13 13 12 2 14 9 4 , 5 6 3 10 6 2 7 6 2 7 8 1 2 14 -> 5 11 15 12 7 6 3 10 11 11 15 12 2 3 12 14 1 14 , 5 15 13 12 14 9 4 5 11 11 11 15 12 14 -> 5 11 11 15 10 6 2 7 11 15 12 3 12 3 12 7 6 14 , 5 15 10 8 1 2 7 8 0 0 0 9 12 14 -> 5 11 15 12 2 3 10 15 12 3 4 5 6 7 15 13 12 14 , 5 15 10 15 10 15 10 8 5 15 4 1 2 14 -> 9 13 12 2 3 12 7 11 15 4 0 0 0 0 1 7 11 8 , 5 11 6 7 6 3 10 15 4 9 13 4 0 0 -> 9 12 3 12 7 8 9 13 4 9 13 12 2 7 11 11 11 8 , 5 11 15 12 7 6 3 4 0 5 15 10 11 8 -> 5 15 12 7 15 13 12 7 11 11 6 14 9 12 7 11 11 8 , 5 6 3 4 1 14 5 15 4 1 3 4 0 0 ->= 5 6 2 3 12 14 1 2 3 13 12 3 12 7 8 9 10 8 , 5 11 11 6 3 12 3 13 10 8 0 0 5 8 ->= 5 11 11 6 3 12 2 3 12 2 14 5 11 15 13 4 5 8 , 0 0 0 0 0 1 2 3 4 0 5 6 7 6 -> 9 10 11 6 2 3 10 6 3 12 2 3 13 12 14 9 10 6 , 0 0 0 5 6 3 13 10 15 10 6 14 1 2 -> 5 15 12 7 8 1 7 6 2 3 12 7 11 11 11 6 7 6 , 0 0 5 8 1 2 3 12 14 1 7 11 11 6 -> 1 7 11 6 14 9 12 2 3 13 10 15 12 3 12 2 7 6 , 0 0 5 15 12 7 15 13 10 15 4 0 0 1 -> 1 3 12 7 15 10 15 13 10 11 6 14 0 9 12 7 11 6 , 0 5 8 1 7 6 7 15 13 12 3 13 4 1 -> 9 10 11 8 5 11 11 6 7 15 4 9 13 12 7 6 3 12 , 0 5 15 13 4 0 5 15 10 6 2 3 12 2 -> 9 4 5 11 6 3 4 5 6 3 12 3 12 2 14 5 6 2 , 0 5 11 11 8 1 3 10 6 2 14 0 5 6 -> 0 9 13 4 1 3 12 3 12 7 6 7 8 5 11 8 5 6 , 1 14 1 7 6 2 2 2 7 15 4 5 15 12 -> 5 11 11 6 7 11 8 1 14 1 3 12 3 12 2 14 5 6 , 1 14 5 15 10 11 8 0 1 3 12 14 1 2 -> 9 12 2 2 2 7 15 13 13 12 7 11 6 7 15 13 12 2 , 1 2 14 0 0 9 10 8 1 3 4 1 7 6 -> 1 3 13 13 12 7 11 15 12 2 3 12 14 9 4 9 10 6 , 1 2 3 12 14 9 13 4 5 8 0 0 0 1 -> 9 13 12 7 11 11 6 3 4 1 14 9 10 6 2 14 5 6 , 1 7 15 10 6 2 3 4 1 3 10 6 14 1 -> 1 7 15 13 4 9 10 11 8 1 3 12 3 13 12 7 6 2 , 9 4 5 11 11 15 13 10 15 4 0 5 11 6 -> 5 11 15 13 4 1 2 3 12 2 3 12 3 13 12 7 11 6 , 9 12 3 4 9 12 14 1 2 14 1 3 4 1 -> 0 0 1 2 7 11 6 2 14 0 5 11 11 11 11 11 15 12 , 9 13 10 6 7 15 13 4 9 13 13 13 4 1 -> 9 12 7 8 1 7 15 13 12 14 0 9 12 2 7 8 0 1 , 9 10 8 5 8 9 12 3 4 5 15 4 1 2 -> 9 12 7 11 8 9 13 12 7 15 4 9 13 13 12 3 12 2 , 9 10 6 14 1 14 0 1 2 14 1 3 12 2 -> 1 7 6 7 11 11 11 15 13 12 7 6 3 12 2 14 5 6 , 9 10 11 6 3 13 10 8 9 13 4 0 1 2 -> 9 10 6 3 13 12 2 7 6 7 11 11 11 8 5 8 0 1 , 9 10 11 6 3 13 10 15 10 6 2 14 1 2 -> 9 13 12 14 9 12 2 2 3 13 12 2 7 11 15 12 7 6 , 5 8 5 8 9 10 15 10 11 11 6 3 12 2 -> 9 12 3 12 7 15 12 7 15 12 3 12 7 6 7 11 6 2 , 5 8 5 8 9 10 11 15 10 15 13 13 12 2 -> 9 13 13 12 7 11 11 15 12 2 3 12 2 2 2 7 6 2 , 5 8 5 6 7 15 4 0 1 3 12 14 0 1 -> 5 6 7 8 5 11 15 13 12 2 3 13 13 12 2 14 9 12 , 5 6 3 10 6 2 7 6 2 7 8 1 2 2 -> 5 11 15 12 7 6 3 10 11 11 15 12 2 3 12 14 1 2 , 5 15 13 12 14 9 4 5 11 11 11 15 12 2 -> 5 11 11 15 10 6 2 7 11 15 12 3 12 3 12 7 6 2 , 5 15 10 8 1 2 7 8 0 0 0 9 12 2 -> 5 11 15 12 2 3 10 15 12 3 4 5 6 7 15 13 12 2 , 5 15 10 15 10 15 10 8 5 15 4 1 2 2 -> 9 13 12 2 3 12 7 11 15 4 0 0 0 0 1 7 11 6 , 5 11 6 7 6 3 10 15 4 9 13 4 0 1 -> 9 12 3 12 7 8 9 13 4 9 13 12 2 7 11 11 11 6 , 5 11 15 12 7 6 3 4 0 5 15 10 11 6 -> 5 15 12 7 15 13 12 7 11 11 6 14 9 12 7 11 11 6 , 5 6 3 4 1 14 5 15 4 1 3 