/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES After renaming modulo { c->0, a->1, b->2 }, it remains to prove termination of the 5-rule system { 0 0 1 -> 0 0 2 , 2 2 0 -> 1 1 2 , 2 1 2 ->= 1 0 2 , 0 1 1 ->= 2 1 2 , 0 0 0 ->= 0 1 0 } The system was reversed. After renaming modulo { 1->0, 0->1, 2->2 }, it remains to prove termination of the 5-rule system { 0 1 1 -> 2 1 1 , 1 2 2 -> 2 0 0 , 2 0 2 ->= 2 1 0 , 0 0 1 ->= 2 0 2 , 1 1 1 ->= 1 0 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: 0 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 1 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2 }, it remains to prove termination of the 4-rule system { 0 1 1 -> 2 1 1 , 1 2 2 -> 2 0 0 , 2 0 2 ->= 2 1 0 , 0 0 1 ->= 2 0 2 } Applying context closure of depth 1 in the following form: System R over Sigma maps to { fold(xly) -> fold(xry) | l -> r in R, x,y in Sigma } over Sigma^2, where fold(a_1...a_n) = (a_1,a_2)...(a_{n-1},a_{n}) After renaming modulo { [0, 0]->0, [0, 1]->1, [1, 1]->2, [1, 0]->3, [0, 2]->4, [2, 1]->5, [1, 2]->6, [2, 2]->7, [2, 0]->8 }, it remains to prove termination of the 36-rule system { 0 1 2 3 -> 4 5 2 3 , 1 6 7 8 -> 4 8 0 0 , 4 8 4 8 ->= 4 5 3 0 , 0 0 1 3 ->= 4 8 4 8 , 0 1 2 2 -> 4 5 2 2 , 1 6 7 5 -> 4 8 0 1 , 4 8 4 5 ->= 4 5 3 1 , 0 0 1 2 ->= 4 8 4 5 , 0 1 2 6 -> 4 5 2 6 , 1 6 7 7 -> 4 8 0 4 , 4 8 4 7 ->= 4 5 3 4 , 0 0 1 6 ->= 4 8 4 7 , 3 1 2 3 -> 6 5 2 3 , 2 6 7 8 -> 6 8 0 0 , 6 8 4 8 ->= 6 5 3 0 , 3 0 1 3 ->= 6 8 4 8 , 3 1 2 2 -> 6 5 2 2 , 2 6 7 5 -> 6 8 0 1 , 6 8 4 5 ->= 6 5 3 1 , 3 0 1 2 ->= 6 8 4 5 , 3 1 2 6 -> 6 5 2 6 , 2 6 7 7 -> 6 8 0 4 , 6 8 4 7 ->= 6 5 3 4 , 3 0 1 6 ->= 6 8 4 7 , 8 1 2 3 -> 7 5 2 3 , 5 6 7 8 -> 7 8 0 0 , 7 8 4 8 ->= 7 5 3 0 , 8 0 1 3 ->= 7 8 4 8 , 8 1 2 2 -> 7 5 2 2 , 5 6 7 5 -> 7 8 0 1 , 7 8 4 5 ->= 7 5 3 1 , 8 0 1 2 ->= 7 8 4 5 , 8 1 2 6 -> 7 5 2 6 , 5 6 7 7 -> 7 8 0 4 , 7 8 4 7 ->= 7 5 3 4 , 8 0 1 6 ->= 7 8 4 7 } 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 0 | | 0 1 | \ / 2 is interpreted by / \ | 1 1 | | 0 1 | \ / 3 is interpreted by / \ | 1 0 | | 0 1 | \ / 4 is interpreted by / \ | 1 0 | | 0 1 | \ / 5 is interpreted by / \ | 1 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 30-rule system { 0 1 2 3 -> 4 5 2 3 , 1 6 7 8 -> 4 8 0 0 , 4 8 4 8 ->= 4 5 3 0 , 0 0 1 3 ->= 4 8 4 8 , 0 1 2 2 -> 4 5 2 2 , 1 6 7 5 -> 4 8 0 1 , 4 8 4 5 ->= 4 5 3 1 , 0 1 2 6 -> 4 5 2 6 , 1 6 7 7 -> 4 8 0 4 , 4 8 4 7 ->= 4 5 3 4 , 0 0 1 6 ->= 4 8 4 7 , 3 1 2 3 -> 6 5 2 3 , 6 8 4 8 ->= 6 5 3 0 , 3 0 1 3 ->= 6 8 4 8 , 3 1 2 2 -> 6 5 2 2 , 6 8 4 5 ->= 6 5 3 1 , 3 1 2 6 -> 6 5 2 6 , 6 8 4 7 ->= 6 5 3 4 , 3 0 1 6 ->= 6 8 4 7 , 8 1 2 3 -> 7 5 2 3 , 5 6 7 8 -> 7 8 0 0 , 7 8 4 8 ->= 7 5 3 0 , 8 0 1 3 ->= 7 8 4 8 , 8 1 2 2 -> 7 5 2 2 , 5 6 7 5 -> 7 8 0 1 , 7 8 4 5 ->= 7 5 3 1 , 8 1 2 6 -> 7 5 2 6 , 5 6 7 7 -> 7 8 0 4 , 7 8 4 7 ->= 7 5 3 4 , 8 0 1 6 ->= 7 8 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 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 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 | \ / 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 1 0 0 0 0 1 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 0 0 0 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 1 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 0 | | 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 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 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 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 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 | \ / 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 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 | \ / 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 1 0 0 | | 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 2 3 -> 4 5 2 3 , 1 6 7 8 -> 4 8 0 0 , 4 8 4 8 ->= 4 5 3 0 , 0 0 1 3 ->= 4 8 4 8 , 0 1 2 2 -> 4 5 2 2 , 1 6 7 5 -> 4 8 0 1 , 4 8 4 5 ->= 4 5 3 1 , 0 1 2 6 -> 4 5 2 6 , 1 6 7 7 -> 4 8 0 4 , 4 8 4 