/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) Strip Symbols Proof [SOUND, 0 ms] (4) QTRS (5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: b(b(b(a(b(a(b(b(a(b(x1)))))))))) -> b(b(a(b(a(b(b(b(a(b(a(b(b(x1))))))))))))) Q is empty. ---------------------------------------- (1) QTRS Reverse (EQUIVALENT) We applied the QTRS Reverse Processor [REVERSE]. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: b(a(b(b(a(b(a(b(b(b(x1)))))))))) -> b(b(a(b(a(b(b(b(a(b(a(b(b(x1))))))))))))) Q is empty. ---------------------------------------- (3) Strip Symbols Proof (SOUND) We were given the following TRS: b(a(b(b(a(b(a(b(b(b(x1)))))))))) -> b(b(a(b(a(b(b(b(a(b(a(b(b(x1))))))))))))) By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: a(b(b(a(b(a(b(b(b(x1))))))))) -> b(a(b(a(b(b(b(a(b(a(b(b(x1)))))))))))) ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(b(b(a(b(a(b(b(b(x1))))))))) -> b(a(b(a(b(b(b(a(b(a(b(b(x1)))))))))))) Q is empty. ---------------------------------------- (5) RFCMatchBoundsTRSProof (EQUIVALENT) Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R. The following rules were used to construct the certificate: a(b(b(a(b(a(b(b(b(x1))))))))) -> b(a(b(a(b(b(b(a(b(a(b(b(x1)))))))))))) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 125, 126, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 161, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194 Node 125 is start node and node 126 is final node. Those nodes are connected through the following edges: * 125 to 140 labelled b_1(0)* 126 to 126 labelled #_1(0)* 140 to 141 labelled a_1(0)* 141 to 142 labelled b_1(0)* 142 to 143 labelled a_1(0)* 143 to 144 labelled b_1(0)* 144 to 145 labelled b_1(0)* 145 to 146 labelled b_1(0)* 146 to 147 labelled a_1(0)* 146 to 173 labelled b_1(1)* 147 to 148 labelled b_1(0)* 148 to 149 labelled a_1(0)* 148 to 161 labelled b_1(1)* 149 to 150 labelled b_1(0)* 150 to 126 labelled b_1(0)* 161 to 163 labelled a_1(1)* 163 to 164 labelled b_1(1)* 164 to 165 labelled a_1(1)* 165 to 166 labelled b_1(1)* 166 to 167 labelled b_1(1)* 167 to 168 labelled b_1(1)* 168 to 169 labelled a_1(1)* 168 to 184 labelled b_1(2)* 169 to 170 labelled b_1(1)* 170 to 171 labelled a_1(1)* 170 to 161 labelled b_1(1)* 171 to 172 labelled b_1(1)* 172 to 126 labelled b_1(1)* 173 to 174 labelled a_1(1)* 174 to 175 labelled b_1(1)* 175 to 176 labelled a_1(1)* 176 to 177 labelled b_1(1)* 177 to 178 labelled b_1(1)* 178 to 179 labelled b_1(1)* 179 to 180 labelled a_1(1)* 179 to 184 labelled b_1(2)* 180 to 181 labelled b_1(1)* 181 to 182 labelled a_1(1)* 181 to 161 labelled b_1(1)* 182 to 183 labelled b_1(1)* 183 to 168 labelled b_1(1)* 184 to 185 labelled a_1(2)* 185 to 186 labelled b_1(2)* 186 to 187 labelled a_1(2)* 187 to 188 labelled b_1(2)* 188 to 189 labelled b_1(2)* 189 to 190 labelled b_1(2)* 190 to 191 labelled a_1(2)* 190 to 184 labelled b_1(2)* 191 to 192 labelled b_1(2)* 192 to 193 labelled a_1(2)* 192 to 161 labelled b_1(1)* 193 to 194 labelled b_1(2)* 194 to 168 labelled b_1(2) ---------------------------------------- (6) YES