/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES After renaming modulo { a->0, b->1, c->2 }, it remains to prove termination of the 7-rule system { 0 0 1 -> 0 2 1 , 2 2 2 -> 0 1 0 , 1 2 1 -> 1 0 2 , 1 1 2 ->= 2 0 1 , 1 1 1 ->= 0 1 1 , 1 1 2 ->= 1 2 2 , 1 0 0 ->= 0 2 2 } The length-preserving system was inverted. After renaming modulo { 0->0, 2->1, 1->2 }, it remains to prove termination of the 7-rule system { 0 1 2 -> 0 0 2 , 0 2 0 -> 1 1 1 , 2 0 1 -> 2 1 2 , 1 0 2 ->= 2 2 1 , 0 2 2 ->= 2 2 2 , 2 1 1 ->= 2 2 1 , 0 1 1 ->= 2 0 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, 2]->2, [2, 0]->3, [0, 2]->4, [1, 1]->5, [1, 0]->6, [2, 1]->7, [2, 2]->8 }, it remains to prove termination of the 63-rule system { 0 1 2 3 -> 0 0 4 3 , 0 4 3 0 -> 1 5 5 6 , 4 3 1 6 -> 4 7 2 3 , 1 6 4 3 ->= 4 8 7 6 , 0 4 8 3 ->= 4 8 8 3 , 4 7 5 6 ->= 4 8 7 6 , 0 1 5 6 ->= 4 3 0 0 , 0 1 2 7 -> 0 0 4 7 , 0 4 3 1 -> 1 5 5 5 , 4 3 1 5 -> 4 7 2 7 , 1 6 4 7 ->= 4 8 7 5 , 0 4 8 7 ->= 4 8 8 7 , 4 7 5 5 ->= 4 8 7 5 , 0 1 5 5 ->= 4 3 0 1 , 0 1 2 8 -> 0 0 4 8 , 0 4 3 4 -> 1 5 5 2 , 4 3 1 2 -> 4 7 2 8 , 1 6 4 8 ->= 4 8 7 2 , 0 4 8 8 ->= 4 8 8 8 , 4 7 5 2 ->= 4 8 7 2 , 0 1 5 2 ->= 4 3 0 4 , 6 1 2 3 -> 6 0 4 3 , 6 4 3 0 -> 5 5 5 6 , 2 3 1 6 -> 2 7 2 3 , 5 6 4 3 ->= 2 8 7 6 , 6 4 8 3 ->= 2 8 8 3 , 2 7 5 6 ->= 2 8 7 6 , 6 1 5 6 ->= 2 3 0 0 , 6 1 2 7 -> 6 0 4 7 , 6 4 3 1 -> 5 5 5 5 , 2 3 1 5 -> 2 7 2 7 , 5 6 4 7 ->= 2 8 7 5 , 6 4 8 7 ->= 2 8 8 7 , 2 7 5 5 ->= 2 8 7 5 , 6 1 5 5 ->= 2 3 0 1 , 6 1 2 8 -> 6 0 4 8 , 6 4 3 4 -> 5 5 5 2 , 2 3 1 2 -> 2 7 2 8 , 5 6 4 8 ->= 2 8 7 2 , 6 4 8 8 ->= 2 8 8 8 , 2 7 5 2 ->= 2 8 7 2 , 6 1 5 2 ->= 2 3 0 4 , 3 1 2 3 -> 3 0 4 3 , 3 4 3 0 -> 7 5 5 6 , 8 3 1 6 -> 8 7 2 3 , 7 6 4 3 ->= 8 8 7 6 , 3 4 8 3 ->= 8 8 8 3 , 8 7 5 6 ->= 8 8 7 6 , 3 1 5 6 ->= 8 3 0 0 , 3 1 2 7 -> 3 0 4 7 , 3 4 3 1 -> 7 5 5 5 , 8 3 1 5 -> 8 7 2 7 , 7 6 4 7 ->= 8 8 7 5 , 3 4 8 7 ->= 8 8 8 7 , 8 7 5 5 ->= 8 8 7 5 , 3 1 5 5 ->= 8 3 0 1 , 3 1 2 8 -> 3 0 4 8 , 3 4 3 4 -> 7 5 5 2 , 8 3 1 2 -> 8 7 2 8 , 7 6 4 8 ->= 8 8 7 2 , 3 4 8 8 ->= 8 8 8 8 , 8 7 5 2 ->= 8 8 7 2 , 3 1 5 2 ->= 8 3 0 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 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 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, 6->6, 7->7, 8->8 }, it remains to prove termination of the 32-rule system { 0 1 2 3 -> 0 0 4 3 , 0 4 3 0 -> 1 5 5 6 , 4 3 1 6 -> 4 7 2 3 , 0 1 5 6 ->= 4 3 0 0 , 0 1 2 7 -> 0 0 4 7 , 0 4 3 1 -> 1 5 5 5 , 4 3 1 5 -> 4 7 2 7 , 0 1 5 5 ->= 4 3 0 1 , 0 1 2 8 -> 0 0 4 8 , 0 4 3 4 -> 1 5 5 2 , 1 6 4 8 ->= 4 8 7 2 , 0 1 5 2 ->= 4 3 0 4 , 6 1 2 3 -> 6 0 4 3 , 6 4 3 0 -> 5 5 5 6 , 2 3 1 6 -> 2 7 2 3 , 6 1 5 6 ->= 2 3 0 0 , 6 1 2 7 -> 6 0 4 7 , 6 4 3 1 -> 5 5 5 5 , 2 3 1 5 -> 2 7 2 7 , 6 1 5 5 ->= 2 3 0 1 , 6 1 2 8 -> 6 0 4 8 , 6 4 3 4 -> 5 5 5 2 , 5 6 4 8 ->= 2 8 7 2 , 6 1 5 2 ->= 2 3 0 4 , 3 1 2 3 -> 3 0 4 3 , 3 4 3 0 -> 7 5 5 6 , 8 3 1 6 -> 8 7 2 3 , 3 1 2 7 -> 3 0 4 7 , 3 4 3 1 -> 7 5 5 5 , 8 3 1 5 -> 8 7 2 7 , 3 1 2 8 -> 3 0 4 8 , 3 4 3 4 -> 7 5 5 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 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 1 | | 0 1 | \ / 6 is interpreted by / \ | 1 1 | | 