/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Strip Symbols Proof [SOUND, 0 ms] (2) QTRS (3) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]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(a(b(b(a(a(a(a(b(x1)))))))))) -> a(a(b(b(a(a(a(a(b(b(a(a(b(x1))))))))))))) Q is empty. ---------------------------------------- (1) Strip Symbols Proof (SOUND) We were given the following TRS: b(a(a(b(b(a(a(a(a(b(x1)))))))))) -> a(a(b(b(a(a(a(a(b(b(a(a(b(x1))))))))))))) By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: b(a(a(b(b(a(a(a(a(x))))))))) -> a(a(b(b(a(a(a(a(b(b(a(a(x)))))))))))) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: b(a(a(b(b(a(a(a(a(x))))))))) -> a(a(b(b(a(a(a(a(b(b(a(a(x)))))))))))) Q is empty. ---------------------------------------- (3) 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: b(a(a(b(b(a(a(a(a(x))))))))) -> a(a(b(b(a(a(a(a(b(b(a(a(x)))))))))))) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 197, 198, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292 Node 197 is start node and node 198 is final node. Those nodes are connected through the following edges: * 197 to 247 labelled a_1(0)* 198 to 198 labelled #_1(0)* 247 to 248 labelled a_1(0)* 248 to 249 labelled b_1(0)* 249 to 250 labelled b_1(0)* 250 to 251 labelled a_1(0)* 251 to 252 labelled a_1(0)* 252 to 253 labelled a_1(0)* 253 to 254 labelled a_1(0)* 254 to 255 labelled b_1(0)* 254 to 271 labelled a_1(1)* 255 to 256 labelled b_1(0)* 255 to 258 labelled a_1(1)* 256 to 257 labelled a_1(0)* 257 to 198 labelled a_1(0)* 258 to 259 labelled a_1(1)* 259 to 260 labelled b_1(1)* 260 to 261 labelled b_1(1)* 261 to 262 labelled a_1(1)* 262 to 263 labelled a_1(1)* 263 to 264 labelled a_1(1)* 264 to 265 labelled a_1(1)* 265 to 266 labelled b_1(1)* 265 to 282 labelled a_1(2)* 266 to 267 labelled b_1(1)* 266 to 258 labelled a_1(1)* 267 to 268 labelled a_1(1)* 268 to 198 labelled a_1(1)* 271 to 272 labelled a_1(1)* 272 to 273 labelled b_1(1)* 273 to 274 labelled b_1(1)* 274 to 275 labelled a_1(1)* 275 to 276 labelled a_1(1)* 276 to 277 labelled a_1(1)* 277 to 278 labelled a_1(1)* 278 to 279 labelled b_1(1)* 278 to 282 labelled a_1(2)* 279 to 280 labelled b_1(1)* 279 to 258 labelled a_1(1)* 280 to 281 labelled a_1(1)* 281 to 265 labelled a_1(1)* 282 to 283 labelled a_1(2)* 283 to 284 labelled b_1(2)* 284 to 285 labelled b_1(2)* 285 to 286 labelled a_1(2)* 286 to 287 labelled a_1(2)* 287 to 288 labelled a_1(2)* 288 to 289 labelled a_1(2)* 289 to 290 labelled b_1(2)* 289 to 282 labelled a_1(2)* 290 to 291 labelled b_1(2)* 290 to 258 labelled a_1(1)* 291 to 292 labelled a_1(2)* 292 to 265 labelled a_1(2) ---------------------------------------- (4) YES