/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES After renaming modulo { c->0, a->1, b->2 }, it remains to prove termination of the 6-rule system { 0 0 0 -> 0 1 1 , 2 1 2 -> 2 2 0 , 0 1 1 -> 0 2 1 , 2 1 1 -> 1 2 0 , 2 2 0 -> 1 1 0 , 1 0 0 ->= 2 1 0 } Applying context closure of depth 1 in the following form: System R over Sigma maps to { fold(xly) -> fold(xry) | l -> r in R, x,y in Sigma } over Sigma^2, where fold(a_1...a_n) = (a_1,a_2)...(a_{n-1},a_{n}) After renaming modulo { [0, 0]->0, [0, 1]->1, [1, 1]->2, [1, 0]->3, [0, 2]->4, [2, 1]->5, [1, 2]->6, [2, 0]->7, [2, 2]->8 }, it remains to prove termination of the 54-rule system { 0 0 0 0 -> 0 1 2 3 , 4 5 6 7 -> 4 8 7 0 , 0 1 2 3 -> 0 4 5 3 , 4 5 2 3 -> 1 6 7 0 , 4 8 7 0 -> 1 2 3 0 , 1 3 0 0 ->= 4 5 3 0 , 0 0 0 1 -> 0 1 2 2 , 4 5 6 5 -> 4 8 7 1 , 0 1 2 2 -> 0 4 5 2 , 4 5 2 2 -> 1 6 7 1 , 4 8 7 1 -> 1 2 3 1 , 1 3 0 1 ->= 4 5 3 1 , 0 0 0 4 -> 0 1 2 6 , 4 5 6 8 -> 4 8 7 4 , 0 1 2 6 -> 0 4 5 6 , 4 5 2 6 -> 1 6 7 4 , 4 8 7 4 -> 1 2 3 4 , 1 3 0 4 ->= 4 5 3 4 , 3 0 0 0 -> 3 1 2 3 , 6 5 6 7 -> 6 8 7 0 , 3 1 2 3 -> 3 4 5 3 , 6 5 2 3 -> 2 6 7 0 , 6 8 7 0 -> 2 2 3 0 , 2 3 0 0 ->= 6 5 3 0 , 3 0 0 1 -> 3 1 2 2 , 6 5 6 5 -> 6 8 7 1 , 3 1 2 2 -> 3 4 5 2 , 6 5 2 2 -> 2 6 7 1 , 6 8 7 1 -> 2 2 3 1 , 2 3 0 1 ->= 6 5 3 1 , 3 0 0 4 -> 3 1 2 6 , 6 5 6 8 -> 6 8 7 4 , 3 1 2 6 -> 3 4 5 6 , 6 5 2 6 -> 2 6 7 4 , 6 8 7 4 -> 2 2 3 4 , 2 3 0 4 ->= 6 5 3 4 , 7 0 0 0 -> 7 1 2 3 , 8 5 6 7 -> 8 8 7 0 , 7 1 2 3 -> 7 4 5 3 , 8 5 2 3 -> 5 6 7 0 , 8 8 7 0 -> 5 2 3 0 , 5 3 0 0 ->= 8 5 3 0 , 7 0 0 1 -> 7 1 2 2 , 8 5 6 5 -> 8 8 7 1 , 7 1 2 2 -> 7 4 5 2 , 8 5 2 2 -> 5 6 7 1 , 8 8 7 1 -> 5 2 3 1 , 5 3 0 1 ->= 8 5 3 1 , 7 0 0 4 -> 7 1 2 6 , 8 5 6 8 -> 8 8 7 4 , 7 1 2 6 -> 7 4 5 6 , 8 5 2 6 -> 5 6 7 4 , 8 8 7 4 -> 5 2 3 4 , 5 3 0 4 ->= 8 5 3 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 is interpreted by / \ | 1 1 | | 0 1 | \ / 1 is interpreted by / \ | 1 0 | | 0 1 | \ / 2 is interpreted by / \ | 1 1 | | 0 1 | \ / 3 is interpreted by / \ | 1 0 | | 0 1 | \ / 4 is interpreted by / \ | 1 0 | | 0 1 | \ / 5 is interpreted by / \ | 1 1 | | 0 1 | \ / 6 is interpreted by / \ | 1 1 | | 0 1 | \ / 7 is interpreted by / \ | 1 0 | | 0 1 | \ / 8 is interpreted by / \ | 1 1 | | 0 1 | \ / After renaming modulo { 4->0, 5->1, 6->2, 7->3, 8->4, 0->5, 1->6, 2->7, 3->8 }, it remains to prove termination of the 39-rule system { 0 1 2 3 -> 0 4 3 5 , 5 6 7 8 -> 5 0 1 8 , 0 1 7 8 -> 6 2 3 5 , 0 4 3 5 -> 6 7 8 5 , 6 8 5 5 ->= 0 1 8 5 , 5 5 5 6 -> 5 6 7 7 , 5 6 7 7 -> 5 0 1 7 , 0 4 3 6 -> 6 7 8 6 , 6 8 5 6 ->= 0 1 8 6 , 5 5 5 0 -> 5 6 7 2 , 5 6 7 2 -> 5 0 1 2 , 0 4 3 0 -> 6 7 8 0 , 6 8 5 0 ->= 0 1 8 0 , 2 1 2 3 -> 2 4 3 5 , 8 6 7 8 -> 8 0 1 8 , 2 1 7 8 -> 7 2 3 5 , 2 4 3 5 -> 7 7 8 5 , 7 8 5 5 ->= 2 1 8 5 , 8 5 5 6 -> 8 6 7 7 , 8 6 7 7 -> 8 0 1 7 , 2 4 3 6 -> 7 7 8 6 , 7 8 5 6 ->= 2 1 8 6 , 8 5 5 0 -> 8 6 7 2 , 8 6 7 2 -> 8 0 1 2 , 2 4 3 0 -> 7 7 8 0 , 7 8 5 0 ->= 2 1 8 0 , 4 1 2 3 -> 4 4 3 5 , 3 6 7 8 -> 3 0 1 8 , 4 1 7 8 -> 1 2 3 5 , 4 4 3 5 -> 1 7 8 5 , 1 8 5 5 ->= 4 1 8 5 , 3 5 5 6 -> 3 6 7 7 , 3 6 7 7 -> 3 0 1 7 , 4 4 3 6 -> 1 7 8 6 , 1 8 5 6 ->= 4 1 8 6 , 3 5 5 0 -> 3 6 7 2 , 3 6 7 2 -> 3 0 1 2 , 4 4 3 0 -> 1 7 8 0 , 1 8 5 0 ->= 4 1 8 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 1 0 0 0 | \ / 6 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, it remains to prove termination of the 38-rule system { 0 1 2 3 -> 0 4 3 5 , 5 6 7 8 -> 5 0 1 8 , 0 1 7 8 -> 6 2 3 5 , 0 4 3 5 -> 6 7 8 5 , 5 5 5 6 -> 5 6 7 7 , 5 6 7 7 -> 5 0 1 7 , 0 4 3 6 -> 6 7 8 6 , 6 8 5 6 ->= 0 1 8 6 , 5 5 5 0 -> 5 6 7 2 , 5 6 7 2 -> 5 0 1 2 , 0 4 3 0 -> 6 7 8 0 , 6 8 5 0 ->= 0 1 8 0 , 2 1 2 3 -> 2 4 3 5 , 8 6 7 8 -> 8 0 1 8 , 2 1 7 8 -> 7 2 3 5 , 2 4 3 5 -> 7 7 8 5 , 7 8 5 5 ->= 2 1 8 5 , 8 5 5 6 -> 8 6 7 7 , 8 6 7 7 -> 8 0 1 7 , 2 4 3 6 -> 7 7 8 6 , 7 8 5 6 ->= 2 1 8 6 , 8 5 5 0 -> 8 6 7 2 , 8 6 7 2 -> 8 0 1 2 , 2 4 3 0 -> 7 7 8 0 , 7 8 5 0 ->= 2 1 8 0 , 4 1 2 3 -> 4 4 3 5 , 3 6 7 8 -> 3 0 1 8 , 4 1 7 8 -> 1 2 3 5 , 4 4 3 5 -> 1 7 8 5 , 1 8 5 5 ->= 4 1 8 5 , 3 5 5 6 -> 3 6 7 7 , 3 6 7 7 -> 3 0 1 7 , 4 4 3 6 -> 1 7 8 6 , 1 8 5 6 ->= 4 1 8 6 , 3 5 5 0 -> 3 6 7 2 , 3 6 7 2 -> 3 0 1 2 , 4 4 3 0 -> 1 7 8 0 , 1 8 5 0 ->= 4 1 8 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 11: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 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 