/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES After renaming modulo { c->0, a->1, b->2 }, it remains to prove termination of the 6-rule system { 0 1 1 -> 0 0 2 , 0 1 2 -> 0 2 1 , 2 2 1 -> 2 2 0 , 2 0 2 -> 1 1 1 , 0 1 1 ->= 1 2 1 , 1 2 0 ->= 1 1 0 } The length-preserving system was inverted. After renaming modulo { 0->0, 2->1, 1->2 }, it remains to prove termination of the 6-rule system { 0 0 1 -> 0 2 2 , 0 1 2 -> 0 2 1 , 1 1 0 -> 1 1 2 , 2 2 2 -> 1 0 1 , 2 1 2 ->= 0 2 2 , 2 2 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, 0]->2, [0, 2]->3, [2, 2]->4, [2, 0]->5, [1, 2]->6, [2, 1]->7, [1, 1]->8 }, it remains to prove termination of the 54-rule system { 0 0 1 2 -> 0 3 4 5 , 0 1 6 5 -> 0 3 7 2 , 1 8 2 0 -> 1 8 6 5 , 3 4 4 5 -> 1 2 1 2 , 3 7 6 5 ->= 0 3 4 5 , 3 4 5 0 ->= 3 7 2 0 , 0 0 1 8 -> 0 3 4 7 , 0 1 6 7 -> 0 3 7 8 , 1 8 2 1 -> 1 8 6 7 , 3 4 4 7 -> 1 2 1 8 , 3 7 6 7 ->= 0 3 4 7 , 3 4 5 1 ->= 3 7 2 1 , 0 0 1 6 -> 0 3 4 4 , 0 1 6 4 -> 0 3 7 6 , 1 8 2 3 -> 1 8 6 4 , 3 4 4 4 -> 1 2 1 6 , 3 7 6 4 ->= 0 3 4 4 , 3 4 5 3 ->= 3 7 2 3 , 2 0 1 2 -> 2 3 4 5 , 2 1 6 5 -> 2 3 7 2 , 8 8 2 0 -> 8 8 6 5 , 6 4 4 5 -> 8 2 1 2 , 6 7 6 5 ->= 2 3 4 5 , 6 4 5 0 ->= 6 7 2 0 , 2 0 1 8 -> 2 3 4 7 , 2 1 6 7 -> 2 3 7 8 , 8 8 2 1 -> 8 8 6 7 , 6 4 4 7 -> 8 2 1 8 , 6 7 6 7 ->= 2 3 4 7 , 6 4 5 1 ->= 6 7 2 1 , 2 0 1 6 -> 2 3 4 4 , 2 1 6 4 -> 2 3 7 6 , 8 8 2 3 -> 8 8 6 4 , 6 4 4 4 -> 8 2 1 6 , 6 7 6 4 ->= 2 3 4 4 , 6 4 5 3 ->= 6 7 2 3 , 5 0 1 2 -> 5 3 4 5 , 5 1 6 5 -> 5 3 7 2 , 7 8 2 0 -> 7 8 6 5 , 4 4 4 5 -> 7 2 1 2 , 4 7 6 5 ->= 5 3 4 5 , 4 4 5 0 ->= 4 7 2 0 , 5 0 1 8 -> 5 3 4 7 , 5 1 6 7 -> 5 3 7 8 , 7 8 2 1 -> 7 8 6 7 , 4 4 4 7 -> 7 2 1 8 , 4 7 6 7 ->= 5 3 4 7 , 4 4 5 1 ->= 4 7 2 1 , 5 0 1 6 -> 5 3 4 4 , 5 1 6 4 -> 5 3 7 6 , 7 8 2 3 -> 7 8 6 4 , 4 4 4 4 -> 7 2 1 6 , 4 7 6 4 ->= 5 3 4 4 , 4 4 5 3 ->= 4 7 2 3 } 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 1 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 1 | | 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 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 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 53-rule system { 0 0 1 2 -> 0 3 4 5 , 0 1 6 5 -> 0 3 7 2 , 1 8 2 0 -> 1 8 6 5 , 3 4 4 5 -> 1 2 1 2 , 3 7 6 5 ->= 0 3 4 5 , 3 4 5 0 ->= 3 7 2 0 , 0 0 1 8 -> 0 3 4 7 , 0 1 6 7 -> 0 3 7 8 , 1 8 2 1 -> 1 8 6 7 , 3 4 4 7 -> 1 2 1 8 , 3 7 6 7 ->= 0 3 4 7 , 3 4 5 1 ->= 3 7 2 1 , 0 1 6 4 -> 0 3 7 6 , 1 8 2 3 -> 1 8 6 4 , 3 4 4 4 -> 1 2 1 6 , 3 7 6 4 ->= 0 3 4 4 , 3 4 5 3 ->= 3 7 2 3 , 2 0 1 2 -> 2 3 4 5 , 2 1 6 5 -> 2 3 7 2 , 8 8 2 0 -> 8 8 6 5 , 6 4 4 5 -> 8 2 1 2 , 6 7 6 5 ->= 2 3 4 5 , 6 4 5 0 ->= 6 7 2 0 , 2 0 1 8 -> 2 3 4 7 , 2 1 6 7 -> 2 3 7 8 , 8 8 2 1 -> 8 8 6 7 , 6 4 4 7 -> 8 2 1 8 , 6 7 6 7 ->= 2 3 4 7 , 6 4 5 1 ->= 6 7 2 1 , 2 0 1 6 -> 2 3 4 4 , 2 1 6 4 -> 2 3 7 6 , 8 8 2 3 -> 8 8 6 4 , 6 4 4 4 -> 8 2 1 6 , 6 7 6 4 ->= 2 3 4 4 , 6 4 5 3 ->= 6 7 2 3 , 5 0 1 2 -> 5 3 4 5 , 5 1 6 5 -> 5 3 7 2 , 7 8 2 0 -> 7 8 6 5 , 4 4 4 5 -> 7 2 1 2 , 4 7 6 5 ->= 5 3 4 5 , 4 4 5 0 ->= 4 7 2 0 , 5 0 1 8 -> 5 3 4 7 , 5 1 6 7 -> 5 3 7 8 , 7 8 2 1 -> 7 8 6 7 , 4 4 4 7 -> 7 2 1 8 , 4 7 6 7 ->= 5 3 4 7 , 4 4 5 1 ->= 4 7 2 1 , 5 0 1 6 -> 5 3 4 4 , 5 1 6 4 -> 5 3 7 6 , 7 8 2 3 -> 7 8 6 4 , 4 4 4 4 -> 7 2 1 6 , 4 7 6 4 ->= 5 3 4 4 , 4 4 5 3 ->= 4 7 2 3 } 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 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 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 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 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 52-rule system { 0 0 1 2 -> 0 3 4 5 , 0 1 6 5 -> 0 3 7 2 , 1 8 2 0 -> 1 8 6 5 , 3 4 4 5 -> 1 2 1 2 , 3 7 6 5 ->= 0 3 4 5 , 3 4 5 0 ->= 3 7 2 0 , 0 0 1 8 -> 0 3 4 7 , 0 1 6 7 -> 0 3 7 8 , 1 8 2 1 -> 1 8 6 7 , 3 4 4 7 -> 1 2 1 8 , 3 7 6 7 ->= 0 3 4 7 , 3 4 5 1 ->= 3 7 2 1 , 1 8 2 3 -> 1 8 6 4 , 3 4 4 4 -> 1 2 1 6 , 3 7 6 4 ->= 0 3 4 4 , 3 4 5 3 ->= 3 7 2 3 , 2 0 1 2 -> 2 3 4 5 , 2 1 6 5 -> 2 3 7 2 , 8 8 2 0 -> 8 8 6 5 , 6 4 4 5 -> 8 2 1 2 , 6 7 6 5 ->= 2 3 4 5 , 6 4 5 0 ->= 6 7 2 0 , 2 0 1 8 -> 2 3 4 7 , 2 1 6 7 -> 2 3 7 8 , 8 8 2 1 -> 8 8 6 7 , 6 4 4 7 -> 8 2 1 8 , 6 7 6 7 ->= 2 3 4 7 , 6 4 5 1 ->= 6 7 2 1 , 2 0 1 6 -> 2 3 4 4 , 2 1 6 4 -> 2 3 7 6 , 8 8 2 3 -> 8 8 6 4 , 6 4 4 4 -> 8 2 1 6 , 6 7 6 4 ->= 2 3 4 4 , 6 4 5 3 ->= 6 7 2 3 , 5 0 1 2 -> 5 3 4 5 , 5 1 6 5 -> 5 3 7 2 , 7 8 2 0 -> 7 8 6 5 , 4 4 4 5 -> 7 2 1 2 , 4 7 6 5 ->= 5 3 4 5 , 4 4 5 0 ->= 4 7 2 0 , 5 0 1 8 -> 5 3 4 7 , 5 1 6 7 -> 5 3 7 8 , 7 8 2 1 -> 7 8 6 7 , 4 4 4 7 -> 7 2 1 8 , 4 7 6 7 ->= 5 3 4 7 , 4 4 5 1 ->= 4 7 2 1 , 5 0 1 6 -> 5 3 4 4 , 5 1 6 4 -> 5 3 7 6 , 7 8 2 3 -> 7 8 6 4 , 4 4 4 4 -> 7 2 1 6 , 4 7 6 4 ->= 5 3 4 4 , 4 4 5 3 ->= 4 7 2 3 } 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 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 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 