/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) Strip Symbols Proof [SOUND, 0 ms] (4)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, 1 ms] (6) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(b(b(a(a(b(b(a(a(b(a(x1))))))))))) -> a(b(a(a(b(b(a(a(b(b(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(b(a(a(b(b(a(a(b(b(a(x1))))))))))) -> b(a(a(b(b(a(a(b(b(a(a(b(a(x1))))))))))))) Q is empty. ---------------------------------------- (3) Strip Symbols Proof (SOUND) We were given the following TRS: a(b(a(a(b(b(a(a(b(b(a(x1))))))))))) -> b(a(a(b(b(a(a(b(b(a(a(b(a(x1))))))))))))) By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: a(b(a(a(b(b(a(a(b(b(x)))))))))) -> b(a(a(b(b(a(a(b(b(a(a(b(x)))))))))))) ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(b(a(a(b(b(a(a(b(b(x)))))))))) -> b(a(a(b(b(a(a(b(b(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(b(a(a(b(b(a(a(b(b(x)))))))))) -> b(a(a(b(b(a(a(b(b(a(a(b(x)))))))))))) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 196, 197, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264 Node 196 is start node and node 197 is final node. Those nodes are connected through the following edges: * 196 to 209 labelled b_1(0)* 197 to 197 labelled #_1(0)* 209 to 210 labelled a_1(0)* 210 to 211 labelled a_1(0)* 211 to 212 labelled b_1(0)* 212 to 213 labelled b_1(0)* 213 to 214 labelled a_1(0)* 214 to 215 labelled a_1(0)* 215 to 216 labelled b_1(0)* 216 to 217 labelled b_1(0)* 217 to 218 labelled a_1(0)* 217 to 243 labelled b_1(1)* 218 to 219 labelled a_1(0)* 218 to 220 labelled b_1(1)* 219 to 197 labelled b_1(0)* 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)* 225 to 226 labelled a_1(1)* 226 to 227 labelled b_1(1)* 227 to 228 labelled b_1(1)* 228 to 229 labelled a_1(1)* 228 to 254 labelled b_1(2)* 229 to 230 labelled a_1(1)* 229 to 220 labelled b_1(1)* 230 to 197 labelled b_1(1)* 243 to 244 labelled a_1(1)* 244 to 245 labelled a_1(1)* 245 to 246 labelled b_1(1)* 246 to 247 labelled b_1(1)* 247 to 248 labelled a_1(1)* 248 to 249 labelled a_1(1)* 249 to 250 labelled b_1(1)* 250 to 251 labelled b_1(1)* 251 to 252 labelled a_1(1)* 251 to 254 labelled b_1(2)* 252 to 253 labelled a_1(1)* 252 to 220 labelled b_1(1)* 253 to 228 labelled b_1(1)* 254 to 255 labelled a_1(2)* 255 to 256 labelled a_1(2)* 256 to 257 labelled b_1(2)* 257 to 258 labelled b_1(2)* 258 to 259 labelled a_1(2)* 259 to 260 labelled a_1(2)* 260 to 261 labelled b_1(2)* 261 to 262 labelled b_1(2)* 262 to 263 labelled a_1(2)* 262 to 254 labelled b_1(2)* 263 to 264 labelled a_1(2)* 263 to 220 labelled b_1(1)* 264 to 228 labelled b_1(2) ---------------------------------------- (6) YES