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 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 | \ / 4 is interpreted by / \ | 1 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 1 0 0 2 0 0 | | 0 0 0 0 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 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 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 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, it remains to prove termination of the 37-rule system { 0 1 2 3 -> 0 4 3 5 , 5 6 7 8 -> 5 0 1 8 , 0 1 7 8 -> 6 2 3 5 , 0 4 3 5 -> 6 7 8 5 , 5 5 5 6 -> 5 6 7 7 , 5 6 7 7 -> 5 0 1 7 , 0 4 3 6 -> 6 7 8 6 , 6 8 5 6 ->= 0 1 8 6 , 5 5 5 0 -> 5 6 7 2 , 5 6 7 2 -> 5 0 1 2 , 0 4 3 0 -> 6 7 8 0 , 6 8 5 0 ->= 0 1 8 0 , 2 1 2 3 -> 2 4 3 5 , 8 6 7 8 -> 8 0 1 8 , 2 1 7 8 -> 7 2 3 5 , 2 4 3 5 -> 7 7 8 5 , 7 8 5 5 ->= 2 1 8 5 , 8 5 5 6 -> 8 6 7 7 , 8 6 7 7 -> 8 0 1 7 , 2 4 3 6 -> 7 7 8 6 , 7 8 5 6 ->= 2 1 8 6 , 8 5 5 0 -> 8 6 7 2 , 8 6 7 2 -> 8 0 1 2 , 2 4 3 0 -> 7 7 8 0 , 7 8 5 0 ->= 2 1 8 0 , 4 1 2 3 -> 4 4 3 5 , 3 6 7 8 -> 3 0 1 8 , 4 4 3 5 -> 1 7 8 5 , 1 8 5 5 ->= 4 1 8 5 , 3 5 5 6 -> 3 6 7 7 , 3 6 7 7 -> 3 0 1 7 , 4 4 3 6 -> 1 7 8 6 , 1 8 5 6 ->= 4 1 8 6 , 3 5 5 0 -> 3 6 7 2 , 3 6 7 2 -> 3 0 1 2 , 4 4 3 0 -> 1 7 8 0 , 1 8 5 0 ->= 4 1 8 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 4 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, it remains to prove termination of the 36-rule system { 0 1 2 3 -> 0 4 3 5 , 5 6 7 8 -> 5 0 1 8 , 0 1 7 8 -> 6 2 3 5 , 0 4 3 5 -> 6 7 8 5 , 5 5 5 6 -> 5 6 7 7 , 5 6 7 7 -> 5 0 1 7 , 0 4 3 6 -> 6 7 8 6 , 6 8 5 6 ->= 0 1 8 6 , 5 5 5 0 -> 5 6 7 2 , 5 6 7 2 -> 5 0 1 2 , 0 4 3 0 -> 6 7 8 0 , 6 8 5 0 ->= 0 1 8 0 , 2 1 2 3 -> 2 4 3 5 , 8 6 7 8 -> 8 0 1 8 , 2 1 7 8 -> 7 2 3 5 , 2 4 3 5 -> 7 7 8 5 , 7 8 5 5 ->= 2 1 8 5 , 8 5 5 6 -> 8 6 7 7 , 8 6 7 7 -> 8 0 1 7 , 2 4 3 6 -> 7 7 8 6 , 7 8 5 6 ->= 2 1 8 6 , 8 5 5 0 -> 8 6 7 2 , 8 6 7 2 -> 8 0 1 2 , 2 4 3 0 -> 7 7 8 0 , 7 8 5 0 ->= 2 1 8 0 , 3 6 7 8 -> 3 0 1 8 , 4 4 3 5 -> 1 7 8 5 , 1 8 5 5 ->= 4 1 8 5 , 3 5 5 6 -> 3 6 7 7 , 3 6 7 7 -> 3 0 1 7 , 4 4 3 6 -> 1 7 8 6 , 1 8 5 6 ->= 4 1 8 6 , 3 5 5 0 -> 3 6 7 2 , 3 6 7 2 -> 3 0 1 2 , 4 4 