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 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, 8->6, 6->7, 7->8 }, it remains to prove termination of the 51-rule system { 0 0 1 2 -> 0 3 4 5 , 1 6 2 0 -> 1 6 7 5 , 3 4 4 5 -> 1 2 1 2 , 3 8 7 5 ->= 0 3 4 5 , 3 4 5 0 ->= 3 8 2 0 , 0 0 1 6 -> 0 3 4 8 , 0 1 7 8 -> 0 3 8 6 , 1 6 2 1 -> 1 6 7 8 , 3 4 4 8 -> 1 2 1 6 , 3 8 7 8 ->= 0 3 4 8 , 3 4 5 1 ->= 3 8 2 1 , 1 6 2 3 -> 1 6 7 4 , 3 4 4 4 -> 1 2 1 7 , 3 8 7 4 ->= 0 3 4 4 , 3 4 5 3 ->= 3 8 2 3 , 2 0 1 2 -> 2 3 4 5 , 2 1 7 5 -> 2 3 8 2 , 6 6 2 0 -> 6 6 7 5 , 7 4 4 5 -> 6 2 1 2 , 7 8 7 5 ->= 2 3 4 5 , 7 4 5 0 ->= 7 8 2 0 , 2 0 1 6 -> 2 3 4 8 , 2 1 7 8 -> 2 3 8 6 , 6 6 2 1 -> 6 6 7 8 , 7 4 4 8 -> 6 2 1 6 , 7 8 7 8 ->= 2 3 4 8 , 7 4 5 1 ->= 7 8 2 1 , 2 0 1 7 -> 2 3 4 4 , 2 1 7 4 -> 2 3 8 7 , 6 6 2 3 -> 6 6 7 4 , 7 4 4 4 -> 6 2 1 7 , 7 8 7 4 ->= 2 3 4 4 , 7 4 5 3 ->= 7 8 2 3 , 5 0 1 2 -> 5 3 4 5 , 5 1 7 5 -> 5 3 8 2 , 8 6 2 0 -> 8 6 7 5 , 4 4 4 5 -> 8 2 1 2 , 4 8 7 5 ->= 5 3 4 5 , 4 4 5 0 ->= 4 8 2 0 , 5 0 1 6 -> 5 3 4 8 , 5 1 7 8 -> 5 3 8 6 , 8 6 2 1 -> 8 6 7 8 , 4 4 4 8 -> 8 2 1 6 , 4 8 7 8 ->= 5 3 4 8 , 4 4 5 1 ->= 4 8 2 1 , 5 0 1 7 -> 5 3 4 4 , 5 1 7 4 -> 5 3 8 7 , 8 6 2 3 -> 8 6 7 4 , 4 4 4 4 -> 8 2 1 7 , 4 8 7 4 ->= 5 3 4 4 , 4 4 5 3 ->= 4 8 2 3 } 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 1 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 1 | | 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 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 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 1 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 50-rule system { 0 0 1 2 -> 0 3 4 5 , 1 6 2 0 -> 1 6 7 5 , 3 4 4 5 -> 1 2 1 2 , 3 8 7 5 ->= 0 3 4 5 , 3 4 5 0 ->= 3 8 2 0 , 0 1 7 8 -> 0 3 8 6 , 1 6 2 1 -> 1 6 7 8 , 3 4 4 8 -> 1 2 1 6 , 3 8 7 8 ->= 0 3 4 8 , 3 4 5 1 ->= 3 8 2 1 , 1 6 2 3 -> 1 6 7 4 , 3 4 4 4 -> 1 2 1 7 , 3 8 7 4 ->= 0 3 4 4 , 3 4 5 3 ->= 3 8 2 3 , 2 0 1 2 -> 2 3 4 5 , 2 1 7 5 -> 2 3 8 2 , 6 6 2 0 -> 6 6 7 5 , 7 4 4 5 -> 6 2 1 2 , 7 8 7 5 ->= 2 3 4 5 , 7 4 5 0 ->= 7 8 2 0 , 2 0 1 6 -> 2 3 4 8 , 2 1 7 8 -> 2 3 8 6 , 6 6 2 1 -> 6 6 7 8 , 7 4 4 8 -> 6 2 1 6 , 7 8 7 8 ->= 2 3 4 8 , 7 4 5 1 ->= 7 8 2 1 , 2 0 1 7 -> 2 3 4 4 , 2 1 7 4 -> 2 3 8 7 , 6 6 2 3 -> 6 6 7 4 , 7 4 4 4 -> 6 2 1 7 , 7 8 7 4 ->= 2 3 4 4 , 7 4 5 3 ->= 7 8 2 3 , 5 0 1 2 -> 5 3 4 5 , 5 1 7 5 -> 5 3 8 2 , 8 6 2 0 -> 8 6 7 5 , 4 4 4 5 -> 8 2 1 2 , 4 8 7 5 ->= 5 3 4 5 , 4 4 5 0 ->= 4 8 2 0 , 5 0 1 6 -> 5 3 4 8 , 5 1 7 8 -> 5 3 8 6 , 8 6 2 1 -> 8 6 7 8 , 4 4 4 8 -> 8 2 1 6 , 4 8 7 8 ->= 5 3 4 8 , 4 4 5 1 ->= 4 8 2 1 , 5 0 1 7 -> 5 3 4 4 , 5 1 7 4 -> 5 3 8 7 , 8 6 2 3 -> 8 6 7 4 , 4 4 4 4 -> 8 2 1 7 , 4 8 7 4 ->= 5 3 4 4 , 4 4 5 3 ->= 4 8 2 3 } 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 1 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 1 | | 0 0 0 0 0 | \ / 2 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 | \ / 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 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 1 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 48-rule system { 0 0 1 2 -> 0 3 4 5 , 1 6 2 0 -> 1 6 7 5 , 3 4 4 5 -> 1 2 1 2 , 3 8 7 5 ->= 0 3 4 5 , 3 4 5 0 ->= 3 8 2 0 , 0 1 7 8 -> 0 3 8 6 , 1 6 2 1 -> 1 6 7 8 , 3 4 4 8 -> 1 2 1 6 , 3 8 7 8 ->= 0 3 4 8 , 3 4 5 1 ->= 3 8 2 1 , 1 6 2 3 -> 1 6 7 4 , 3 4 4 4 -> 1 2 1 7 , 3 8 7 4 ->= 0 3 4 4 , 3 4 5 3 ->= 3 8 2 3 , 2 0 1 2 -> 2 3 4 5 , 2 1 7 5 -> 2 3 8 2 , 6 6 2 0 -> 6 6 7 5 , 7 4 4 5 -> 6 2 1 2 , 7 8 7 5 ->= 2 3 4 5 , 7 4 5 0 ->= 7 8 2 0 , 2 0 1 6 -> 2 3 4 8 , 2 1 7 8 -> 2 3 8 6 , 6 6 2 1 -> 6 6 7 8 , 7 4 4 8 -> 6 2 1 6 , 7 8 7 8 ->= 2 3 4 8 , 7 4 5 1 ->= 7 8 2 1 , 2 1 7 4 -> 2 3 8 7 , 6 6 2 3 -> 6 6 7 4 , 7 4 4 4 -> 6 2 1 7 , 7 8 7 4 ->= 2 3 4 4 , 7 4 5 3 ->= 7 8 2 3 , 5 0 1 2 -> 5 3 4 5 , 5 1 7 5 -> 5 3 8 2 , 8 6 2 0 -> 8 6 7 5 , 4 4 4 5 -> 8 2 1 2 , 4 8 7 5 ->= 5 3 4 5 , 4 4 5 0 ->= 4 8 2 0 , 5 0 1 6 -> 5 3 4 8 , 5 1 7 8 -> 5 3 8 6 , 8 6 2 1 -> 8 6 7 8 , 4 4 4 8 -> 8 2 1 6 , 4 8 7 8 ->= 5 3 4 8 , 4 4 5 1 ->= 4 8 2 1 , 5 1 7 4 -> 5 3 8 7 , 8 6 2 3 -> 8 6 7 4 , 4 4 4 4 -> 8 2 1 7 , 4 8 7 4 ->= 5 3 4 4 , 4 4 5 3 ->= 4 8 2 3 } 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 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 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 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 | \ / 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 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 1 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 0 | | 0 1 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 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 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 1 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 { 1->0, 6->1, 2->2, 0->3, 7->4, 5->5, 3->6, 4->7, 8->8 }, it remains to prove termination of the 47-rule