7 ->= 4 5 3 4 , 0 0 1 6 ->= 4 8 4 7 , 3 1 2 3 -> 6 5 2 3 , 6 8 4 8 ->= 6 5 3 0 , 3 0 1 3 ->= 6 8 4 8 , 3 1 2 2 -> 6 5 2 2 , 6 8 4 5 ->= 6 5 3 1 , 3 1 2 6 -> 6 5 2 6 , 6 8 4 7 ->= 6 5 3 4 , 3 0 1 6 ->= 6 8 4 7 , 8 1 2 3 -> 7 5 2 3 , 7 8 4 8 ->= 7 5 3 0 , 8 0 1 3 ->= 7 8 4 8 , 8 1 2 2 -> 7 5 2 2 , 7 8 4 5 ->= 7 5 3 1 , 8 1 2 6 -> 7 5 2 6 , 7 8 4 7 ->= 7 5 3 4 , 8 0 1 6 ->= 7 8 4 7 } 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 1 | | 0 1 | \ / 5 is interpreted by / \ | 1 0 | | 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 { 1->0, 6->1, 7->2, 8->3, 4->4, 0->5, 5->6, 3->7, 2->8 }, it remains to prove termination of the 18-rule system { 0 1 2 3 -> 4 3 5 5 , 4 3 4 3 ->= 4 6 7 5 , 0 1 2 6 -> 4 3 5 0 , 4 3 4 6 ->= 4 6 7 0 , 7 0 8 7 -> 1 6 8 7 , 1 3 4 3 ->= 1 6 7 5 , 7 5 0 7 ->= 1 3 4 3 , 7 0 8 8 -> 1 6 8 8 , 1 3 4 6 ->= 1 6 7 0 , 7 0 8 1 -> 1 6 8 1 , 7 5 0 1 ->= 1 3 4 2 , 3 0 8 7 -> 2 6 8 7 , 2 3 4 3 ->= 2 6 7 5 , 3 5 0 7 ->= 2 3 4 3 , 3 0 8 8 -> 2 6 8 8 , 2 3 4 6 ->= 2 6 7 0 , 3 0 8 1 -> 2 6 8 1 , 3 5 0 1 ->= 2 3 4 2 } 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 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 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 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 | \ / 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 0 0 | | 0 0 0 0 0 0 1 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 1 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 1 0 0 0 0 | \ / 7 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 1 0 0 0 0 0 0 | | 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 | | 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 17-rule system { 0 1 2 3 -> 4 3 5 5 , 4 3 4 3 ->= 4 6 7 5 , 0 1 2 6 -> 4 3 5 0 , 4 3 4 6 ->= 4 6 7 0 , 1 3 4 3 ->= 1 6 7 5 , 7 5 0 7 ->= 1 3 4 3 , 7 0 8 8 -> 1 6 8 8 , 1 3 4 6 ->= 1 6 7 0 , 7 0 8 1 -> 1 6 8 1 , 7 5 0 1 ->= 1 3 4 2 , 3 0 8 7 -> 2 6 8 7 , 2 3 4 3 ->= 2 6 7 5 , 3 5 0 7 ->= 2 3 4 3 , 3 0 8 8 -> 2 6 8 8 , 2 3 4 6 ->= 2 6 7 0 , 3 0 8 1 -> 2 6 8 1 , 3 5 0 1 ->= 2 3 4 2 } 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 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 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 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 | \ / 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 0 0 | | 0 0 0 0 0 0 1 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 1 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 1 0 0 0 0 | \ / 7 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 | \ / 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 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 | \ / 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 -> 4 3 5 5 , 4 3 4 3 ->= 4 6 7 5 , 0 1 2 6 -> 4 3 5 0 , 4 3 4 6 ->= 4 6 7 0 , 1 3 4 3 ->= 1 6 7 5 , 7 5 0 7 ->= 1 3 4 3 , 1 3 4 6 ->= 1 6 7 0 , 7 0 8 1 -> 1 6 8 1 , 7 5 0 1 ->= 1 3 4 2 , 3 0 8 7 -> 2 6 8 7 , 2 3 4 3 ->= 2 6 7 5 , 3 5 0 7 ->= 2 3 4 3 , 3 0 8 8 -> 2 6 8 8 , 2 3 4 6 ->= 2 6 7 0 , 3 0 8 1 -> 2 6 8 1 , 3 5 0 1 ->= 2 3 4 2 } 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 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 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 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 | \ / 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 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 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 1 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 1 0 0 0 0 | \ / 7 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 | \ / 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 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 | \ / 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 15-rule system { 0 1 2 3 -> 4 3 5 5 , 4 3 4 3 ->= 4 6 7 5 , 0 1 2 6 -> 4 3 5 0 , 4 3 4 6 ->= 4 6 7 0 , 1 3 4 3 ->= 1 6 7 5 , 7 5 0 7 ->= 1 3 4 3 , 1 3 4 6 ->= 1 6 7 0 , 7 0 8 1 -> 1 6 8 1 , 7 5 0 1 ->= 1 3 4 2 , 3 0 8 7 -> 2 6 8 7 , 2 3 4 3 ->= 2 