3 0 -> 1 7 8 0 , 1 8 5 0 ->= 4 1 8 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, it remains to prove termination of the 35-rule system { 0 1 2 3 -> 0 4 3 5 , 5 6 7 8 -> 5 0 1 8 , 0 1 7 8 -> 6 2 3 5 , 0 4 3 5 -> 6 7 8 5 , 5 5 5 6 -> 5 6 7 7 , 5 6 7 7 -> 5 0 1 7 , 0 4 3 6 -> 6 7 8 6 , 6 8 5 6 ->= 0 1 8 6 , 5 5 5 0 -> 5 6 7 2 , 5 6 7 2 -> 5 0 1 2 , 0 4 3 0 -> 6 7 8 0 , 6 8 5 0 ->= 0 1 8 0 , 2 1 2 3 -> 2 4 3 5 , 8 6 7 8 -> 8 0 1 8 , 2 1 7 8 -> 7 2 3 5 , 2 4 3 5 -> 7 7 8 5 , 7 8 5 5 ->= 2 1 8 5 , 8 5 5 6 -> 8 6 7 7 , 8 6 7 7 -> 8 0 1 7 , 2 4 3 6 -> 7 7 8 6 , 7 8 5 6 ->= 2 1 8 6 , 8 5 5 0 -> 8 6 7 2 , 8 6 7 2 -> 8 0 1 2 , 2 4 3 0 -> 7 7 8 0 , 7 8 5 0 ->= 2 1 8 0 , 3 6 7 8 -> 3 0 1 8 , 1 8 5 5 ->= 4 1 8 5 , 3 5 5 6 -> 3 6 7 7 , 3 6 7 7 -> 3 0 1 7 , 4 4 3 6 -> 1 7 8 6 , 1 8 5 6 ->= 4 1 8 6 , 3 5 5 0 -> 3 6 7 2 , 3 6 7 2 -> 3 0 1 2 , 4 4 3 0 -> 1 7 8 0 , 1 8 5 0 ->= 4 1 8 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 1 0 0 0 | \ / 6 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, it remains to prove termination of the 33-rule system { 0 1 2 3 -> 0 4 3 5 , 5 6 7 8 -> 5 0 1 8 , 0 1 7 8 -> 6 2 3 5 , 0 4 3 5 -> 6 7 8 5 , 5 5 5 6 -> 5 6 7 7 , 5 6 7 7 -> 5 0 1 7 , 0 4 3 6 -> 6 7 8 6 , 5 5 5 0 -> 5 6 7 2 , 5 6 7 2 -> 5 0 1 2 , 0 4 3 0 -> 6 7 8 0 , 2 1 2 3 -> 2 4 3 5 , 8 6 7 8 -> 8 0 1 8 , 2 1 7 8 -> 7 2 3 5 , 2 4 3 5 -> 7 7 8 5 , 7 8 5 5 ->= 2 1 8 5 , 8 5 5 6 -> 8 6 7 7 , 8 6 7 7 -> 8 0 1 7 , 2 4 3 6 -> 7 7 8 6 , 7 8 5 6 ->= 2 1 8 6 , 8 5 5 0 -> 8 6 7 2 , 8 6 7 2 -> 8 0 1 2 , 2 4 3 0 -> 7 7 8 0 , 7 8 5 0 ->= 2 1 8 0 , 3 6 7 8 -> 3 0 1 8 , 1 8 5 5 ->= 4 1 8 5 , 3 5 5 6 -> 3 6 7 7 , 3 6 7 7 -> 3 0 1 7 , 4 4 3 6 -> 1 7 8 6 , 1 8 5 6 ->= 4 1 8 6 , 3 5 5 0 -> 3 6 7 2 , 3 6 7 2 -> 3 0 1 2 , 4 4 3 0 -> 1 7 8 0 , 1 8 5 0 ->= 4 1 8 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, it remains to prove termination of the 31-rule system { 0 1 2 3 -> 0 4 3 5 , 5 6 7 8 -> 5 0 1 8 , 0 1 7 8 -> 6 2 3 5 , 0 4 3 5 -> 6 7 8 5 , 5 5 5 6 -> 5 6 7 7 , 5 6 7 7 -> 5 0 1 7 , 0 4 3 6 -> 6 7 8 6 , 5 5 5 0 -> 5 6 7 2 , 5 6 7 2 -> 5 0 1 2 , 0 4 3 0 -> 6 7 8 0 , 2 1 2 3 -> 2 4 3 5 , 8 6 7 8 -> 8 0 1 8 , 2 1 7 8 -> 7 2 3 5 , 2 4 3 5 -> 7 7 8 5 , 7 8 