system { 0 1 2 3 -> 0 1 4 5 , 6 7 7 5 -> 0 2 0 2 , 6 8 4 5 ->= 3 6 7 5 , 6 7 5 3 ->= 6 8 2 3 , 3 0 4 8 -> 3 6 8 1 , 0 1 2 0 -> 0 1 4 8 , 6 7 7 8 -> 0 2 0 1 , 6 8 4 8 ->= 3 6 7 8 , 6 7 5 0 ->= 6 8 2 0 , 0 1 2 6 -> 0 1 4 7 , 6 7 7 7 -> 0 2 0 4 , 6 8 4 7 ->= 3 6 7 7 , 6 7 5 6 ->= 6 8 2 6 , 2 3 0 2 -> 2 6 7 5 , 2 0 4 5 -> 2 6 8 2 , 1 1 2 3 -> 1 1 4 5 , 4 7 7 5 -> 1 2 0 2 , 4 8 4 5 ->= 2 6 7 5 , 4 7 5 3 ->= 4 8 2 3 , 2 3 0 1 -> 2 6 7 8 , 2 0 4 8 -> 2 6 8 1 , 1 1 2 0 -> 1 1 4 8 , 4 7 7 8 -> 1 2 0 1 , 4 8 4 8 ->= 2 6 7 8 , 4 7 5 0 ->= 4 8 2 0 , 2 0 4 7 -> 2 6 8 4 , 1 1 2 6 -> 1 1 4 7 , 4 7 7 7 -> 1 2 0 4 , 4 8 4 7 ->= 2 6 7 7 , 4 7 5 6 ->= 4 8 2 6 , 5 3 0 2 -> 5 6 7 5 , 5 0 4 5 -> 5 6 8 2 , 8 1 2 3 -> 8 1 4 5 , 7 7 7 5 -> 8 2 0 2 , 7 8 4 5 ->= 5 6 7 5 , 7 7 5 3 ->= 7 8 2 3 , 5 3 0 1 -> 5 6 7 8 , 5 0 4 8 -> 5 6 8 1 , 8 1 2 0 -> 8 1 4 8 , 7 7 7 8 -> 8 2 0 1 , 7 8 4 8 ->= 5 6 7 8 , 7 7 5 0 ->= 7 8 2 0 , 5 0 4 7 -> 5 6 8 4 , 8 1 2 6 -> 8 1 4 7 , 7 7 7 7 -> 8 2 0 4 , 7 8 4 7 ->= 5 6 7 7 , 7 7 5 6 ->= 7 8 2 6 } 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 1 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 1 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 1 | | 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 1 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 1 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 46-rule system { 0 1 2 3 -> 0 1 4 5 , 6 7 7 5 -> 0 2 0 2 , 6 8 4 5 ->= 3 6 7 5 , 6 7 5 3 ->= 6 8 2 3 , 0 1 2 0 -> 0 1 4 8 , 6 7 7 8 -> 0 2 0 1 , 6 8 4 8 ->= 3 6 7 8 , 6 7 5 0 ->= 6 8 2 0 , 0 1 2 6 -> 0 1 4 7 , 6 7 7 7 -> 0 2 0 4 , 6 8 4 7 ->= 3 6 7 7 , 6 7 5 6 ->= 6 8 2 6 , 2 3 0 2 -> 2 6 7 5 , 2 0 4 5 -> 2 6 8 2 , 1 1 2 3 -> 1 1 4 5 , 4 7 7 5 -> 1 2 0 2 , 4 8 4 5 ->= 2 6 7 5 , 4 7 5 3 ->= 4 8 2 3 , 2 3 0 1 -> 2 6 7 8 , 2 0 4 8 -> 2 6 8 1 , 1 1 2 0 -> 1 1 4 8 , 4 7 7 8 -> 1 2 0 1 , 4 8 4 8 ->= 2 6 7 8 , 4 7 5 0 ->= 4 8 2 0 , 2 0 4 7 -> 2 6 8 4 , 1 1 2 6 -> 1 1 4 7 , 4 7 7 7 -> 1 2 0 4 , 4 8 4 7 ->= 2 6 7 7 , 4 7 5 6 ->= 4 8 2 6 , 5 3 0 2 -> 5 6 7 5 , 5 0 4 5 -> 5 6 8 2 , 8 1 2 3 -> 8 1 4 5 , 7 7 7 5 -> 8 2 0 2 , 7 8 4 5 ->= 5 6 7 5 , 7 7 5 3 ->= 7 8 2 3 , 5 3 0 1 -> 5 6 7 8 , 5 0 4 8 -> 5 6 8 1 , 8 1 2 0 -> 8 1 4 8 , 7 7 7 8 -> 8 2 0 1 , 7 8 4 8 ->= 5 6 7 8 , 7 7 5 0 ->= 7 8 2 0 , 5 0 4 7 -> 5 6 8 4 , 8 1 2 6 -> 8 1 4 7 , 7 7 7 7 -> 8 2 0 4 , 7 8 4 7 ->= 5 6 7 7 , 7 7 5 6 ->= 7 8 2 6 } 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 1 | | 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 1 0 0 0 | \ / 2 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 | \ / 3 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 | \ / 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 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 44-rule system { 0 1 2 3 -> 0 1 4 5 , 6 7 7 5 -> 0 2 0 2 , 6 8 4 5 ->= 3 6 7 5 , 6 7 5 3 ->= 6 8 2 3 , 0 1 2 0 -> 0 1 4 8 , 6 7 7 8 -> 0 2 0 1 , 6 8 4 8 ->= 3 6 7 8 , 6 7 5 0 ->= 6 8 2 0 , 0 1 2 6 -> 0 1 4 7 , 6 7 7 7 -> 0 2 0 4 , 6 8 4 7 ->= 3 6 7 7 , 6 7 5 6 ->= 6 8 2 6 , 2 3 0 2 -> 2 6 7 5 , 2 0 4 5 -> 2 6 8 2 , 1 1 2 3 -> 1 1 4 5 , 4 7 7 5 -> 1 2 0 2 , 4 8 4 5 ->= 2 6 7 5 , 4 7 5 3 ->= 4 8 2 3 , 2 0 4 8 -> 2 6 8 1 , 1 1 2 0 -> 1 1 4 8 , 4 7 7 8 -> 1 2 0 1 , 4 8 4 8 ->= 2 6 7 8 , 4 7 5 0 ->= 4 8 2 0 , 2 0 4 7 -> 2 6 8 4 , 1 1 2 6 -> 1 1 4 7 , 4 7 7 7 -> 1 2 0 4 , 4 8 4 7 ->= 2 6 7 7 , 4 7 5 6 ->= 4 8 2 6 , 5 3 0 2 -> 5 6 7 5 , 5 0 4 5 -> 5 6 8 2 , 8 1 2 3 -> 8 1 4 5 , 7 7 7 5 -> 8 2 0 2 , 7 8 4 5 ->= 5 6 7 5 , 7 7 5 3 ->= 7 8 2 3 , 5 0 4 8 -> 5 6 8 1 , 8 1 2 0 -> 8 1 4 8 , 7 7 7 8 -> 8 2 0 1 , 7 8 4 8 ->= 5 6 7 8 , 7 7 5 0 ->= 7 8 2 0 , 5 0 4 7 -> 5 6 8 4 , 8 1 2 6 -> 8 1 4 7 , 7 7 7 7 -> 8 2 0 4 , 7 8 4 7 ->= 5 6 7 7 , 7 7 5 6 ->= 7 8 2 6 } 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 1 | | 0 1 | \ / 4 is interpreted by / \ | 1 1 | | 0 1 | \ / 5 is interpreted by / \ | 1 1 | | 0 1 | \ / 6 is interpreted by / \ | 1 1 | | 0 1 | \ / 7 is interpreted by / \ | 1 1 | | 0 1 | \ / 8 is interpreted by / \ | 1 1 | | 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 37-rule system { 0 1 2 3 -> 0 1 4 5 , 6 7 7 5 -> 0 2 0 2 , 6 8 4 5 ->= 3 6 7 5 , 6 7 5 3 ->= 6 8 2 3 , 0 1 2 0 -> 0 1 4 8 , 6 8 4 8 ->= 3 6 7 8 , 6 7 5 0 ->= 6 8 2 0 , 0 1 2 6 -> 0 1 4 7 , 6 7 7 7 -> 0 2 0 4 , 6 8 4 7 ->= 3 6 7 7 , 6 7 5 6 ->= 6 8 2 6 , 2 3 0 2 -> 2 6 7 5 , 2 0 4 5 -> 2 6 8 2 , 1 1 2 3 -> 1 1 4 5 , 4 8 4 5 ->= 2 6 7 5 , 4 7 5 3 ->= 4 8 2 3 , 1 1 2 0 -> 1 1 4 8 , 4 8 4 8 ->= 2 6 7 8 , 4 7 5 0 ->= 4 8 2 0 , 2 0 4 7 -> 2 6 8 4 , 1 1 2 6 -> 1 1 4 7 , 4 8 4 7 ->= 2 6 7 7 , 4 7 5 6 ->= 4 8 2 6 , 5 3 0 2 -> 5 6 7 5 , 5 0 4 5 -> 5 6 8 2 , 8 1 2 3 -> 8 1 4 5 , 7 7 7 5 -> 8 2 0 2 , 7 8 4 5 ->= 5 6 7 5 , 7 7 5 3 ->= 7 8 2 3 , 8 1 2 0 -> 8 1 4 8 , 7 8 4 8 ->= 5 6 7 8 , 7 7 5 0 ->= 7 8 2 0 , 5 0 4 7 -> 5 6 8 4 , 8 1 2 6 -> 8 1 4 7 , 7 7 7 7 -> 8 2 0 4 , 7 8 4 7 ->= 5 6 7 7 , 7 7 5 6 ->= 7 8 2 6 } 