4 0 1 ->= 5 6 2 3 12 14 1 2 3 13 12 3 12 7 8 9 10 6 , 5 11 11 6 3 12 3 13 10 8 0 0 5 6 ->= 5 11 11 6 3 12 2 3 12 2 14 5 11 15 13 4 5 6 , 0 0 0 0 0 1 2 3 4 0 5 6 7 15 -> 9 10 11 6 2 3 10 6 3 12 2 3 13 12 14 9 10 15 , 0 0 0 5 6 3 13 10 15 10 6 14 1 3 -> 5 15 12 7 8 1 7 6 2 3 12 7 11 11 11 6 7 15 , 0 0 5 8 1 2 3 12 14 1 7 11 11 15 -> 1 7 11 6 14 9 12 2 3 13 10 15 12 3 12 2 7 15 , 0 0 5 15 12 7 15 13 10 15 4 0 0 9 -> 1 3 12 7 15 10 15 13 10 11 6 14 0 9 12 7 11 15 , 0 5 8 1 7 6 7 15 13 12 3 13 4 9 -> 9 10 11 8 5 11 11 6 7 15 4 9 13 12 7 6 3 13 , 0 5 15 13 4 0 5 15 10 6 2 3 12 3 -> 9 4 5 11 6 3 4 5 6 3 12 3 12 2 14 5 6 3 , 0 5 11 11 8 1 3 10 6 2 14 0 5 15 -> 0 9 13 4 1 3 12 3 12 7 6 7 8 5 11 8 5 15 , 1 14 1 7 6 2 2 2 7 15 4 5 15 13 -> 5 11 11 6 7 11 8 1 14 1 3 12 3 12 2 14 5 15 , 1 14 5 15 10 11 8 0 1 3 12 14 1 3 -> 9 12 2 2 2 7 15 13 13 12 7 11 6 7 15 13 12 3 , 1 2 14 0 0 9 10 8 1 3 4 1 7 15 -> 1 3 13 13 12 7 11 15 12 2 3 12 14 9 4 9 10 15 , 1 2 3 12 14 9 13 4 5 8 0 0 0 9 -> 9 13 12 7 11 11 6 3 4 1 14 9 10 6 2 14 5 15 , 1 7 15 10 6 2 3 4 1 3 10 6 14 9 -> 1 7 15 13 4 9 10 11 8 1 3 12 3 13 12 7 6 3 , 9 4 5 11 11 15 13 10 15 4 0 5 11 15 -> 5 11 15 13 4 1 2 3 12 2 3 12 3 13 12 7 11 15 , 9 12 3 4 9 12 14 1 2 14 1 3 4 9 -> 0 0 1 2 7 11 6 2 14 0 5 11 11 11 11 11 15 13 , 9 13 10 6 7 15 13 4 9 13 13 13 4 9 -> 9 12 7 8 1 7 15 13 12 14 0 9 12 2 7 8 0 9 , 9 10 8 5 8 9 12 3 4 5 15 4 1 3 -> 9 12 7 11 8 9 13 12 7 15 4 9 13 13 12 3 12 3 , 9 10 6 14 1 14 0 1 2 14 1 3 12 3 -> 1 7 6 7 11 11 11 15 13 12 7 6 3 12 2 14 5 15 , 9 10 11 6 3 13 10 8 9 13 4 0 1 3 -> 9 10 6 3 13 12 2 7 6 7 11 11 11 8 5 8 0 9 , 9 10 11 6 3 13 10 15 10 6 2 14 1 3 -> 9 13 12 14 9 12 2 2 3 13 12 2 7 11 15 12 7 15 , 5 8 5 8 9 10 15 10 11 11 6 3 12 3 -> 9 12 3 12 7 15 12 7 15 12 3 12 7 6 7 11 6 3 , 5 8 5 8 9 10 11 15 10 15 13 13 12 3 -> 9 13 13 12 7 11 11 15 12 2 3 12 2 2 2 7 6 3 , 5 8 5 6 7 15 4 0 1 3 12 14 0 9 -> 5 6 7 8 5 11 15 13 12 2 3 13 13 12 2 14 9 13 , 5 6 3 10 6 2 7 6 2 7 8 1 2 3 -> 5 11 15 12 7 6 3 10 11 11 15 12 2 3 12 14 1 3 , 5 15 13 12 14 9 4 5 11 11 11 15 12 3 -> 5 11 11 15 10 6 2 7 11 15 12 3 12 3 12 7 6 3 , 5 15 10 8 1 2 7 8 0 0 0 9 12 3 -> 5 11 15 12 2 3 10 15 12 3 4 5 6 7 15 13 12 3 , 5 15 10 15 10 15 10 8 5 15 4 1 2 3 -> 9 13 12 2 3 12 7 11 15 4 0 0 0 0 1 7 11 15 , 5 11 6 7 6 3 10 15 4 9 13 4 0 9 -> 9 12 3 12 7 8 9 13 4 9 13 12 2 7 11 11 11 15 , 5 11 15 12 7 6 3 4 0 5 15 10 11 15 -> 5 15 12 7 15 13 12 7 11 11 6 14 9 12 7 11 11 15 , 5 6 3 4 1 14 5 15 4 1 3 4 0 9 ->= 5 6 2 3 12 14 1 2 3 13 12 3 12 7 8 9 10 15 , 5 11 11 6 3 12 3 13 10 8 0 0 5 15 ->= 5 11 11 6 3 12 2 3 12 2 14 5 11 15 13 4 5 15 , 0 0 0 0 0 1 2 3 4 0 5 6 7 11 -> 9 10 11 6 2 3 10 6 3 12 2 3 13 12 14 9 10 11 , 0 0 0 5 6 3 13 10 15 10 6 14 1 7 -> 5 15 12 7 8 1 7 6 2 3 12 7 11 11 11 6 7 11 , 0 0 5 8 1 2 3 12 14 1 7 11 11 11 -> 1 7 11 6 14 9 12 2 3 13 10 15 12 3 12 2 7 11 , 0 0 5 15 12 7 15 13 10 15 4 0 0 5 -> 1 3 12 7 15 10 15 13 10 11 6 14 0 9 12 7 11 11 , 0 5 8 1 7 6 7 15 13 12 3 13 4 5 -> 9 10 11 8 5 11 11 6 7 