5 5 ->= 2 1 8 5 , 8 5 5 6 -> 8 6 7 7 , 8 6 7 7 -> 8 0 1 7 , 2 4 3 6 -> 7 7 8 6 , 7 8 5 6 ->= 2 1 8 6 , 8 5 5 0 -> 8 6 7 2 , 8 6 7 2 -> 8 0 1 2 , 2 4 3 0 -> 7 7 8 0 , 7 8 5 0 ->= 2 1 8 0 , 3 6 7 8 -> 3 0 1 8 , 1 8 5 5 ->= 4 1 8 5 , 3 5 5 6 -> 3 6 7 7 , 3 6 7 7 -> 3 0 1 7 , 1 8 5 6 ->= 4 1 8 6 , 3 5 5 0 -> 3 6 7 2 , 3 6 7 2 -> 3 0 1 2 , 1 8 5 0 ->= 4 1 8 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 11: 0 is interpreted by / \ | 1 0 1 0 2 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 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 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 1 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 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 1 | | 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 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 | \ / After renaming modulo { 5->0, 6->1, 7->2, 8->3, 0->4, 1->5, 2->6, 3->7, 4->8 }, it remains to prove termination of the 30-rule system { 0 1 2 3 -> 0 4 5 3 , 4 5 2 3 -> 1 6 7 0 , 4 8 7 0 -> 1 2 3 0 , 0 0 0 1 -> 0 1 2 2 , 0 1 2 2 -> 0 4 5 2 , 4 8 7 1 -> 1 2 3 1 , 0 0 0 4 -> 0 1 2 6 , 0 1 2 6 -> 0 4 5 6 , 4 8 7 4 -> 1 2 3 4 , 6 5 6 7 -> 6 8 7 0 , 3 1 2 3 -> 3 4 5 3 , 6 5 2 3 -> 2 6 7 0 , 6 8 7 0 -> 2 2 3 0 , 2 3 0 0 ->= 6 5 3 0 , 3 0 0 1 -> 3 1 2 2 , 3 1 2 2 -> 3 4 5 2 , 6 8 7 1 -> 2 2 3 1 , 2 3 0 1 ->= 6 5 3 1 , 3 0 0 4 -> 3 1 2 6 , 3 1 2 6 -> 3 4 5 6 , 6 8 7 4 -> 2 2 3 4 , 2 3 0 4 ->= 6 5 3 4 , 7 1 2 3 -> 7 4 5 3 , 5 3 0 0 ->= 8 5 3 0 , 7 0 0 1 -> 7 1 2 2 , 7 1 2 2 -> 7 4 5 2 , 5 3 0 1 ->= 8 5 3 1 , 7 0 0 4 -> 7 1 2 6 , 7 1 2 6 -> 7 4 5 6 , 5 3 0 4 ->= 8 5 3 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, it remains to prove termination of the 29-rule system { 0 1 2 3 -> 0 4 5 3 , 4 5 2 3 -> 1 6 7 0 , 0 0 0 1 -> 0 1 2 2 , 0 1 2 2 -> 0 4 5 2 , 4 8 7 1 -> 1 2 3 1 , 0 0 0 4 -> 0 1 2 6 , 0 1 2 6 -> 0 4 5 6 , 4 8 7 4 -> 1 2 3 4 , 6 5 6 7 -> 6 8 7 0 , 3 1 2 3 -> 3 4 5 3 , 6 5 2 3 -> 2 6 7 0 , 6 8 7 0 -> 2 2 3 0 , 2 3 0 0 ->= 6 5 3 0 , 3 0 0 1 -> 3 1 2 2 , 3 1 2 2 -> 3 4 5 2 , 6 8 7 1 -> 2 2 3 1 , 2 3 0 1 ->= 6 5 3 1 , 3 0 0 4 -> 3 1 2 6 , 3 1 2 6 -> 3 4 5 6 , 6 8 7 4 -> 2 2 3 4 , 2 3 0 4 ->= 6 5 3 4 , 7 1 2 