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 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 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 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 0 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 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 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 | \ / 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 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 0 | | 0 0 0 0 0 0 0 1 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 1 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 36-rule system { 0 1 2 3 -> 0 1 4 5 , 6 7 7 5 -> 0 2 0 2 , 6 8 4 5 ->= 3 6 7 5 , 6 7 5 3 ->= 6 8 2 3 , 6 8 4 8 ->= 3 6 7 8 , 6 7 5 0 ->= 6 8 2 0 , 0 1 2 6 -> 0 1 4 7 , 6 7 7 7 -> 0 2 0 4 , 6 8 4 7 ->= 3 6 7 7 , 6 7 5 6 ->= 6 8 2 6 , 2 3 0 2 -> 2 6 7 5 , 2 0 4 5 -> 2 6 8 2 , 1 1 2 3 -> 1 1 4 5 , 4 8 4 5 ->= 2 6 7 5 , 4 7 5 3 ->= 4 8 2 3 , 1 1 2 0 -> 1 1 4 8 , 4 8 4 8 ->= 2 6 7 8 , 4 7 5 0 ->= 4 8 2 0 , 2 0 4 7 -> 2 6 8 4 , 1 1 2 6 -> 1 1 4 7 , 4 8 4 7 ->= 2 6 7 7 , 4 7 5 6 ->= 4 8 2 6 , 5 3 0 2 -> 5 6 7 5 , 5 0 4 5 -> 5 6 8 2 , 8 1 2 3 -> 8 1 4 5 , 7 7 7 5 -> 8 2 0 2 , 7 8 4 5 ->= 5 6 7 5 , 7 7 5 3 ->= 7 8 2 3 , 8 1 2 0 -> 8 1 4 8 , 7 8 4 8 ->= 5 6 7 8 , 7 7 5 0 ->= 7 8 2 0 , 5 0 4 7 -> 5 6 8 4 , 8 1 2 6 -> 8 1 4 7 , 7 7 7 7 -> 8 2 0 4 , 7 8 4 7 ->= 5 6 7 7 , 7 7 5 6 ->= 7 8 2 6 } 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 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 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 1 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 0 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 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 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 | \ / 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 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 0 | | 0 0 0 0 0 0 0 1 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 1 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 35-rule system { 0 1 2 3 -> 0 1 4 5 , 6 7 7 5 -> 0 2 0 2 , 6 8 4 5 ->= 3 6 7 5 , 6 7 5 3 ->= 6 8 2 3 , 6 8 4 8 ->= 3 6 7 8 , 6 7 5 0 ->= 6 8 2 0 , 0 1 2 6 -> 0 1 4 7 , 6 7 7 7 -> 0 2 0 4 , 6 8 4 7 ->= 3 6 7 7 , 6 7 5 6 ->= 6 8 2 6 , 2 3 0 2 -> 2 6 7 5 , 2 0 4 5 -> 2 6 8 2 , 1 1 2 3 -> 1 1 4 5 , 4 8 4 5 ->= 2 6 7 5 , 4 7 5 3 ->= 4 8 2 3 , 4 8 4 8 ->= 2 6 7 8 , 4 7 5 0 ->= 4 8 2 0 , 2 0 4 7 -> 2 6 8 4 , 1 1 2 6 -> 1 1 4 7 , 4 8 4 7 ->= 2 6 7 7 , 4 7 5 6 ->= 4 8 2 6 , 5 3 0 2 -> 5 6 7 5 , 5 0 4 5 -> 5 6 8 2 , 8 1 2 3 -> 8 1 4 5 , 7 7 7 5 -> 8 2 0 2 , 7 8 4 5 ->= 5 6 7 5 , 7 7 5 3 ->= 7 8 2 3 , 8 1 2 0 -> 8 1 4 8 , 7 8 4 8 ->= 5 6 7 8 , 7 7 5 0 ->= 7 8 2 0 , 5 0 4 7 -> 5 6 8 4 , 8 1 2 6 -> 8 1 4 7 , 7 7 7 7 -> 8 2 0 4 , 7 8 4 7 ->= 5 6 7 7 , 7 7 5 6 ->= 7 8 2 6 } 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 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 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 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 0 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 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 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 | \ / 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 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 | \ / 8 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 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 | \ / 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 34-rule system { 0 1 2 3 -> 0 1 4 5 , 6 7 7 5 -> 0 2 0 2 , 6 8 4 5 ->= 3 6 7 5 , 6 7 5 3 ->= 6 8 2 3 , 6 8 4 8 ->= 3 6 7 8 , 6 7 5 0 ->= 6 8 2 0 , 0 1 2 6 -> 0 1 4 7 , 6 7 7 7 -> 0 2 0 4 , 6 8 4 7 ->= 3 6 7 7 , 6 7 5 6 ->= 6 8 2 6 , 2 3 0 2 -> 2 6 7 5 , 2 0 4 5 -> 2 6 8 2 , 1 1 2 3 -> 1 1 4 5 , 4 8 4 5 ->= 2 6 7 5 , 4 7 5 3 ->= 4 8 2 3 , 4 8 4 8 ->= 2 6 7 8 , 4 7 5 0 ->= 4 8 2 0 , 2 0 4 7 -> 2 6 8 4 , 1 1 2 6 -> 1 1 4 7 , 4 8 4 7 ->= 2 6 7 7 , 4 7 5 6 ->= 4 8 2 6 , 5 3 0 2 -> 5 6 7 5 , 5 0 4 5 -> 5 6 8 2 , 8 1 2 3 -> 8 1 4 5 , 7 7 7 5 -> 8 2 0 2 , 7 8 4 5 ->= 5 6 7 5 , 7 7 5 3 ->= 7 8 2 3 , 7 8 4 8 ->= 5 6 7 8 , 7 7 5 0 ->= 7 8 2 0 , 5 0 4 7 -> 5 6 8 4 , 8 1 2 6 -> 8 1 4 7 , 7 7 7 7 -> 8 2 0 4 , 7 8 4 7 ->= 5 6 7 7 , 7 7 5 6 ->= 7 8 2 6 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 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 1 0 | | 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 1 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 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 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 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 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 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 1 0 0 0 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 