15 4 9 13 12 7 6 3 10 , 0 5 15 13 4 0 5 15 10 6 2 3 12 7 -> 9 4 5 11 6 3 4 5 6 3 12 3 12 2 14 5 6 7 , 0 5 11 11 8 1 3 10 6 2 14 0 5 11 -> 0 9 13 4 1 3 12 3 12 7 6 7 8 5 11 8 5 11 , 1 14 1 7 6 2 2 2 7 15 4 5 15 10 -> 5 11 11 6 7 11 8 1 14 1 3 12 3 12 2 14 5 11 , 1 14 5 15 10 11 8 0 1 3 12 14 1 7 -> 9 12 2 2 2 7 15 13 13 12 7 11 6 7 15 13 12 7 , 1 2 14 0 0 9 10 8 1 3 4 1 7 11 -> 1 3 13 13 12 7 11 15 12 2 3 12 14 9 4 9 10 11 , 1 2 3 12 14 9 13 4 5 8 0 0 0 5 -> 9 13 12 7 11 11 6 3 4 1 14 9 10 6 2 14 5 11 , 1 7 15 10 6 2 3 4 1 3 10 6 14 5 -> 1 7 15 13 4 9 10 11 8 1 3 12 3 13 12 7 6 7 , 9 4 5 11 11 15 13 10 15 4 0 5 11 11 -> 5 11 15 13 4 1 2 3 12 2 3 12 3 13 12 7 11 11 , 9 12 3 4 9 12 14 1 2 14 1 3 4 5 -> 0 0 1 2 7 11 6 2 14 0 5 11 11 11 11 11 15 10 , 9 13 10 6 7 15 13 4 9 13 13 13 4 5 -> 9 12 7 8 1 7 15 13 12 14 0 9 12 2 7 8 0 5 , 9 10 8 5 8 9 12 3 4 5 15 4 1 7 -> 9 12 7 11 8 9 13 12 7 15 4 9 13 13 12 3 12 7 , 9 10 6 14 1 14 0 1 2 14 1 3 12 7 -> 1 7 6 7 11 11 11 15 13 12 7 6 3 12 2 14 5 11 , 9 10 11 6 3 13 10 8 9 13 4 0 1 7 -> 9 10 6 3 13 12 2 7 6 7 11 11 11 8 5 8 0 5 , 9 10 11 6 3 13 10 15 10 6 2 14 1 7 -> 9 13 12 14 9 12 2 2 3 13 12 2 7 11 15 12 7 11 , 5 8 5 8 9 10 15 10 11 11 6 3 12 7 -> 9 12 3 12 7 15 12 7 15 12 3 12 7 6 7 11 6 7 , 5 8 5 8 9 10 11 15 10 15 13 13 12 7 -> 9 13 13 12 7 11 11 15 12 2 3 12 2 2 2 7 6 7 , 5 8 5 6 7 15 4 0 1 3 12 14 0 5 -> 5 6 7 8 5 11 15 13 12 2 3 13 13 12 2 14 9 10 , 5 6 3 10 6 2 7 6 2 7 8 1 2 7 -> 5 11 15 12 7 6 3 10 11 11 15 12 2 3 12 14 1 7 , 5 15 13 12 14 9 4 5 11 11 11 15 12 7 -> 5 11 11 15 10 6 2 7 11 15 12 3 12 3 12 7 6 7 , 5 15 10 8 1 2 7 8 0 0 0 9 12 7 -> 5 11 15 12 2 3 10 15 12 3 4 5 6 7 15 13 12 7 , 5 15 10 15 10 15 10 8 5 15 4 1 2 7 -> 9 13 12 2 3 12 7 11 15 4 0 0 0 0 1 7 11 11 , 5 11 6 7 6 3 10 15 4 9 13 4 0 5 -> 9 12 3 12 7 8 9 13 4 9 13 12 2 7 11 11 11 11 , 5 11 15 12 7 6 3 4 0 5 15 10 11 11 -> 5 15 12 7 15 13 12 7 11 11 6 14 9 12 7 11 11 11 , 5 6 3 4 1 14 5 15 4 1 3 4 0 5 ->= 5 6 2 3 12 14 1 2 3 13 12 3 12 7 8 9 10 11 , 5 11 11 6 3 12 3 13 10 8 0 0 5 11 ->= 5 11 11 6 3 12 2 3 12 2 14 5 11 15 13 4 5 11 , 14 0 0 0 0 1 2 3 4 0 5 6 7 8 -> 3 10 11 6 2 3 10 6 3 12 2 3 13 12 14 9 10 8 , 14 0 0 5 6 3 13 10 15 10 6 14 1 14 -> 7 15 12 7 8 1 7 6 2 3 12 7 11 11 11 6 7 8 , 14 0 5 8 1 2 3 12 14 1 7 11 11 8 -> 2 7 11 6 14 9 12 2 3 13 10 15 12 3 12 2 7 8 , 14 0 5 15 12 7 15 13 10 15 4 0 0 0 -> 2 3 12 7 15 10 15 13 10 11 6 14 0 9 12 7 11 8 , 14 5 8 1 7 6 7 15 13 12 3 13 4 0 -> 3 10 11 8 5 11 11 6 7 15 4 9 13 12 7 6 3 4 , 14 5 15 13 4 0 5 15 10 6 2 3 12 14 -> 3 4 5 11 6 3 4 5 6 3 12 3 12 2 14 5 6 14 , 14 5 11 11 8 1 3 10 6 2 14 0 5 8 -> 14 9 13 4 1 3 12 3 12 7 6 7 8 5 11 8 5 8 , 2 14 1 7 6 2 2 2 7 15 4 5 15 4 -> 7 11 11 6 7 11 8 1 14 1 3 12 3 12 2 14 5 8 , 2 14 5 15 10 11 8 0 1 3 12 14 1 14 -> 3 12 2 2 2 7 15 13 13 12 7 11 6 7 15 13 12 14 , 2 2 14 0 0 9 10 8 1 3 4 1 7 8 -> 2 3 13 13 12 7 11 15 12 2 3 12 14 9 4 9 10 8 , 2 2 3 12 14 9 13 4 5 8 0 0 0 0 -> 3 13 12 7 11 11 6 3 4 1 14 9 10 6 2 14 5 8 , 2 7 15 10 6 2 3 4 