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 -> 0 0 4 3 , 0 4 3 0 -> 1 5 5 6 , 0 1 5 6 ->= 4 3 0 0 , 0 1 2 7 -> 0 0 4 7 , 0 4 3 1 -> 1 5 5 5 , 0 1 5 5 ->= 4 3 0 1 , 0 1 2 8 -> 0 0 4 8 , 0 4 3 4 -> 1 5 5 2 , 0 1 5 2 ->= 4 3 0 4 , 6 1 2 3 -> 6 0 4 3 , 6 4 3 0 -> 5 5 5 6 , 6 1 5 6 ->= 2 3 0 0 , 6 1 2 7 -> 6 0 4 7 , 6 4 3 1 -> 5 5 5 5 , 6 1 5 5 ->= 2 3 0 1 , 6 1 2 8 -> 6 0 4 8 , 6 4 3 4 -> 5 5 5 2 , 6 1 5 2 ->= 2 3 0 4 , 3 1 2 3 -> 3 0 4 3 , 3 1 2 7 -> 3 0 4 7 , 3 1 2 8 -> 3 0 4 8 } 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 0 | | 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 1 | | 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 13-rule system { 0 1 2 3 -> 0 0 4 3 , 0 4 3 0 -> 1 5 5 6 , 0 1 2 7 -> 0 0 4 7 , 0 1 5 5 ->= 4 3 0 1 , 0 1 2 8 -> 0 0 4 8 , 0 4 3 4 -> 1 5 5 2 , 6 1 2 3 -> 6 0 4 3 , 6 1 2 7 -> 6 0 4 7 , 6 1 5 5 ->= 2 3 0 1 , 6 1 2 8 -> 6 0 4 8 , 3 1 2 3 -> 3 0 4 3 , 3 1 2 7 -> 3 0 4 7 , 3 1 2 8 -> 3 0 4 8 } 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 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 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 12-rule system { 0 1 2 3 -> 0 0 4 3 , 0 4 3 0 -> 1 5 5 6 , 0 1 2 7 -> 0 0 4 7 , 0 1 5 5 ->= 4 3 0 1 , 0 1 2 8 -> 0 0 4 8 , 0 4 3 4 -> 1 5 5 2 , 6 1 2 3 -> 6 0 4 3 , 6 1 2 7 -> 6 0 4 7 , 6 1 5 5 ->= 2 3 0 1 , 6 1 2 8 -> 6 0 4 8 , 3 1 2 3 -> 3 0 4 3 , 3 1 2 8 -> 3 0 4 8 } 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 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 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 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 11-rule system { 0 1 2 3 -> 0 0 4 3 , 0 4 3 0 -> 1 5 5 6 , 0 1 2 7 -> 0 0 4 7 , 0 1 5 5 ->= 4 3 0 1 , 0 1 2 8 -> 0 0 4 8 , 0 4 3 4 -> 1 5 5 2 , 6 1 2 3 -> 6 0 4 3 , 6 1 2 7 -> 6 0 4 7 , 6 1 5 5 ->= 2 3 0 1 , 6 1 2 8 -> 6 0 4 8 , 3 1 2 3 -> 3 0 4 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 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 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 1 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 10-rule system { 0 1 2 3 -> 0 0 4 3 , 0 4 3 0 -> 1 5 5 6 , 0 1 2 7 -> 0 0 4 7 , 0 1 5 5 ->= 4 3 0 1 , 0 1 2 8 -> 0 0 4 8 , 0 4 3 4 -> 1 5 5 2 , 6 1 2 3 -> 6 0 4 3 , 6 1 2 7 -> 6 0 4 7 , 6 1 5 5 ->= 2 3 0 1 , 6 1 2 8 -> 6 0 4 8 } 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 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 | \ / 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 1 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 1 | | 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 1 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 | \ / 5 is interpreted by / \ | 1 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 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 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, 8->7, 7->8 }, it remains to prove termination of the 9-rule system { 0 1 2 3 -> 0 0 4 3 , 0 4 3 0 -> 1 5 5 6 , 0 1 5 5 ->= 4 3 0 1 , 0 1 2 7 -> 0 0 4 7 , 0 4 3 4 -> 1 5 5 2 , 6 1 2 3 -> 6 0 4 3 , 6 1 2 8 -> 6 0 4 8 , 6 1 5 5 ->= 2 3 0 1 , 6 1 2 7 -> 6 0 4 7 } 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 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 | \ / 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 1 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 1 | | 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 1 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 | \ / 5 is interpreted by / \ | 1 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 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 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, 8->7, 7->8 }, it remains to prove termination of the 8-rule system { 0 1 2 3 -> 0 0 4 3 , 0 4 3 0 -> 1 5 5 6 , 0 1 5 5 ->= 4 3 0 1 , 0 4 3 4 -> 1 5 5 2 , 6 1 2 3 -> 6 0 4 3 , 6 1 2 7 -> 6 0 4 7 , 6 1 5 5 ->= 2 3 0 1 , 6 1 2 8 -> 6 0 4 8 } 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 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 | \ / 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 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 | \ / 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 1 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 | \ / 5 is interpreted by / \ | 1 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 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 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 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, 8->7 }, it remains to prove termination of the 7-rule system { 0 1 2 3 -> 0 0 4 3 , 0 4 3 0 -> 1 5 5 6 , 0 1 5 5 ->= 4 3 0 1 , 0 4 3 4 -> 1 5 5 2 , 6 1 2 3 -> 6 0 4 3 , 6 1 5 5 ->= 2 3 0 1 , 6 1 2 7 -> 6 0 4 7 } 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 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 | \ / 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 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 | \ / 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 1 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 | \ / 5 is interpreted by / \ | 1 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 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 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 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6 }, it remains to prove termination of the 6-rule system { 0 1 2 3 -> 0 0 4 3 , 0 4 3 0 -> 1 5 5 6 , 0 1 5 5 ->= 4 3 0 1 , 0 4 3 4 -> 1 5 5 2 , 6 1 2 3 -> 6 0 4 3 , 6 1 5 5 ->= 2 3 0 1 } 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 1 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 1 | | 0 1 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 2 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 1 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 1 0 1 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 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6 }, it remains to prove termination of the 4-rule system { 0 1 2 3 -> 0 0 4 3 , 0 4 3 0 -> 1 5 5 6 , 0 4 3 4 -> 1 5 5 2 , 6 1 2 3 -> 6 0 4 3 } 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 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 6->5 }, it remains to prove termination of the 2-rule system { 0 1 2 3 -> 0 0 4 3 , 5 1 2 3 -> 5 0 4 3 } 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 | \ / After renaming modulo { }, it remains to prove termination of the 0-rule system { } The system is trivially terminating.