/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) Strip Symbols Proof [SOUND, 0 ms] (4) QTRS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(c(a(c(a(b(c(a(x1)))))))))) -> a(b(c(a(c(a(b(b(c(a(c(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(c(b(a(c(a(c(b(b(a(x1)))))))))) -> b(a(c(a(c(b(b(a(c(a(c(b(a(x1))))))))))))) Q is empty. ---------------------------------------- (3) Strip Symbols Proof (SOUND) We were given the following TRS: a(c(b(a(c(a(c(b(b(a(x1)))))))))) -> b(a(c(a(c(b(b(a(c(a(c(b(a(x1))))))))))))) By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: a(c(b(a(c(a(c(b(b(x))))))))) -> b(a(c(a(c(b(b(a(c(a(c(b(x)))))))))))) ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(c(b(a(c(a(c(b(b(x))))))))) -> b(a(c(a(c(b(b(a(c(a(c(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(c(b(a(c(a(c(b(b(x))))))))) -> b(a(c(a(c(b(b(a(c(a(c(b(x)))))))))))) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 383, 384, 385, 386, 387, 388, 389, 390, 391, 392, 393, 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, 427, 428 Node 383 is start node and node 384 is final node. Those nodes are connected through the following edges: * 383 to 385 labelled b_1(0)* 384 to 384 labelled #_1(0)* 385 to 386 labelled a_1(0)* 386 to 387 labelled c_1(0)* 387 to 388 labelled a_1(0)* 388 to 389 labelled c_1(0)* 389 to 390 labelled b_1(0)* 390 to 391 labelled b_1(0)* 391 to 392 labelled a_1(0)* 391 to 407 labelled b_1(1)* 392 to 393 labelled c_1(0)* 393 to 394 labelled a_1(0)* 393 to 396 labelled b_1(1)* 394 to 395 labelled c_1(0)* 395 to 384 labelled b_1(0)* 396 to 397 labelled a_1(1)* 397 to 398 labelled c_1(1)* 398 to 399 labelled a_1(1)* 399 to 400 labelled c_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 418 labelled b_1(2)* 403 to 404 labelled c_1(1)* 404 to 405 labelled a_1(1)* 404 to 396 labelled b_1(1)* 405 to 406 labelled c_1(1)* 406 to 384 labelled b_1(1)* 407 to 408 labelled a_1(1)* 408 to 409 labelled c_1(1)* 409 to 410 labelled a_1(1)* 410 to 411 labelled c_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 418 labelled b_1(2)* 414 to 415 labelled c_1(1)* 415 to 416 labelled a_1(1)* 415 to 396 labelled b_1(1)* 416 to 417 labelled c_1(1)* 417 to 402 labelled b_1(1)* 418 to 419 labelled a_1(2)* 419 to 420 labelled c_1(2)* 420 to 421 labelled a_1(2)* 421 to 422 labelled c_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 418 labelled b_1(2)* 425 to 426 labelled c_1(2)* 426 to 427 labelled a_1(2)* 426 to 396 labelled b_1(1)* 427 to 428 labelled c_1(2)* 428 to 402 labelled b_1(2) ---------------------------------------- (6) YES