1 3 10 6 14 0 -> 2 7 15 13 4 9 10 11 8 1 3 12 3 13 12 7 6 14 , 3 4 5 11 11 15 13 10 15 4 0 5 11 8 -> 7 11 15 13 4 1 2 3 12 2 3 12 3 13 12 7 11 8 , 3 12 3 4 9 12 14 1 2 14 1 3 4 0 -> 14 0 1 2 7 11 6 2 14 0 5 11 11 11 11 11 15 4 , 3 13 10 6 7 15 13 4 9 13 13 13 4 0 -> 3 12 7 8 1 7 15 13 12 14 0 9 12 2 7 8 0 0 , 3 10 8 5 8 9 12 3 4 5 15 4 1 14 -> 3 12 7 11 8 9 13 12 7 15 4 9 13 13 12 3 12 14 , 3 10 6 14 1 14 0 1 2 14 1 3 12 14 -> 2 7 6 7 11 11 11 15 13 12 7 6 3 12 2 14 5 8 , 3 10 11 6 3 13 10 8 9 13 4 0 1 14 -> 3 10 6 3 13 12 2 7 6 7 11 11 11 8 5 8 0 0 , 3 10 11 6 3 13 10 15 10 6 2 14 1 14 -> 3 13 12 14 9 12 2 2 3 13 12 2 7 11 15 12 7 8 , 7 8 5 8 9 10 15 10 11 11 6 3 12 14 -> 3 12 3 12 7 15 12 7 15 12 3 12 7 6 7 11 6 14 , 7 8 5 8 9 10 11 15 10 15 13 13 12 14 -> 3 13 13 12 7 11 11 15 12 2 3 12 2 2 2 7 6 14 , 7 8 5 6 7 15 4 0 1 3 12 14 0 0 -> 7 6 7 8 5 11 15 13 12 2 3 13 13 12 2 14 9 4 , 7 6 3 10 6 2 7 6 2 7 8 1 2 14 -> 7 11 15 12 7 6 3 10 11 11 15 12 2 3 12 14 1 14 , 7 15 13 12 14 9 4 5 11 11 11 15 12 14 -> 7 11 11 15 10 6 2 7 11 15 12 3 12 3 12 7 6 14 , 7 15 10 8 1 2 7 8 0 0 0 9 12 14 -> 7 11 15 12 2 3 10 15 12 3 4 5 6 7 15 13 12 14 , 7 15 10 15 10 15 10 8 5 15 4 1 2 14 -> 3 13 12 2 3 12 7 11 15 4 0 0 0 0 1 7 11 8 , 7 11 6 7 6 3 10 15 4 9 13 4 0 0 -> 3 12 3 12 7 8 9 13 4 9 13 12 2 7 11 11 11 8 , 7 11 15 12 7 6 3 4 0 5 15 10 11 8 -> 7 15 12 7 15 13 12 7 11 11 6 14 9 12 7 11 11 8 , 7 6 3 4 1 14 5 15 4 1 3 4 0 0 ->= 7 6 2 3 12 14 1 2 3 13 12 3 12 7 8 9 10 8 , 7 11 11 6 3 12 3 13 10 8 0 0 5 8 ->= 7 11 11 6 3 12 2 3 12 2 14 5 11 15 13 4 5 8 , 14 0 0 0 0 1 2 3 4 0 5 6 7 6 -> 3 10 11 6 2 3 10 6 3 12 2 3 13 12 14 9 10 6 , 14 0 0 5 6 3 13 10 15 10 6 14 1 2 -> 7 15 12 7 8 1 7 6 2 3 12 7 11 11 11 6 7 6 , 14 0 5 8 1 2 3 12 14 1 7 11 11 6 -> 2 7 11 6 14 9 12 2 3 13 10 15 12 3 12 2 7 6 , 14 0 5 15 12 7 15 13 10 15 4 0 0 1 -> 2 3 12 7 15 10 15 13 10 11 6 14 0 9 12 7 11 6 , 14 5 8 1 7 6 7 15 13 12 3 13 4 1 -> 3 10 11 8 5 11 11 6 7 15 4 9 13 12 7 6 3 12 , 14 5 15 13 4 0 5 15 10 6 2 3 12 2 -> 3 4 5 11 6 3 4 5 6 3 12 3 12 2 14 5 6 2 , 14 5 11 11 8 1 3 10 6 2 14 0 5 6 -> 14 9 13 4 1 3 12 3 12 7 6 7 8 5 11 8 5 6 , 2 14 1 7 6 2 2 2 7 15 4 5 15 12 -> 7 11 11 6 7 11 8 1 14 1 3 12 3 12 2 14 5 6 , 2 14 5 15 10 11 8 0 1 3 12 14 1 2 -> 3 12 2 2 2 7 15 13 13 12 7 11 6 7 15 13 12 2 , 2 2 14 0 0 9 10 8 1 3 4 1 7 6 -> 2 3 13 13 12 7 11 15 12 2 3 12 14 9 4 9 10 6 , 2 2 3 12 14 9 13 4 5 8 0 0 0 1 -> 3 13 12 7 11 11 6 3 4 1 14 9 10 6 2 14 5 6 , 2 7 15 10 6 2 3 4 1 3 10 6 14 1 -> 2 7 15 13 4 9 10 11 8 1 3 12 3 13 12 7 6 2 , 3 4 5 11 11 15 13 10 15 4 0 5 11 6 -> 7 11 15 13 4 1 2 3 12 2 3 12 3 13 12 7 11 6 , 3 12 3 4 9 12 14 1 2 14 1 3 4 1 -> 14 0 1 2 7 11 6 2 14 0 5 11 11 11 11 11 15 12 , 3 13 10 6 7 15 13 4 9 13 13 13 4 1 -> 3 12 7 8 1 7 15 13 12 14 0 9 12 2 7 8 0 1 , 3 10 8 5 8 9 12 3 4 5 15 4 1 2 -> 3 12 7 11 8 9 13 12 7 15 4 9 13 13 12 3 12 2 , 3 10 6 14 1 14 0 1 2 14 1 3 12 2 -> 2 7 6 7 11 11 11 15 13 12 7 6 3 12 2 14 5 6 , 3 10 11 6 3 13 10 8 9 13 4 0 1 2 -> 3 10 6 3 13 