3 -> 7 4 5 3 , 5 3 0 0 ->= 8 5 3 0 , 7 0 0 1 -> 7 1 2 2 , 7 1 2 2 -> 7 4 5 2 , 5 3 0 1 ->= 8 5 3 1 , 7 0 0 4 -> 7 1 2 6 , 7 1 2 6 -> 7 4 5 6 , 5 3 0 4 ->= 8 5 3 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, it remains to prove termination of the 27-rule system { 0 1 2 3 -> 0 4 5 3 , 4 5 2 3 -> 1 6 7 0 , 0 0 0 1 -> 0 1 2 2 , 0 1 2 2 -> 0 4 5 2 , 0 0 0 4 -> 0 1 2 6 , 0 1 2 6 -> 0 4 5 6 , 6 5 6 7 -> 6 8 7 0 , 3 1 2 3 -> 3 4 5 3 , 6 5 2 3 -> 2 6 7 0 , 6 8 7 0 -> 2 2 3 0 , 2 3 0 0 ->= 6 5 3 0 , 3 0 0 1 -> 3 1 2 2 , 3 1 2 2 -> 3 4 5 2 , 6 8 7 1 -> 2 2 3 1 , 2 3 0 1 ->= 6 5 3 1 , 3 0 0 4 -> 3 1 2 6 , 3 1 2 6 -> 3 4 5 6 , 6 8 7 4 -> 2 2 3 4 , 2 3 0 4 ->= 6 5 3 4 , 7 1 2 3 -> 7 4 5 3 , 5 3 0 0 ->= 8 5 3 0 , 7 0 0 1 -> 7 1 2 2 , 7 1 2 2 -> 7 4 5 2 , 5 3 0 1 ->= 8 5 3 1 , 7 0 0 4 -> 7 1 2 6 , 7 1 2 6 -> 7 4 5 6 , 5 3 0 4 ->= 8 5 3 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, it remains to prove termination of the 26-rule system { 0 1 2 3 -> 0 4 5 3 , 4 5 2 3 -> 1 6 7 0 , 0 0 0 1 -> 0 1 2 2 , 0 1 2 2 -> 0 4 5 2 , 0 0 0 4 -> 0 1 2 6 , 0 1 2 6 -> 0 4 5 6 , 6 5 6 7 -> 6 8 7 0 , 3 1 2 3 -> 3 4 5 3 , 6 5 2 3 -> 2 6 7 0 , 6 8 7 0 -> 2 2 3 0 , 2 3 0 0 ->= 6 5 3 0 , 3 0 0 1 -> 3 1 2 2 , 3 1 2 2 -> 3 4 5 2 , 6 8 7 1 -> 2 2 3 1 , 2 3 0 1 ->= 6 5 3 1 , 3 0 0 4 -> 3 1 2 6 , 3 1 2 6 -> 3 4 5 6 , 6 8 7 4 -> 2 2 3 4 , 2 3 0 4 ->= 6 5 3 4 , 5 3 0 0 ->= 8 5 3 0 , 7 0 0 1 -> 7 1 2 2 , 7 1 2 2 -> 7 4 5 2 , 5 3 0 1 ->= 8 5 3 1 , 7 0 0 4 -> 7 1 2 6 , 7 1 2 6 -> 7 4 5 6 , 5 3 0 4 ->= 8 5 3 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / After renaming modulo { 4->0, 5->1, 2->2, 3->3, 1->4, 6->5, 7->6, 0->7, 8->8 }, it remains to prove termination of the 24-rule system { 0 1 2 3 -> 4 5 6 7 , 7 7 7 4 -> 7 4 2 2 , 7 4 2 2 -> 7 0 1 2 , 7 7 7 0 -> 7 4 2 5 , 7 4 2 5 -> 7 0 1 5 , 5 1 5 6 -> 5 8 6 7 , 5 1 2 3 -> 2 5 6 7 , 5 8 6 7 -> 2 2 3 7 , 2 3 7 7 ->= 5 1 3 7 , 3 7 7 4 -> 3 4 2 2 , 3 4 2 2 -> 3 0 1 2 , 5 8 6 4 -> 2 2 3 4 , 2 3 7 4 ->= 5 1 3 4 , 3 7 7 0 -> 3 4 2 5 , 3 4 2 5 -> 3 0 1 5 , 5 8 6 0 -> 2 2 3 0 , 2 3 7 0 ->= 5 1 3 0 , 1 3 7 7 ->= 8 1 3 7 , 6 7 7 4 -> 6 4 2 2 , 6 4 2 2 -> 6 0 1 2 , 1 3 7 4 ->= 8 1 3 4 , 6 7 7 0 -> 6 4 2 5 , 6 4 2 5 -> 6 