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 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 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 | \ / After renaming modulo { 6->0, 7->1, 5->2, 0->3, 2->4, 8->5, 4->6, 3->7, 1->8 }, it remains to prove termination of the 33-rule system { 0 1 1 2 -> 3 4 3 4 , 0 5 6 2 ->= 7 0 1 2 , 0 1 2 7 ->= 0 5 4 7 , 0 5 6 5 ->= 7 0 1 5 , 0 1 2 3 ->= 0 5 4 3 , 3 8 4 0 -> 3 8 6 1 , 0 1 1 1 -> 3 4 3 6 , 0 5 6 1 ->= 7 0 1 1 , 0 1 2 0 ->= 0 5 4 0 , 4 7 3 4 -> 4 0 1 2 , 4 3 6 2 -> 4 0 5 4 , 8 8 4 7 -> 8 8 6 2 , 6 5 6 2 ->= 4 0 1 2 , 6 1 2 7 ->= 6 5 4 7 , 6 5 6 5 ->= 4 0 1 5 , 6 1 2 3 ->= 6 5 4 3 , 4 3 6 1 -> 4 0 5 6 , 8 8 4 0 -> 8 8 6 1 , 6 5 6 1 ->= 4 0 1 1 , 6 1 2 0 ->= 6 5 4 0 , 2 7 3 4 -> 2 0 1 2 , 2 3 6 2 -> 2 0 5 4 , 5 8 4 7 -> 5 8 6 2 , 1 1 1 2 -> 5 4 3 4 , 1 5 6 2 ->= 2 0 1 2 , 1 1 2 7 ->= 1 5 4 7 , 1 5 6 5 ->= 2 0 1 5 , 1 1 2 3 ->= 1 5 4 3 , 2 3 6 1 -> 2 0 5 6 , 5 8 4 0 -> 5 8 6 1 , 1 1 1 1 -> 5 4 3 6 , 1 5 6 1 ->= 2 0 1 1 , 1 1 2 0 ->= 1 5 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 | | 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 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 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 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 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 | \ / 4 is interpreted by / \ | 1 0 0 0 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 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 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 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 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 32-rule system { 0 1 1 2 -> 3 4 3 4 , 0 5 6 2 ->= 7 0 1 2 , 0 1 2 7 ->= 0 5 4 7 , 0 5 6 5 ->= 7 0 1 5 , 0 1 2 3 ->= 0 5 4 3 , 3 8 4 0 -> 3 8 6 1 , 0 1 1 1 -> 3 4 3 6 , 0 5 6 1 ->= 7 0 1 1 , 0 1 2 0 ->= 0 5 4 0 , 4 7 3 4 -> 4 0 1 2 , 4 3 6 2 -> 4 0 5 4 , 6 5 6 2 ->= 4 0 1 2 , 6 1 2 7 ->= 6 5 4 7 , 6 5 6 5 ->= 4 0 1 5 , 6 1 2 3 ->= 6 5 4 3 , 4 3 6 1 -> 4 0 5 6 , 8 8 4 0 -> 8 8 6 1 , 6 5 6 1 ->= 4 0 1 1 , 6 1 2 0 ->= 6 5 4 0 , 2 7 3 4 -> 2 0 1 2 , 2 3 6 2 -> 2 0 5 4 , 5 8 4 7 -> 5 8 6 2 , 1 1 1 2 -> 5 4 3 4 , 1 5 6 2 ->= 2 0 1 2 , 1 1 2 7 ->= 1 5 4 7 , 1 5 6 5 ->= 2 0 1 5 , 1 1 2 3 ->= 1 5 4 3 , 2 3 6 1 -> 2 0 5 6 , 5 8 4 0 -> 5 8 6 1 , 1 1 1 1 -> 5 4 3 6 , 1 5 6 1 ->= 2 0 1 1 , 1 1 2 0 ->= 1 5 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 | | 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 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 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 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 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 | \ / 4 is interpreted by / \ | 1 0 0 0 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 | \ / 5 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 1 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 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 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 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 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 1 2 -> 3 4 3 4 , 0 5 6 2 ->= 7 0 1 2 , 0 1 2 7 ->= 0 5 4 7 , 0 5 6 5 ->= 7 0 1 5 , 0 1 2 3 ->= 0 5 4 3 , 3 8 4 0 -> 3 8 6 1 , 0 1 1 1 -> 3 4 3 6 , 0 5 6 1 ->= 7 0 1 1 , 0 1 2 0 ->= 0 5 4 0 , 4 7 3 4 -> 4 0 1 2 , 4 3 6 2 -> 4 0 5 4 , 6 5 6 2 ->= 4 0 1 2 , 6 1 2 7 ->= 6 5 4 7 , 6 5 6 5 ->= 4 0 1 5 , 6 1 2 3 ->= 6 5 4 3 , 4 3 6 1 -> 4 0 5 6 , 8 8 4 0 -> 8 8 6 1 , 6 5 6 1 ->= 4 0 1 1 , 6 1 2 0 ->= 6 5 4 0 , 2 7 3 4 -> 2 0 1 2 , 2 3 6 2 -> 2 0 5 4 , 1 1 1 2 -> 5 4 3 4 , 1 5 6 2 ->= 2 0 1 2 , 1 1 2 7 ->= 1 5 4 7 , 1 5 6 5 ->= 2 0 1 5 , 1 1 2 3 ->= 1 5 4 3 , 2 3 6 1 -> 2 0 5 6 , 5 8 4 0 -> 5 8 6 1 , 1 1 1 1 -> 5 4 3 6 , 1 5 6 1 ->= 2 0 1 1 , 1 1 2 0 ->= 1 5 4 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 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 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 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 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 | \ / 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 0 | | 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 1 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 1 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 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 0 0 0 | | 0 0 0 0 0 0 0 0 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 | \ / 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 1 1 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 | \ / 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 1 2 -> 3 4 3 4 , 0 5 6 2 ->= 7 0 1 2 , 0 1 2 7 ->= 0 5 4 7 , 0 5 6 5 ->= 7 0 1 5 , 0 1 2 3 ->= 0 5 4 3 , 3 8 4 0 -> 3 8 6 1 , 0 1 1 1 -> 3 4 3 6 , 0 5 6 1 ->= 7 0 1 1 , 0 1 2 0 ->= 0 5 4 0 , 4 7 3 4 -> 4 0 1 2 , 4 3 6 2 -> 4 0 5 4 , 6 5 6 2 ->= 4 0 1 2 , 6 1 2 7 ->= 6 5 4 7 , 6 5 6 5 ->= 4 0 1 5 , 6 1 2 3 ->= 6 5 4 3 , 4 3 6 1 -> 4 0 5 6 , 8 8 4 0 -> 8 8 6 1 , 6 1 2 0 ->= 6 5 4 0 , 2 7 3 4 -> 2 0 1 2 , 2 3 6 2 -> 2 0 5 4 , 1 1 1 2 -> 5 4 3 4 , 1 5 6 2 ->= 2 0 1 2 , 1 1 2 7 ->= 1 5 4 7 , 1 5 6 5 ->= 2 0 1 5 , 1 1 2 3 ->= 1 5 4 3 , 2 3 6 1 -> 2 0 5 6 , 5 8 4 0 -> 5 8 6 1 , 1 1 1 1 -> 5 4 3 6 , 1 1 2 0 ->= 1 5 4 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 1 0 0 0 0 0 0 0 0 | | 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 | \ / 1 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 1 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 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 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 1 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 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 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 1 0 0 0 0 | | 0 0 0 0 0 0 0 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 | \ / 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 28-rule system { 0 1 1 2 -> 3 4 3 4 , 0 5 6 2 ->= 7 0 1 2 , 0 1 2 7 ->= 0 5 4 7 , 0 5 6 5 ->= 7 0 1 5 , 0 1 2 3 ->= 0 5 4 3 , 3 8 4 0 -> 3 8 6 1 , 0 1 1 1 -> 3 4 3 6 , 0 5 6 1 ->= 7 0 1 1 , 0 1 2 0 ->= 0 5 4 0 , 4 7 3 4 -> 4 0 1 2 , 4 3 6 2 -> 4 0 5 4 , 6 5 6 2 ->= 4 0 1 2 , 6 1 2 7 ->= 6 5 4 7 , 6 5 6 5 ->= 4 0 1 5 , 6 1 2 3 ->= 6 5 4 3 , 4 3 6 1 -> 4 0 5 6 , 8 8 4 0 -> 8 8 6 1 , 6 1 2 0 ->= 6 5 4 0 , 2 7 3 4 -> 2 0 1 2 , 2 3 6 2 -> 2 0 5 4 , 1 1 1 2 -> 5 4 3 4 , 1 5 6 2 ->= 2 0 1 2 , 1 1 2 7 ->= 1 5 4 7 , 1 5 6 5 ->= 2 0 1 5 , 1 1 2 3 ->= 1 5 4 3 , 2 3 6 1 -> 2 0 5 6 , 5 8 4 0 -> 5 8 6 1 , 1 1 2 0 ->= 1 5 4 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 0 0 0 0 1 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 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 1 | | 0 0 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 1 0 | | 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 1 0 0 0 | \ / 2 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 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 | \ / 4 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 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 | | 0 0 0 0 0 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 | \ / 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 27-rule system { 0 1 1 2 -> 3 4 3 4 , 0 5 6 2 ->= 7 0 1 2 , 0 1 2 7 ->= 0 5 4 7 , 0 5 6 5 ->= 7 0 1 5 , 0 1 2 3 ->= 0 5 4 3 , 3 8 4 0 -> 3 8 6 1 , 0 1 1 1 -> 3 4 3 6 , 0 1 2 0 ->= 0 5 4 0 , 4 7 3 4 -> 4 0 1 2 , 4 3 6 2 -> 4 0 5 4 , 6 5 6 2 ->= 4 0 1 2 , 6 1 2 7 ->= 6 5 4 7 , 6 5 6 5 ->= 4 0 1 5 , 6 1 2 3 ->= 6 5 4 3 , 4 3 6 1 -> 4 0 5 6 , 8 8 4 0 -> 8 8 6 1 , 6 1 2 0 ->= 6 5 4 0 , 2 7 3 4 -> 2 0 1 2 , 2 3 6 2 -> 2 0 5 4 , 1 1 1 2 -> 5 4 3 4 , 1 5 6 2 ->= 2 0 1 2 , 1 1 2 7 ->= 1 5 4 7 , 1 5 6 5 ->= 2 0 1 5 , 1 1 2 3 ->= 1 5 4 3 , 2 3 6 1 -> 2 0 5 6 , 5 8 4 0 -> 5 8 6 1 , 1 1 2 0 ->= 1 5 4 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 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 1 | | 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 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 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 26-rule system { 0 1 1 2 -> 3 4 3 4 , 0 5 6 2 ->= 7 0 1 2 , 0 1 2 7 ->= 0 5 4 7 , 0 5 6 5 ->= 7 0 1 5 , 0 1 2 3 ->= 0 5 4 3 , 3 8 4 0 -> 3 8 6 1 , 0 1 2 0 ->= 0 5 4 0 , 4 7 3 4 -> 4 0 1 2 , 4 3 6 2 -> 4 0 5 4 , 6 5 6 2 ->= 4 0 1 2 , 6 1 2 7 ->= 6 5 4 7 , 6 5 6 5 ->= 4 0 1 5 , 6 1 2 3 ->= 6 5 4 3 , 4 3 6 1 -> 4 0 5 6 , 8 8 4 0 -> 8 8 6 1 , 6 1 2 0 ->= 6 5 4 0 , 2 7 3 4 -> 2 0 1 2 , 2 3 6 2 -> 2 0 5 4 , 1 1 1 2 -> 5 4 3 4 , 1 5 6 2 ->= 2 0 1 2 , 1 1 2 7 ->= 1 5 4 7 , 1 5 6 5 ->= 2 0 1 5 , 1 1 2 3 ->= 1 5 4 3 , 2 3 6 1 -> 2 0 5 6 , 5 8 4 0 -> 5 8 6 1 , 1 1 2 0 ->= 1 5 4 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 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 1 | | 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 1 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 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, 5->1, 6->2, 2->3, 7->4, 1->5, 4->6, 3->7, 8->8 }, it remains to prove termination of the 25-rule system { 0 1 2 3 ->= 4 0 5 3 , 0 5 3 4 ->= 0 1 6 4 , 0 1 2 1 ->= 4 0 5 1 , 0 5 3 7 ->= 0 1 6 7 , 7 8 6 0 -> 7 8 2 5 , 0 5 3 0 ->= 0 1 6 0 , 6 4 7 6 -> 6 0 5 3 , 6 7 2 3 -> 6 0 1 6 , 2 1 2 3 ->= 6 0 5 3 , 2 5 3 4 ->= 2 1 6 4 , 2 1 2 1 ->= 6 0 5 1 , 2 5 3 7 ->= 2 1 6 7 , 6 7 2 5 -> 6 0 1 2 , 8 8 6 0 -> 8 8 2 5 , 2 5 3 0 ->= 2 1 6 0 , 3 4 7 6 -> 3 0 5 3 , 3 7 2 3 -> 3 0 1 6 , 5 5 5 3 -> 1 6 7 6 , 5 1 2 3 ->= 3 0 5 3 , 5 5 3 4 ->= 5 1 6 4 , 5 1 2 1 ->= 3 0 5 1 , 5 5 3 7 ->= 5 1 6 7 , 3 7 2 5 -> 3 0 1 2 , 1 8 6 0 -> 1 8 2 5 , 5 5 3 0 ->= 5 1 6 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 1 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 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 