12 2 7 6 7 11 11 11 8 5 8 0 1 , 3 10 11 6 3 13 10 15 10 6 2 14 1 2 -> 3 13 12 14 9 12 2 2 3 13 12 2 7 11 15 12 7 6 , 7 8 5 8 9 10 15 10 11 11 6 3 12 2 -> 3 12 3 12 7 15 12 7 15 12 3 12 7 6 7 11 6 2 , 7 8 5 8 9 10 11 15 10 15 13 13 12 2 -> 3 13 13 12 7 11 11 15 12 2 3 12 2 2 2 7 6 2 , 7 8 5 6 7 15 4 0 1 3 12 14 0 1 -> 7 6 7 8 5 11 15 13 12 2 3 13 13 12 2 14 9 12 , 7 6 3 10 6 2 7 6 2 7 8 1 2 2 -> 7 11 15 12 7 6 3 10 11 11 15 12 2 3 12 14 1 2 , 7 15 13 12 14 9 4 5 11 11 11 15 12 2 -> 7 11 11 15 10 6 2 7 11 15 12 3 12 3 12 7 6 2 , 7 15 10 8 1 2 7 8 0 0 0 9 12 2 -> 7 11 15 12 2 3 10 15 12 3 4 5 6 7 15 13 12 2 , 7 15 10 15 10 15 10 8 5 15 4 1 2 2 -> 3 13 12 2 3 12 7 11 15 4 0 0 0 0 1 7 11 6 , 7 11 6 7 6 3 10 15 4 9 13 4 0 1 -> 3 12 3 12 7 8 9 13 4 9 13 12 2 7 11 11 11 6 , 7 11 15 12 7 6 3 4 0 5 15 10 11 6 -> 7 15 12 7 15 13 12 7 11 11 6 14 9 12 7 11 11 6 , 7 6 3 4 1 14 5 15 4 1 3 4 0 1 ->= 7 6 2 3 12 14 1 2 3 13 12 3 12 7 8 9 10 6 , 7 11 11 6 3 12 3 13 10 8 0 0 5 6 ->= 7 11 11 6 3 12 2 3 12 2 14 5 11 15 13 4 5 6 , 14 0 0 0 0 1 2 3 4 0 5 6 7 15 -> 3 10 11 6 2 3 10 6 3 12 2 3 13 12 14 9 10 15 , 14 0 0 5 6 3 13 10 15 10 6 14 1 3 -> 7 15 12 7 8 1 7 6 2 3 12 7 11 11 11 6 7 15 , 14 0 5 8 1 2 3 12 14 1 7 11 11 15 -> 2 7 11 6 14 9 12 2 3 13 10 15 12 3 12 2 7 15 , 14 0 5 15 12 7 15 13 10 15 4 0 0 9 -> 2 3 12 7 15 10 15 13 10 11 6 14 0 9 12 7 11 15 , 14 5 8 1 7 6 7 15 13 12 3 13 4 9 -> 3 10 11 8 5 11 11 6 7 15 4 9 13 12 7 6 3 13 , 14 5 15 13 4 0 5 15 10 6 2 3 12 3 -> 3 4 5 11 6 3 4 5 6 3 12 3 12 2 14 5 6 3 , 14 5 11 11 8 1 3 10 6 2 14 0 5 15 -> 14 9 13 4 1 3 12 3 12 7 6 7 8 5 11 8 5 15 , 2 14 1 7 6 2 2 2 7 15 4 5 15 13 -> 7 11 11 6 7 11 8 1 14 1 3 12 3 12 2 14 5 15 , 2 14 5 15 10 11 8 0 1 3 12 14 1 3 -> 3 12 2 2 2 7 15 13 13 12 7 11 6 7 15 13 12 3 , 2 2 14 0 0 9 10 8 1 3 4 1 7 15 -> 2 3 13 13 12 7 11 15 12 2 3 12 14 9 4 9 10 15 , 2 2 3 12 14 9 13 4 5 8 0 0 0 9 -> 3 13 12 7 11 11 6 3 4 1 14 9 10 6 2 14 5 15 , 2 7 15 10 6 2 3 4 1 3 10 6 14 9 -> 2 7 15 13 4 9 10 11 8 1 3 12 3 13 12 7 6 3 , 3 4 5 11 11 15 13 10 15 4 0 5 11 15 -> 7 11 15 13 4 1 2 3 12 2 3 12 3 13 12 7 11 15 , 3 12 3 4 9 12 14 1 2 14 1 3 4 9 -> 14 0 1 2 7 11 6 2 14 0 5 11 11 11 11 11 15 13 , 3 13 10 6 7 15 13 4 9 13 13 13 4 9 -> 3 12 7 8 1 7 15 13 12 14 0 9 12 2 7 8 0 9 , 3 10 8 5 8 9 12 3 4 5 15 4 1 3 -> 3 12 7 11 8 9 13 12 7 15 4 9 13 13 12 3 12 3 , 3 10 6 14 1 14 0 1 2 14 1 3 12 3 -> 2 7 6 7 11 11 11 15 13 12 7 6 3 12 2 14 5 15 , 3 10 11 6 3 13 10 8 9 13 4 0 1 3 -> 3 10 6 3 13 12 2 7 6 7 11 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11 11 8 5 8 0 0 , 15 10 11 6 3 13 10 15 10 6 2 14 1 14 -> 15 13 12 14 9 12 2 2 3 13 12 2 7 11 15 12 7 8 , 11 8 5 8 9 10 15 10 11 11 6 3 12 14 -> 15 12 3 12 7 15 12 7 15 12 3 12 7 6 7 11 6 14 , 11 8 5 8 9 10 11 15 10 15 13 13 12 14 -> 15 13 13 12 7 11 11 15 12 2 3 12 2 2 2 7 6 14 , 11 8 5 6 7 15 4 0 1 3 12 14 0 0 -> 11 6 7 8 5 11 15 13 12 2 3 13 13 12 2 14 9 4 , 11 6 3 10 6 2 7 6 2 7 8 1 2 14 -> 11 11 15 12 7 6 3 10 11 11 15 12 2 3 12 14 1 14 , 11 15 13 