0 1 5 , 1 3 7 0 ->= 8 1 3 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 11: 0 is interpreted by / \ | 1 0 1 0 2 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 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 1 | | 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 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 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 1 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 | \ / 5 is interpreted by / \ | 1 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 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 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 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, it remains to prove termination of the 23-rule system { 0 1 2 3 -> 4 5 6 7 , 7 7 7 4 -> 7 4 2 2 , 7 4 2 2 -> 7 0 1 2 , 7 7 7 0 -> 7 4 2 5 , 7 4 2 5 -> 7 0 1 5 , 5 1 2 3 -> 2 5 6 7 , 5 8 6 7 -> 2 2 3 7 , 2 3 7 7 ->= 5 1 3 7 , 3 7 7 4 -> 3 4 2 2 , 3 4 2 2 -> 3 0 1 2 , 5 8 6 4 -> 2 2 3 4 , 2 3 7 4 ->= 5 1 3 4 , 3 7 7 0 -> 3 4 2 5 , 3 4 2 5 -> 3 0 1 5 , 5 8 6 0 -> 2 2 3 0 , 2 3 7 0 ->= 5 1 3 0 , 1 3 7 7 ->= 8 1 3 7 , 6 7 7 4 -> 6 4 2 2 , 6 4 2 2 -> 6 0 1 2 , 1 3 7 4 ->= 8 1 3 4 , 6 7 7 0 -> 6 4 2 5 , 6 4 2 5 -> 6 0 1 5 , 1 3 7 0 ->= 8 1 3 0 } 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 0 | | 0 1 | \ / 1 is interpreted by / \ | 1 1 | | 0 1 | \ / 2 is interpreted by / \ | 1 0 | | 0 1 | \ / 3 is interpreted by / \ | 1 2 | | 0 1 | \ / 4 is interpreted by / \ | 1 1 | | 0 1 | \ / 5 is interpreted by / \ | 1 0 | | 0 1 | \ / 6 is interpreted by / \ | 1 0 | | 0 1 | \ / 7 is interpreted by / \ | 1 2 | | 0 1 | \ / 8 is interpreted by / \ | 1 2 | | 0 1 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, it remains to prove termination of the 13-rule system { 0 1 2 3 -> 4 5 6 7 , 7 4 2 2 -> 7 0 1 2 , 7 4 2 5 -> 7 0 1 5 , 5 8 6 7 -> 2 2 3 7 , 3 4 2 2 -> 3 0 1 2 , 5 8 6 4 -> 2 2 3 4 , 3 4 2 5 -> 3 0 1 5 , 5 8 6 0 -> 2 2 3 0 , 1 3 7 7 ->= 8 1 3 7 , 6 4 2 2 -> 6 0 1 2 , 1 3 7 4 ->= 8 1 3 4 , 6 4 2 5 -> 6 0 1 5 , 1 3 7 0 ->= 8 1 3 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, it remains to prove termination of the 12-rule system { 0 1 2 3 -> 