1 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 23-rule system { 0 1 2 3 ->= 4 0 5 3 , 0 5 3 4 ->= 0 1 6 4 , 0 1 2 1 ->= 4 0 5 1 , 0 5 3 7 ->= 0 1 6 7 , 7 8 6 0 -> 7 8 2 5 , 0 5 3 0 ->= 0 1 6 0 , 6 4 7 6 -> 6 0 5 3 , 6 7 2 3 -> 6 0 1 6 , 2 1 2 3 ->= 6 0 5 3 , 2 5 3 4 ->= 2 1 6 4 , 2 1 2 1 ->= 6 0 5 1 , 2 5 3 7 ->= 2 1 6 7 , 8 8 6 0 -> 8 8 2 5 , 2 5 3 0 ->= 2 1 6 0 , 3 4 7 6 -> 3 0 5 3 , 3 7 2 3 -> 3 0 1 6 , 5 5 5 3 -> 1 6 7 6 , 5 1 2 3 ->= 3 0 5 3 , 5 5 3 4 ->= 5 1 6 4 , 5 1 2 1 ->= 3 0 5 1 , 5 5 3 7 ->= 5 1 6 7 , 1 8 6 0 -> 1 8 2 5 , 5 5 3 0 ->= 5 1 6 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 0 | | 0 1 | \ / 2 is interpreted by / \ | 1 1 | | 0 1 | \ / 3 is interpreted by / \ | 1 0 | | 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 0 | | 0 1 | \ / 8 is interpreted by / \ | 1 0 | | 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 21-rule system { 0 1 2 3 ->= 4 0 5 3 , 0 5 3 4 ->= 0 1 6 4 , 0 1 2 1 ->= 4 0 5 1 , 0 5 3 7 ->= 0 1 6 7 , 7 8 6 0 -> 7 8 2 5 , 0 5 3 0 ->= 0 1 6 0 , 6 4 7 6 -> 6 0 5 3 , 6 7 2 3 -> 6 0 1 6 , 2 5 3 4 ->= 2 1 6 4 , 2 5 3 7 ->= 2 1 6 7 , 8 8 6 0 -> 8 8 2 5 , 2 5 3 0 ->= 2 1 6 0 , 3 4 7 6 -> 3 0 5 3 , 3 7 2 3 -> 3 0 1 6 , 5 5 5 3 -> 1 6 7 6 , 5 1 2 3 ->= 3 0 5 3 , 5 5 3 4 ->= 5 1 6 4 , 5 1 2 1 ->= 3 0 5 1 , 5 5 3 7 ->= 5 1 6 7 , 1 8 6 0 -> 1 8 2 5 , 5 5 3 0 ->= 5 1 6 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 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 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 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, 5->1, 3->2, 4->3, 1->4, 6->5, 2->6, 7->7, 8->8 }, it remains to prove termination of the 20-rule system { 0 1 2 3 ->= 0 4 5 3 , 0 4 6 4 ->= 3 0 1 4 , 0 1 2 7 ->= 0 4 5 7 , 7 8 5 0 -> 7 8 6 1 , 0 1 2 0 ->= 0 4 5 0 , 5 3 7 5 -> 5 0 1 2 , 5 7 6 2 -> 5 0 4 5 , 6 1 2 3 ->= 6 4 5 3 , 6 1 2 7 ->= 6 4 5 7 , 8 8 5 0 -> 8 8 6 1 , 6 1 2 0 ->= 6 4 5 0 , 2 3 7 5 -> 2 0 1 2 , 2 7 6 2 -> 2 0 4 5 , 1 1 1 2 -> 4 5 7 5 , 1 4 6 2 ->= 2 0 1 2 , 1 1 2 3 ->= 1 4 5 3 , 1 4 6 4 ->= 2 0 1 4 , 1 1 2 7 ->= 1 4 5 7 , 4 8 5 0 -> 4 8 6 1 , 1 1 2 0 ->= 1 4 5 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 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 1 | | 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 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 19-rule system { 0 1 2 3 ->= 0 4 5 3 , 0 4 6 4 ->= 3 0 1 4 , 0 1 2 7 ->= 0 4 5 7 , 0 1 2 0 ->= 0 4 5 0 , 5 3 7 5 -> 5 0 1 2 , 5 7 6 2 -> 5 0 4 5 , 6 1 2 3 ->= 6 4 5 3 , 6 1 2 7 ->= 6 4 5 7 , 8 8 5 0 -> 8 8 6 1 , 6 1 2 0 ->= 6 4 5 0 , 2 3 7 5 -> 2 0 1 2 , 2 7 6 2 -> 2 0 4 5 , 1 1 1 2 -> 4 5 7 5 , 1 4 6 2 ->= 2 0 1 2 , 1 1 2 3 ->= 1 4 5 3 , 1 4 6 4 ->= 2 0 1 4 , 1 1 2 7 ->= 1 4 5 7 , 4 8 5 0 -> 4 8 6 1 , 1 1 2 0 ->= 1 4 5 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 1 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 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 0 | | 0 0 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 1 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 18-rule system { 0 1 2 3 ->= 0 4 5 3 , 0 4 6 4 ->= 3 0 1 4 , 0 1 2 7 ->= 0 4 5 7 , 0 1 2 0 ->= 0 4 5 0 , 5 3 7 5 -> 5 0 1 2 , 5 7 6 2 -> 5 0 4 5 , 6 1 2 3 ->= 6 4 5 3 , 8 8 5 0 -> 8 8 6 1 , 6 1 2 0 ->= 6 4 5 0 , 2 3 7 5 -> 2 0 1 2 , 2 7 6 2 -> 2 0 4 5 , 1 1 1 2 -> 4 5 7 5 , 1 4 6 2 ->= 2 0 1 2 , 1 1 2 3 ->= 1 4 5 3 , 1 4 6 4 ->= 2 0 1 4 , 1 1 2 7 ->= 1 4 5 7 , 4 8 5 0 -> 4 8 6 1 , 1 1 2 0 ->= 1 4 5 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 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 1 | | 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 1 0 0 0 | \ / 8 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 | \ / 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 17-rule system { 0 1 2 3 ->= 0 4 5 3 , 0 4 6 4 ->= 3 0 1 4 , 0 1 2 7 ->= 0 4 5 7 , 0 1 2 0 ->= 0 4 5 0 , 5 3 7 5 -> 5 0 1 2 , 5 7 6 2 -> 5 0 4 5 , 6 1 2 3 ->= 6 4 5 3 , 6 1 2 0 ->= 6 4 5 0 , 2 3 7 5 -> 2 0 1 2 , 2 7 6 2 -> 2 0 4 5 , 1 1 1 2 -> 4 5 7 5 , 1 4 6 2 ->= 2 0 1 2 , 1 1 2 3 ->= 1 4 5 3 , 1 4 6 4 ->= 2 0 1 4 , 1 1 2 7 ->= 1 4 5 7 , 4 8 5 0 -> 4 8 6 1 , 1 1 2 0 ->= 1 4 5 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 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 1 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 0 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 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 | \ / 4 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 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 1 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 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 | \ / 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 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 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 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 