YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) Strip Symbols Proof [SOUND, 0 ms] (4)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(a(a(a(a(a(b(a(a(x1)))))))))) -> a(a(a(a(a(b(a(b(a(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(a(b(a(x1)))))))))) -> b(a(a(a(a(a(b(a(b(a(a(a(a(a(x1)))))))))))))) Q is empty. ---------------------------------------- (3) Strip Symbols Proof (SOUND) We were given the following TRS: a(a(b(a(a(a(a(a(b(a(x1)))))))))) -> b(a(a(a(a(a(b(a(b(a(a(a(a(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(a(b(x))))))))) -> b(a(a(a(a(a(b(a(b(a(a(a(a(x))))))))))))) ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(a(b(a(a(a(a(a(b(x))))))))) -> b(a(a(a(a(a(b(a(b(a(a(a(a(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(a(b(x))))))))) -> b(a(a(a(a(a(b(a(b(a(a(a(a(x))))))))))))) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 377, 378, 466, 467, 468, 469, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511, 512, 513, 526, 527, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537 Node 377 is start node and node 378 is final node. Those nodes are connected through the following edges: * 377 to 466 labelled b_1(0)* 378 to 378 labelled #_1(0)* 466 to 467 labelled a_1(0)* 467 to 468 labelled a_1(0)* 468 to 469 labelled a_1(0)* 469 to 470 labelled a_1(0)* 470 to 471 labelled a_1(0)* 471 to 472 labelled b_1(0)* 472 to 473 labelled a_1(0)* 473 to 474 labelled b_1(0)* 474 to 475 labelled a_1(0)* 474 to 502 labelled b_1(1)* 475 to 476 labelled a_1(0)* 475 to 502 labelled b_1(1)* 476 to 477 labelled a_1(0)* 476 to 478 labelled b_1(1)* 477 to 378 labelled a_1(0)* 477 to 478 labelled b_1(1)* 478 to 479 labelled a_1(1)* 479 to 480 labelled a_1(1)* 480 to 481 labelled a_1(1)* 481 to 482 labelled a_1(1)* 482 to 483 labelled a_1(1)* 483 to 484 labelled b_1(1)* 484 to 485 labelled a_1(1)* 485 to 486 labelled b_1(1)* 486 to 487 labelled a_1(1)* 486 to 526 labelled b_1(2)* 487 to 488 labelled a_1(1)* 487 to 526 labelled b_1(2)* 488 to 489 labelled a_1(1)* 488 to 478 labelled b_1(1)* 489 to 378 labelled a_1(1)* 489 to 478 labelled b_1(1)* 502 to 503 labelled a_1(1)* 503 to 504 labelled a_1(1)* 504 to 505 labelled a_1(1)* 505 to 506 labelled a_1(1)* 506 to 507 labelled a_1(1)* 507 to 508 labelled b_1(1)* 508 to 509 labelled a_1(1)* 509 to 510 labelled b_1(1)* 510 to 511 labelled a_1(1)* 511 to 512 labelled a_1(1)* 511 to 526 labelled b_1(2)* 512 to 513 labelled a_1(1)* 513 to 484 labelled a_1(1)* 513 to 478 labelled b_1(1)* 526 to 527 labelled a_1(2)* 527 to 528 labelled a_1(2)* 528 to 529 labelled a_1(2)* 529 to 530 labelled a_1(2)* 530 to 531 labelled a_1(2)* 531 to 532 labelled b_1(2)* 532 to 533 labelled a_1(2)* 533 to 534 labelled b_1(2)* 534 to 535 labelled a_1(2)* 535 to 536 labelled a_1(2)* 535 to 526 labelled b_1(2)* 536 to 537 labelled a_1(2)* 537 to 484 labelled a_1(2)* 537 to 478 labelled b_1(1) ---------------------------------------- (6) YES