4 5 6 7 , 7 4 2 2 -> 7 0 1 2 , 7 4 2 5 -> 7 0 1 5 , 3 4 2 2 -> 3 0 1 2 , 5 8 6 4 -> 2 2 3 4 , 3 4 2 5 -> 3 0 1 5 , 5 8 6 0 -> 2 2 3 0 , 1 3 7 7 ->= 8 1 3 7 , 6 4 2 2 -> 6 0 1 2 , 1 3 7 4 ->= 8 1 3 4 , 6 4 2 5 -> 6 0 1 5 , 1 3 7 0 ->= 8 1 3 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 6 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, it remains to prove termination of the 11-rule system { 0 1 2 3 -> 4 5 6 7 , 7 4 2 2 -> 7 0 1 2 , 7 4 2 5 -> 7 0 1 5 , 3 4 2 2 -> 3 0 1 2 , 5 8 6 4 -> 2 2 3 4 , 3 4 2 5 -> 3 0 1 5 , 5 8 6 0 -> 2 2 3 0 , 1 3 7 7 ->= 8 1 3 7 , 6 4 2 2 -> 6 0 1 2 , 1 3 7 4 ->= 8 1 3 4 , 1 3 7 0 ->= 8 1 3 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 5 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, it remains to prove termination of the 9-rule system { 0 1 2 3 -> 4 5 6 7 , 7 4 2 2 -> 7 0 1 2 , 7 4 2 5 -> 7 0 1 5 , 3 4 2 2 -> 3 0 1 2 , 3 4 2 5 -> 3 0 1 5 , 1 3 7 7 ->= 8 1 3 7 , 6 4 2 2 -> 6 0 1 2 , 1 3 7 4 ->= 8 1 3 4 , 1 3 7 0 ->= 8 1 3 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 is interpreted by / \ | 1 1 | | 0 1 | \ / 1 is interpreted by / \ | 1 1 | | 0 1 | \ / 2 is interpreted by / \ | 1 1 | | 0 1 | \ / 3 is interpreted by / \ | 1 1 | | 0 1 | \ / 4 is interpreted by / \ | 1 1 | | 0 1 | \ / 5 is interpreted by / \ | 1 0 | | 0 1 | \ / 6 is interpreted by / \ | 1 0 | | 0 1 | \ / 7 is interpreted by / \ | 1 1 | | 0 1 | \ / 8 is interpreted by / \ | 1 0 | | 0 1 | \ / After renaming modulo { 7->0, 4->1, 2->2, 0->3, 1->4, 5->5, 3->6, 6->7 }, it remains to prove termination of the 5-rule system { 0 1 2 2 -> 0 3 4 2 , 0 1 2 5 -> 0 3 4 5 , 6 1 2 2 -> 6 3 4 2 , 6 1 2 5 -> 6 3 4 5 , 7 1 2 2 -> 7 3 4 2 } 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 0 | | 0 1 | \ / 1 is interpreted by / \ | 1 1 | | 0 1 | \ / 2 is interpreted by / \ | 1 1 | | 0 1 | \ / 3 is interpreted by / \ | 1 0 | | 0 1 | \ / 4 is interpreted by / \ | 1 0 | | 0 1 | \ / 5 is interpreted by / \ | 1 0 | | 0 1 | \ / 6 is interpreted by / \ | 1 0 | | 0 1 | \ / 7 is interpreted by / \ | 1 0 | | 0 1 | \ / After renaming modulo { }, it remains to prove termination of the 0-rule system { } The system is trivially terminating.