/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) Strip Symbols Proof [SOUND, 0 ms] (4)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, 6 ms] (6) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(b(b(a(a(a(a(b(a(a(x1)))))))))) -> a(b(a(a(a(a(b(b(a(a(a(a(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: a(a(b(a(a(a(a(b(b(a(x1)))))))))) -> b(a(a(a(a(b(b(a(a(a(a(b(a(x1))))))))))))) Q is empty. ---------------------------------------- (3) Strip Symbols Proof (SOUND) We were given the following TRS: a(a(b(a(a(a(a(b(b(a(x1)))))))))) -> b(a(a(a(a(b(b(a(a(a(a(b(a(x1))))))))))))) By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: a(a(b(a(a(a(a(b(b(x))))))))) -> b(a(a(a(a(b(b(a(a(a(a(b(x)))))))))))) ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(a(b(a(a(a(a(b(b(x))))))))) -> b(a(a(a(a(b(b(a(a(a(a(b(x)))))))))))) 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(a(b(a(a(a(a(b(b(x))))))))) -> b(a(a(a(a(b(b(a(a(a(a(b(x)))))))))))) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239 Node 194 is start node and node 195 is final node. Those nodes are connected through the following edges: * 194 to 196 labelled b_1(0)* 195 to 195 labelled #_1(0)* 196 to 197 labelled a_1(0)* 197 to 198 labelled a_1(0)* 198 to 199 labelled a_1(0)* 199 to 200 labelled a_1(0)* 200 to 201 labelled b_1(0)* 201 to 202 labelled b_1(0)* 202 to 203 labelled a_1(0)* 202 to 218 labelled b_1(1)* 203 to 204 labelled a_1(0)* 204 to 205 labelled a_1(0)* 204 to 207 labelled b_1(1)* 205 to 206 labelled a_1(0)* 206 to 195 labelled b_1(0)* 207 to 208 labelled a_1(1)* 208 to 209 labelled a_1(1)* 209 to 210 labelled a_1(1)* 210 to 211 labelled a_1(1)* 211 to 212 labelled b_1(1)* 212 to 213 labelled b_1(1)* 213 to 214 labelled a_1(1)* 213 to 229 labelled b_1(2)* 214 to 215 labelled a_1(1)* 215 to 216 labelled a_1(1)* 215 to 207 labelled b_1(1)* 216 to 217 labelled a_1(1)* 217 to 195 labelled b_1(1)* 218 to 219 labelled a_1(1)* 219 to 220 labelled a_1(1)* 220 to 221 labelled a_1(1)* 221 to 222 labelled a_1(1)* 222 to 223 labelled b_1(1)* 223 to 224 labelled b_1(1)* 224 to 225 labelled a_1(1)* 224 to 229 labelled b_1(2)* 225 to 226 labelled a_1(1)* 226 to 227 labelled a_1(1)* 226 to 207 labelled b_1(1)* 227 to 228 labelled a_1(1)* 228 to 213 labelled b_1(1)* 229 to 230 labelled a_1(2)* 230 to 231 labelled a_1(2)* 231 to 232 labelled a_1(2)* 232 to 233 labelled a_1(2)* 233 to 234 labelled b_1(2)* 234 to 235 labelled b_1(2)* 235 to 236 labelled a_1(2)* 235 to 229 labelled b_1(2)* 236 to 237 labelled a_1(2)* 237 to 238 labelled a_1(2)* 237 to 207 labelled b_1(1)* 238 to 239 labelled a_1(2)* 239 to 213 labelled b_1(2) ---------------------------------------- (6) YES