/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) Strip Symbols Proof [SOUND, 0 ms] (4) QTRS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(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: 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 394, 395, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423, 424, 425, 426 Node 336 is start node and node 337 is final node. Those nodes are connected through the following edges: * 336 to 338 labelled b_1(0)* 337 to 337 labelled #_1(0)* 338 to 339 labelled a_1(0)* 339 to 340 labelled a_1(0)* 340 to 341 labelled b_1(0)* 341 to 342 labelled b_1(0)* 342 to 343 labelled a_1(0)* 343 to 344 labelled a_1(0)* 344 to 345 labelled b_1(0)* 345 to 346 labelled b_1(0)* 346 to 347 labelled a_1(0)* 346 to 405 labelled b_1(1)* 347 to 348 labelled a_1(0)* 347 to 394 labelled b_1(1)* 348 to 337 labelled b_1(0)* 394 to 395 labelled a_1(1)* 395 to 396 labelled a_1(1)* 396 to 397 labelled b_1(1)* 397 to 398 labelled b_1(1)* 398 to 399 labelled a_1(1)* 399 to 400 labelled a_1(1)* 400 to 401 labelled b_1(1)* 401 to 402 labelled b_1(1)* 402 to 403 labelled a_1(1)* 402 to 416 labelled b_1(2)* 403 to 404 labelled a_1(1)* 403 to 394 labelled b_1(1)* 404 to 337 labelled b_1(1)* 405 to 406 labelled a_1(1)* 406 to 407 labelled a_1(1)* 407 to 408 labelled b_1(1)* 408 to 409 labelled b_1(1)* 409 to 410 labelled a_1(1)* 410 to 411 labelled a_1(1)* 411 to 412 labelled b_1(1)* 412 to 413 labelled b_1(1)* 413 to 414 labelled a_1(1)* 413 to 416 labelled b_1(2)* 414 to 415 labelled a_1(1)* 414 to 394 labelled b_1(1)* 415 to 402 labelled b_1(1)* 416 to 417 labelled a_1(2)* 417 to 418 labelled a_1(2)* 418 to 419 labelled b_1(2)* 419 to 420 labelled b_1(2)* 420 to 421 labelled a_1(2)* 421 to 422 labelled a_1(2)* 422 to 423 labelled b_1(2)* 423 to 424 labelled b_1(2)* 424 to 425 labelled a_1(2)* 424 to 416 labelled b_1(2)* 425 to 426 labelled a_1(2)* 425 to 394 labelled b_1(1)* 426 to 402 labelled b_1(2) ---------------------------------------- (6) YES