/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Strip Symbols Proof [SOUND, 0 ms] (2) QTRS (3) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: b(a(b(a(a(a(x1)))))) -> a(a(a(b(a(b(a(b(a(x1))))))))) Q is empty. ---------------------------------------- (1) Strip Symbols Proof (SOUND) We were given the following TRS: b(a(b(a(a(a(x1)))))) -> a(a(a(b(a(b(a(b(a(x1))))))))) By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: b(a(b(a(a(x))))) -> a(a(a(b(a(b(a(b(x)))))))) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: b(a(b(a(a(x))))) -> a(a(a(b(a(b(a(b(x)))))))) Q is empty. ---------------------------------------- (3) RFCMatchBoundsTRSProof (EQUIVALENT) Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 4. This implies Q-termination of R. The following rules were used to construct the certificate: b(a(b(a(a(x))))) -> a(a(a(b(a(b(a(b(x)))))))) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 69, 70, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 243, 244, 245, 246, 247, 248, 249, 257, 258, 259, 260, 261, 262, 263, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291 Node 69 is start node and node 70 is final node. Those nodes are connected through the following edges: * 69 to 145 labelled a_1(0)* 70 to 70 labelled #_1(0)* 145 to 146 labelled a_1(0)* 146 to 147 labelled a_1(0)* 147 to 148 labelled b_1(0)* 147 to 159 labelled a_1(1)* 148 to 149 labelled a_1(0)* 149 to 150 labelled b_1(0)* 149 to 152 labelled a_1(1)* 150 to 151 labelled a_1(0)* 151 to 70 labelled b_1(0)* 151 to 152 labelled a_1(1)* 152 to 153 labelled a_1(1)* 153 to 154 labelled a_1(1)* 154 to 155 labelled b_1(1)* 154 to 215 labelled a_1(2)* 155 to 156 labelled a_1(1)* 156 to 157 labelled b_1(1)* 156 to 152 labelled a_1(1)* 157 to 158 labelled a_1(1)* 158 to 70 labelled b_1(1)* 158 to 152 labelled a_1(1)* 159 to 160 labelled a_1(1)* 160 to 161 labelled a_1(1)* 161 to 162 labelled b_1(1)* 162 to 163 labelled a_1(1)* 163 to 164 labelled b_1(1)* 163 to 222 labelled a_1(2)* 164 to 165 labelled a_1(1)* 165 to 152 labelled b_1(1)* 215 to 216 labelled a_1(2)* 216 to 217 labelled a_1(2)* 217 to 218 labelled b_1(2)* 218 to 219 labelled a_1(2)* 219 to 220 labelled b_1(2)* 219 to 222 labelled a_1(2)* 220 to 221 labelled a_1(2)* 221 to 152 labelled b_1(2)* 222 to 223 labelled a_1(2)* 223 to 224 labelled a_1(2)* 224 to 225 labelled b_1(2)* 225 to 226 labelled a_1(2)* 226 to 227 labelled b_1(2)* 226 to 243 labelled a_1(3)* 227 to 228 labelled a_1(2)* 228 to 154 labelled b_1(2)* 243 to 244 labelled a_1(3)* 244 to 245 labelled a_1(3)* 245 to 246 labelled b_1(3)* 245 to 271 labelled a_1(4)* 246 to 247 labelled a_1(3)* 247 to 248 labelled b_1(3)* 248 to 249 labelled a_1(3)* 249 to 216 labelled b_1(3)* 249 to 257 labelled a_1(3)* 257 to 258 labelled a_1(3)* 258 to 259 labelled a_1(3)* 259 to 260 labelled b_1(3)* 260 to 261 labelled a_1(3)* 261 to 262 labelled b_1(3)* 261 to 278 labelled a_1(3)* 262 to 263 labelled a_1(3)* 263 to 222 labelled b_1(3)* 271 to 272 labelled a_1(4)* 272 to 273 labelled a_1(4)* 273 to 274 labelled b_1(4)* 274 to 275 labelled a_1(4)* 275 to 276 labelled b_1(4)* 275 to 285 labelled a_1(4)* 276 to 277 labelled a_1(4)* 277 to 257 labelled b_1(4)* 278 to 279 labelled a_1(3)* 279 to 280 labelled a_1(3)* 280 to 281 labelled b_1(3)* 281 to 282 labelled a_1(3)* 282 to 283 labelled b_1(3)* 283 to 284 labelled a_1(3)* 284 to 224 labelled b_1(3)* 285 to 286 labelled a_1(4)* 286 to 287 labelled a_1(4)* 287 to 288 labelled b_1(4)* 288 to 289 labelled a_1(4)* 289 to 290 labelled b_1(4)* 290 to 291 labelled a_1(4)* 291 to 259 labelled b_1(4) ---------------------------------------- (4) YES