12 14 9 4 5 11 11 11 15 12 14 -> 11 11 11 15 10 6 2 7 11 15 12 3 12 3 12 7 6 14 , 11 15 10 8 1 2 7 8 0 0 0 9 12 14 -> 11 11 15 12 2 3 10 15 12 3 4 5 6 7 15 13 12 14 , 11 15 10 15 10 15 10 8 5 15 4 1 2 14 -> 15 13 12 2 3 12 7 11 15 4 0 0 0 0 1 7 11 8 , 11 11 6 7 6 3 10 15 4 9 13 4 0 0 -> 15 12 3 12 7 8 9 13 4 9 13 12 2 7 11 11 11 8 , 11 11 15 12 7 6 3 4 0 5 15 10 11 8 -> 11 15 12 7 15 13 12 7 11 11 6 14 9 12 7 11 11 8 , 11 6 3 4 1 14 5 15 4 1 3 4 0 0 ->= 11 6 2 3 12 14 1 2 3 13 12 3 12 7 8 9 10 8 , 11 11 11 6 3 12 3 13 10 8 0 0 5 8 ->= 11 11 11 6 3 12 2 3 12 2 14 5 11 15 13 4 5 8 , 8 0 0 0 0 1 2 3 4 0 5 6 7 6 -> 15 10 11 6 2 3 10 6 3 12 2 3 13 12 14 9 10 6 , 8 0 0 5 6 3 13 10 15 10 6 14 1 2 -> 11 15 12 7 8 1 7 6 2 3 12 7 11 11 11 6 7 6 , 8 0 5 8 1 2 3 12 14 1 7 11 11 6 -> 6 7 11 6 14 9 12 2 3 13 10 15 12 3 12 2 7 6 , 8 0 5 15 12 7 15 13 10 15 4 0 0 1 -> 6 3 12 7 15 10 15 13 10 11 6 14 0 9 12 7 11 6 , 8 5 8 1 7 6 7 15 13 12 3 13 4 1 -> 15 10 11 8 5 11 11 6 7 15 4 9 13 12 7 6 3 12 , 8 5 15 13 4 0 5 15 10 6 2 3 12 2 -> 15 4 5 11 6 3 4 5 6 3 12 3 12 2 14 5 6 2 , 8 5 11 11 8 1 3 10 6 2 14 0 5 6 -> 8 9 13 4 1 3 12 3 12 7 6 7 8 5 11 8 5 6 , 6 14 1 7 6 2 2 2 7 15 4 5 15 12 -> 11 11 11 6 7 11 8 1 14 1 3 12 3 12 2 14 5 6 , 6 14 5 15 10 11 8 0 1 3 12 14 1 2 -> 15 12 2 2 2 7 15 13 13 12 7 11 6 7 15 13 12 2 , 6 2 14 0 0 9 10 8 1 3 4 1 7 6 -> 6 3 13 13 12 7 11 15 12 2 3 12 14 9 4 9 10 6 , 6 2 3 12 14 9 13 4 5 8 0 0 0 1 -> 15 13 12 7 11 11 6 3 4 1 14 9 10 6 2 14 5 6 , 6 7 15 10 6 2 3 4 1 3 10 6 14 1 -> 6 7 15 13 4 9 10 11 8 1 3 12 3 13 12 7 6 2 , 15 4 5 11 11 15 13 10 15 4 0 5 11 6 -> 11 11 15 13 4 1 2 3 12 2 3 12 3 13 12 7 11 6 , 15 12 3 4 9 12 14 1 2 14 1 3 4 1 -> 8 0 1 2 7 11 6 2 14 0 5 11 11 11 11 11 15 12 , 15 13 10 6 7 15 13 4 9 13 13 13 4 1 -> 15 12 7 8 1 7 15 13 12 14 0 9 12 2 7 8 0 1 , 15 10 8 5 8 9 12 3 4 5 15 4 1 2 -> 15 12 7 11 8 9 13 12 7 15 4 9 13 13 12 3 12 2 , 15 10 6 14 1 14 0 1 2 14 1 3 12 2 -> 6 7 6 7 11 11 11 15 13 12 7 6 3 12 2 14 5 6 , 15 10 11 6 3 13 10 8 9 13 4 0 1 2 -> 15 10 6 3 13 12 2 7 6 7 11 11 11 8 5 8 0 1 , 15 10 11 6 3 13 10 15 10 6 2 14 1 2 -> 15 13 12 14 9 12 2 2 3 13 12 2 7 11 15 12 7 6 , 11 8 5 8 9 10 15 10 11 11 6 3 12 2 -> 15 12 3 12 7 15 12 7 15 12 3 12 7 6 7 11 6 2 , 11 8 5 8 9 10 11 15 10 15 13 13 12 2 -> 15 13 13 12 7 11 11 15 12 2 3 12 2 2 2 7 6 2 , 11 8 5 6 7 15 4 0 1 3 12 14 0 1 -> 11 6 7 8 5 11 15 13 12 2 3 13 13 12 2 14 9 12 , 11 6 3 10 6 2 7 6 2 7 8 1 2 2 -> 11 11 15 12 7 6 3 10 11 11 15 12 2 3 12 14 1 2 , 11 15 13 12 14 9 4 5 11 11 11 15 12 2 -> 11 11 11 15 10 6 2 7 11 15 12 3 12 3 12 7 6 2 , 11 15 10 8 1 2 7 8 0 0 0 9 12 2 -> 11 11 15 12 2 3 10 15 12 3 4 5 6 7 15 13 12 2 , 11 15 10 15 10 15 10 8 5 15 4 1 2 2 -> 15 13 12 2 3 12 7 11 15 4 0 0 0 0 1 7 11 6 , 11 11 6 7 6 3 10 15 4 9 13 4 0 1 -> 15 12 3 12 7 8 9 13 4 9 13 12 2 7 11 11 11 6 , 11 11 15 12 7 6 3 4 0 5 15 10 11 6 -> 11 15 12 7 15 13 12 7 11 11 6 14 9 12 7 11 11 6 , 11 6 3 4 1 14 5 15 4 1 3 4 0 1 ->= 11 6 2 3 12 14 1 2 3 13 12 3 12 7 8 9 10 6 , 11 