6 7 5 , 3 5 0 7 ->= 2 3 4 3 , 2 3 4 6 ->= 2 6 7 0 , 3 0 8 1 -> 2 6 8 1 , 3 5 0 1 ->= 2 3 4 2 } 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 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 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 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 | \ / 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 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 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 1 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 1 0 0 0 0 | \ / 7 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 1 0 0 0 0 0 0 | | 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 | | 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 14-rule system { 0 1 2 3 -> 4 3 5 5 , 4 3 4 3 ->= 4 6 7 5 , 0 1 2 6 -> 4 3 5 0 , 4 3 4 6 ->= 4 6 7 0 , 1 3 4 3 ->= 1 6 7 5 , 7 5 0 7 ->= 1 3 4 3 , 1 3 4 6 ->= 1 6 7 0 , 7 0 8 1 -> 1 6 8 1 , 7 5 0 1 ->= 1 3 4 2 , 2 3 4 3 ->= 2 6 7 5 , 3 5 0 7 ->= 2 3 4 3 , 2 3 4 6 ->= 2 6 7 0 , 3 0 8 1 -> 2 6 8 1 , 3 5 0 1 ->= 2 3 4 2 } 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 1 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 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 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 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 1 0 0 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 1 0 0 0 0 0 0 | \ / 4 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 1 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 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 1 0 0 0 0 0 0 | | 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 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 | \ / 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, 7->7, 8->8 }, it remains to prove termination of the 13-rule system { 0 1 2 3 -> 4 3 5 5 , 4 3 4 3 ->= 4 6 7 5 , 0 1 2 6 -> 4 3 5 0 , 1 3 4 3 ->= 1 6 7 5 , 7 5 0 7 ->= 1 3 4 3 , 1 3 4 6 ->= 1 6 7 0 , 7 0 8 1 -> 1 6 8 1 , 7 5 0 1 ->= 1 3 4 2 , 2 3 4 3 ->= 2 6 7 5 , 3 5 0 7 ->= 2 3 4 3 , 2 3 4 6 ->= 2 6 7 0 , 3 0 8 1 -> 2 6 8 1 , 3 5 0 1 ->= 2 3 4 2 } 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 1 0 0 0 | | 0 1 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 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 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 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 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 { 4->0, 3->1, 6->2, 7->3, 5->4, 0->5, 1->6, 2->7 }, it remains to prove termination of the 6-rule system { 0 1 0 1 ->= 0 2 3 4 , 5 6 7 2 -> 0 1 4 5 , 3 4 5 3 ->= 6 1 0 1 , 6 1 0 2 ->= 6 2 3 5 , 1 4 5 3 ->= 7 1 0 1 , 7 1 0 2 ->= 7 2 3 5 } 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 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 | \ / 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 1 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 1 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 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 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 1 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 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 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 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 | | 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 0 0 0 0 0 0 0 | | 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 }, it remains to prove termination of the 5-rule system { 0 1 0 1 ->= 0 2 3 4 , 5 6 7 2 -> 0 1 4 5 , 6 1 0 2 ->= 6 2 3 5 , 1 4 5 3 ->= 7 1 0 1 , 7 1 0 2 ->= 7 2 3 5 } 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 0 | | 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 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 6->5, 5->6, 7->7 }, it remains to prove termination of the 4-rule system { 0 1 0 1 ->= 0 2 3 4 , 5 1 0 2 ->= 5 2 3 6 , 1 4 6 3 ->= 7 1 0 1 , 7 1 0 2 ->= 7 2 3 6 } The system is trivially terminating.