16-rule system { 0 1 2 3 ->= 0 4 5 3 , 0 4 6 4 ->= 3 0 1 4 , 0 1 2 7 ->= 0 4 5 7 , 0 1 2 0 ->= 0 4 5 0 , 5 3 7 5 -> 5 0 1 2 , 5 7 6 2 -> 5 0 4 5 , 6 1 2 3 ->= 6 4 5 3 , 6 1 2 0 ->= 6 4 5 0 , 2 3 7 5 -> 2 0 1 2 , 2 7 6 2 -> 2 0 4 5 , 1 1 1 2 -> 4 5 7 5 , 1 4 6 2 ->= 2 0 1 2 , 1 1 2 3 ->= 1 4 5 3 , 1 4 6 4 ->= 2 0 1 4 , 4 8 5 0 -> 4 8 6 1 , 1 1 2 0 ->= 1 4 5 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 1 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 1 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 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 1 | | 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 14-rule system { 0 1 2 3 ->= 0 4 5 3 , 0 4 6 4 ->= 3 0 1 4 , 0 1 2 7 ->= 0 4 5 7 , 0 1 2 0 ->= 0 4 5 0 , 5 7 6 2 -> 5 0 4 5 , 6 1 2 3 ->= 6 4 5 3 , 6 1 2 0 ->= 6 4 5 0 , 2 7 6 2 -> 2 0 4 5 , 1 1 1 2 -> 4 5 7 5 , 1 4 6 2 ->= 2 0 1 2 , 1 1 2 3 ->= 1 4 5 3 , 1 4 6 4 ->= 2 0 1 4 , 4 8 5 0 -> 4 8 6 1 , 1 1 2 0 ->= 1 4 5 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 0 | | 0 1 | \ / 4 is interpreted by / \ | 1 1 | | 0 1 | \ / 5 is interpreted by / \ | 1 1 | | 0 1 | \ / 6 is interpreted by / \ | 1 1 | | 0 1 | \ / 7 is interpreted by / \ | 1 1 | | 0 1 | \ / 8 is interpreted by / \ | 1 0 | | 0 1 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 7->6, 6->7, 8->8 }, it remains to prove termination of the 13-rule system { 0 1 2 3 ->= 0 4 5 3 , 0 1 2 6 ->= 0 4 5 6 , 0 1 2 0 ->= 0 4 5 0 , 5 6 7 2 -> 5 0 4 5 , 7 1 2 3 ->= 7 4 5 3 , 7 1 2 0 ->= 7 4 5 0 , 2 6 7 2 -> 2 0 4 5 , 1 1 1 2 -> 4 5 6 5 , 1 4 7 2 ->= 2 0 1 2 , 1 1 2 3 ->= 1 4 5 3 , 1 4 7 4 ->= 2 0 1 4 , 4 8 5 0 -> 4 8 7 1 , 1 1 2 0 ->= 1 4 5 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 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 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 0 1 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, 6->3, 4->4, 5->5, 7->6, 3->7, 8->8 }, it remains to prove termination of the 12-rule system { 0 1 2 3 ->= 0 4 5 3 , 0 1 2 0 ->= 0 4 5 0 , 5 3 6 2 -> 5 0 4 5 , 6 1 2 7 ->= 6 4 5 7 , 6 1 2 0 ->= 6 4 5 0 , 2 3 6 2 -> 2 0 4 5 , 1 1 1 2 -> 4 5 3 5 , 1 4 6 2 ->= 2 0 1 2 , 1 1 2 7 ->= 1 4 5 7 , 1 4 6 4 ->= 2 0 1 4 , 4 8 5 0 -> 4 8 6 1 , 1 1 2 0 ->= 1 4 5 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 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 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 1 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, 4->3, 5->4, 3->5, 6->6, 7->7, 8->8 }, it remains to prove termination of the 11-rule system { 0 1 2 0 ->= 0 3 4 0 , 4 5 6 2 -> 4 0 3 4 , 6 1 2 7 ->= 6 3 4 7 , 6 1 2 0 ->= 6 3 4 0 , 2 5 6 2 -> 2 0 3 4 , 1 1 1 2 -> 3 4 5 4 , 1 3 6 2 ->= 2 0 1 2 , 1 1 2 7 ->= 1 3 4 7 , 1 3 6 3 ->= 2 0 1 3 , 3 8 4 0 -> 3 8 6 1 , 1 1 2 0 ->= 1 3 4 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 1 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 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 0 | | 0 0 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 1 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 10-rule system { 0 1 2 0 ->= 0 3 4 0 , 4 5 6 2 -> 4 0 3 4 , 6 1 2 0 ->= 6 3 4 0 , 2 5 6 2 -> 2 0 3 4 , 1 1 1 2 -> 3 4 5 4 , 1 3 6 2 ->= 2 0 1 2 , 1 1 2 7 ->= 1 3 4 7 , 1 3 6 3 ->= 2 0 1 3 , 3 8 4 0 -> 3 8 6 1 , 1 1 2 0 ->= 1 3 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 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 | \ / 3 is interpreted by / \ | 1 0 0 0 0 1 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 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 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 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 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 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 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 8->7 }, it remains to prove termination of the 9-rule system { 0 1 2 0 ->= 0 3 4 0 , 4 5 6 2 -> 4 0 3 4 , 6 1 2 0 ->= 6 3 4 0 , 2 5 6 2 -> 2 0 3 4 , 1 1 1 2 -> 3 4 5 4 , 1 3 6 2 ->= 2 0 1 2 , 1 3 6 3 ->= 2 0 1 3 , 3 7 4 0 -> 3 7 6 1 , 1 1 2 0 ->= 1 3 4 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 1 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 1 | | 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 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 }, it remains to prove termination of the 8-rule system { 0 1 2 0 ->= 0 3 4 0 , 4 5 6 2 -> 4 0 3 4 , 6 1 2 0 ->= 6 3 4 0 , 2 5 6 2 -> 2 0 3 4 , 1 1 1 2 -> 3 4 5 4 , 1 3 6 2 ->= 2 0 1 2 , 1 3 6 3 ->= 2 0 1 3 , 1 1 2 0 ->= 1 3 4 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 1 | | 0 1 | \ / 3 is interpreted by / \ | 1 1 | | 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 | \ / After renaming modulo { }, it remains to prove termination of the 0-rule system { } The system is trivially terminating.