11 11 6 3 12 3 13 10 8 0 0 5 6 ->= 11 11 11 6 3 12 2 3 12 2 14 5 11 15 13 4 5 6 , 8 0 0 0 0 1 2 3 4 0 5 6 7 15 -> 15 10 11 6 2 3 10 6 3 12 2 3 13 12 14 9 10 15 , 8 0 0 5 6 3 13 10 15 10 6 14 1 3 -> 11 15 12 7 8 1 7 6 2 3 12 7 11 11 11 6 7 15 , 8 0 5 8 1 2 3 12 14 1 7 11 11 15 -> 6 7 11 6 14 9 12 2 3 13 10 15 12 3 12 2 7 15 , 8 0 5 15 12 7 15 13 10 15 4 0 0 9 -> 6 3 12 7 15 10 15 13 10 11 6 14 0 9 12 7 11 15 , 8 5 8 1 7 6 7 15 13 12 3 13 4 9 -> 15 10 11 8 5 11 11 6 7 15 4 9 13 12 7 6 3 13 , 8 5 15 13 4 0 5 15 10 6 2 3 12 3 -> 15 4 5 11 6 3 4 5 6 3 12 3 12 2 14 5 6 3 , 8 5 11 11 8 1 3 10 6 2 14 0 5 15 -> 8 9 13 4 1 3 12 3 12 7 6 7 8 5 11 8 5 15 , 6 14 1 7 6 2 2 2 7 15 4 5 15 13 -> 11 11 11 6 7 11 8 1 14 1 3 12 3 12 2 14 5 15 , 6 14 5 15 10 11 8 0 1 3 12 14 1 3 -> 15 12 2 2 2 7 15 13 13 12 7 11 6 7 15 13 12 3 , 6 2 14 0 0 9 10 8 1 3 4 1 7 15 -> 6 3 13 13 12 7 11 15 12 2 3 12 14 9 4 9 10 15 , 6 2 3 12 14 9 13 4 5 8 0 0 0 9 -> 15 13 12 7 11 11 6 3 4 1 14 9 10 6 2 14 5 15 , 6 7 15 10 6 2 3 4 1 3 10 6 14 9 -> 6 7 15 13 4 9 10 11 8 1 3 12 3 13 12 7 6 3 , 15 4 5 11 11 15 13 10 15 4 0 5 11 15 -> 11 11 15 13 4 1 2 3 12 2 3 12 3 13 12 7 11 15 , 15 12 3 4 9 12 14 1 2 14 1 3 4 9 -> 8 0 1 2 7 11 6 2 14 0 5 11 11 11 11 11 15 13 , 15 13 10 6 7 15 13 4 9 13 13 13 4 9 -> 15 12 7 8 1 7 15 13 12 14 0 9 12 2 7 8 0 9 , 15 10 8 5 8 9 12 3 4 5 15 4 1 3 -> 15 12 7 11 8 9 13 12 7 15 4 9 13 13 12 3 12 3 , 15 10 6 14 1 14 0 1 2 14 1 3 12 3 -> 6 7 6 7 11 11 11 15 13 12 7 6 3 12 2 14 5 15 , 15 10 11 6 3 13 10 8 9 13 4 0 1 3 -> 15 10 6 3 13 12 2 7 6 7 11 11 11 8 5 8 0 9 , 15 10 11 6 3 13 10 15 10 6 2 14 1 3 -> 15 13 12 14 9 12 2 2 3 13 12 2 7 11 15 12 7 15 , 11 8 5 8 9 10 15 10 11 11 6 3 12 3 -> 15 12 3 12 7 15 12 7 15 12 3 12 7 6 7 11 6 3 , 11 8 5 8 9 10 11 15 10 15 13 13 12 3 -> 15 13 13 12 7 11 11 15 12 2 3 12 2 2 2 7 6 3 , 11 8 5 6 7 15 4 0 1 3 12 14 0 9 -> 11 6 7 8 5 11 15 13 12 2 3 13 13 12 2 14 9 13 , 11 6 3 10 6 2 7 6 2 7 8 1 2 3 -> 11 11 15 12 7 6 3 10 11 11 15 12 2 3 12 14 1 3 , 11 15 13 12 14 9 4 5 11 11 11 15 12 3 -> 11 11 11 15 10 6 2 7 11 15 12 3 12 3 12 7 6 3 , 11 15 10 8 1 2 7 8 0 0 0 9 12 3 -> 11 11 15 12 2 3 10 15 12 3 4 5 6 7 15 13 12 3 , 11 15 10 15 10 15 10 8 5 15 4 1 2 3 -> 15 13 12 2 3 12 7 11 15 4 0 0 0 0 1 7 11 15 , 11 11 6 7 6 3 10 15 4 9 13 4 0 9 -> 15 12 3 12 7 8 9 13 4 9 13 12 2 7 11 11 11 15 , 11 11 15 12 7 6 3 4 0 5 15 10 11 15 -> 11 15 12 7 15 13 12 7 11 11 6 14 9 12 7 11 11 15 , 11 6 3 4 1 14 5 15 4 1 3 4 0 9 ->= 11 6 2 3 12 14 1 2 3 13 12 3 12 7 8 9 10 15 , 11 11 11 6 3 12 3 13 10 8 0 0 5 15 ->= 11 11 11 6 3 12 2 3 12 2 14 5 11 15 13 4 5 15 , 8 0 0 0 0 1 2 3 4 0 5 6 7 11 -> 15 10 11 6 2 3 10 6 3 12 2 3 13 12 14 9 10 11 , 8 0 0 5 6 3 13 10 15 10 6 14 1 7 -> 11 15 12 7 8 1 7 6 2 3 12 7 11 11 11 6 7 11 , 8 0 5 8 1 2 3 12 14 1 7 11 11 11 -> 6 7 11 6 14 9 12 2 3 13 10 15 12 3 12 2 7 11 , 8 0 5 15 12 7 15 13 10 15 4 0 0 5 -> 6 3 12 7 15 10 15 13 10 11 6 14 0 9 12 7 11 11 , 8 5 8 1 7 6 7 15 13 12 3 13 4 5 -> 15 10 11 8 5 11 11 6 7 15 4 9 13 12 