/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) Strip Symbols Proof [SOUND, 0 ms] (4) QTRS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: 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: 229, 230, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357 Node 229 is start node and node 230 is final node. Those nodes are connected through the following edges: * 229 to 314 labelled b_1(0)* 230 to 230 labelled #_1(0)* 314 to 315 labelled a_1(0)* 315 to 316 labelled a_1(0)* 316 to 317 labelled a_1(0)* 317 to 318 labelled a_1(0)* 318 to 319 labelled b_1(0)* 319 to 320 labelled b_1(0)* 320 to 321 labelled a_1(0)* 320 to 336 labelled b_1(1)* 321 to 322 labelled a_1(0)* 322 to 323 labelled a_1(0)* 322 to 325 labelled b_1(1)* 323 to 324 labelled a_1(0)* 324 to 230 labelled b_1(0)* 325 to 326 labelled a_1(1)* 326 to 327 labelled a_1(1)* 327 to 328 labelled a_1(1)* 328 to 329 labelled a_1(1)* 329 to 330 labelled b_1(1)* 330 to 331 labelled b_1(1)* 331 to 332 labelled a_1(1)* 331 to 347 labelled b_1(2)* 332 to 333 labelled a_1(1)* 333 to 334 labelled a_1(1)* 333 to 325 labelled b_1(1)* 334 to 335 labelled a_1(1)* 335 to 230 labelled b_1(1)* 336 to 337 labelled a_1(1)* 337 to 338 labelled a_1(1)* 338 to 339 labelled a_1(1)* 339 to 340 labelled a_1(1)* 340 to 341 labelled b_1(1)* 341 to 342 labelled b_1(1)* 342 to 343 labelled a_1(1)* 342 to 347 labelled b_1(2)* 343 to 344 labelled a_1(1)* 344 to 345 labelled a_1(1)* 344 to 325 labelled b_1(1)* 345 to 346 labelled a_1(1)* 346 to 331 labelled b_1(1)* 347 to 348 labelled a_1(2)* 348 to 349 labelled a_1(2)* 349 to 350 labelled a_1(2)* 350 to 351 labelled a_1(2)* 351 to 352 labelled b_1(2)* 352 to 353 labelled b_1(2)* 353 to 354 labelled a_1(2)* 353 to 347 labelled b_1(2)* 354 to 355 labelled a_1(2)* 355 to 356 labelled a_1(2)* 355 to 325 labelled b_1(1)* 356 to 357 labelled a_1(2)* 357 to 331 labelled b_1(2) ---------------------------------------- (6) YES