7 6 3 10 , 8 5 15 13 4 0 5 15 10 6 2 3 12 7 -> 15 4 5 11 6 3 4 5 6 3 12 3 12 2 14 5 6 7 , 8 5 11 11 8 1 3 10 6 2 14 0 5 11 -> 8 9 13 4 1 3 12 3 12 7 6 7 8 5 11 8 5 11 , 6 14 1 7 6 2 2 2 7 15 4 5 15 10 -> 11 11 11 6 7 11 8 1 14 1 3 12 3 12 2 14 5 11 , 6 14 5 15 10 11 8 0 1 3 12 14 1 7 -> 15 12 2 2 2 7 15 13 13 12 7 11 6 7 15 13 12 7 , 6 2 14 0 0 9 10 8 1 3 4 1 7 11 -> 6 3 13 13 12 7 11 15 12 2 3 12 14 9 4 9 10 11 , 6 2 3 12 14 9 13 4 5 8 0 0 0 5 -> 15 13 12 7 11 11 6 3 4 1 14 9 10 6 2 14 5 11 , 6 7 15 10 6 2 3 4 1 3 10 6 14 5 -> 6 7 15 13 4 9 10 11 8 1 3 12 3 13 12 7 6 7 , 15 4 5 11 11 15 13 10 15 4 0 5 11 11 -> 11 11 15 13 4 1 2 3 12 2 3 12 3 13 12 7 11 11 , 15 12 3 4 9 12 14 1 2 14 1 3 4 5 -> 8 0 1 2 7 11 6 2 14 0 5 11 11 11 11 11 15 10 , 15 13 10 6 7 15 13 4 9 13 13 13 4 5 -> 15 12 7 8 1 7 15 13 12 14 0 9 12 2 7 8 0 5 , 15 10 8 5 8 9 12 3 4 5 15 4 1 7 -> 15 12 7 11 8 9 13 12 7 15 4 9 13 13 12 3 12 7 , 15 10 6 14 1 14 0 1 2 14 1 3 12 7 -> 6 7 6 7 11 11 11 15 13 12 7 6 3 12 2 14 5 11 , 15 10 11 6 3 13 10 8 9 13 4 0 1 7 -> 15 10 6 3 13 12 2 7 6 7 11 11 11 8 5 8 0 5 , 15 10 11 6 3 13 10 15 10 6 2 14 1 7 -> 15 13 12 14 9 12 2 2 3 13 12 2 7 11 15 12 7 11 , 11 8 5 8 9 10 15 10 11 11 6 3 12 7 -> 15 12 3 12 7 15 12 7 15 12 3 12 7 6 7 11 6 7 , 11 8 5 8 9 10 11 15 10 15 13 13 12 7 -> 15 13 13 12 7 11 11 15 12 2 3 12 2 2 2 7 6 7 , 11 8 5 6 7 15 4 0 1 3 12 14 0 5 -> 11 6 7 8 5 11 15 13 12 2 3 13 13 12 2 14 9 10 , 11 6 3 10 6 2 7 6 2 7 8 1 2 7 -> 11 11 15 12 7 6 3 10 11 11 15 12 2 3 12 14 1 7 , 11 15 13 12 14 9 4 5 11 11 11 15 12 7 -> 11 11 11 15 10 6 2 7 11 15 12 3 12 3 12 7 6 7 , 11 15 10 8 1 2 7 8 0 0 0 9 12 7 -> 11 11 15 12 2 3 10 15 12 3 4 5 6 7 15 13 12 7 , 11 15 10 15 10 15 10 8 5 15 4 1 2 7 -> 15 13 12 2 3 12 7 11 15 4 0 0 0 0 1 7 11 11 , 11 11 6 7 6 3 10 15 4 9 13 4 0 5 -> 15 12 3 12 7 8 9 13 4 9 13 12 2 7 11 11 11 11 , 11 11 15 12 7 6 3 4 0 5 15 10 11 11 -> 11 15 12 7 15 13 12 7 11 11 6 14 9 12 7 11 11 11 , 11 6 3 4 1 14 5 15 4 1 3 4 0 5 ->= 11 6 2 3 12 14 1 2 3 13 12 3 12 7 8 9 10 11 , 11 11 11 6 3 12 3 13 10 8 0 0 5 11 ->= 11 11 11 6 3 12 2 3 12 2 14 5 11 15 13 4 5 11 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 is interpreted by / \ | 1 27 | | 0 1 | \ / 1 is interpreted by / \ | 1 48 | | 0 1 | \ / 2 is interpreted by / \ | 1 13 | | 0 1 | \ / 3 is interpreted by / \ | 1 0 | | 0 1 | \ / 4 is interpreted by / \ | 1 44 | | 0 1 | \ / 5 is interpreted by / \ | 1 13 | | 0 1 | \ / 6 is interpreted by / \ | 1 0 | | 0 1 | \ / 7 is interpreted by / \ | 1 1 | | 0 1 | \ / 8 is interpreted by / \ | 1 8 | | 0 1 | \ / 9 is interpreted by / \ | 1 7 | | 0 1 | \ / 10 is interpreted by / \ | 1 30 | | 0 1 | \ / 11 is interpreted by / \ | 1 0 | | 0 1 | \ / 12 is interpreted by / \ | 1 0 | | 0 1 | \ / 13 is interpreted by / \ | 1 8 | | 0 1 | \ / 14 is interpreted by / \ | 1 0 | | 0 1 | \ / 15 is interpreted by / \ | 1 8 | | 0 1 | \ / After renaming modulo { }, it remains to prove termination of the 0-rule system { } The system is trivially terminating.