YES proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) Strip Symbols Proof [SOUND, 0 ms] (4)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(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: 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 443, 455, 456, 457, 458, 459, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 480, 481, 482, 483, 484, 485, 486, 487 Node 431 is start node and node 432 is final node. Those nodes are connected through the following edges: * 431 to 433 labelled b_1(0)* 432 to 432 labelled #_1(0)* 433 to 434 labelled a_1(0)* 434 to 435 labelled a_1(0)* 435 to 436 labelled a_1(0)* 436 to 437 labelled a_1(0)* 437 to 438 labelled b_1(0)* 438 to 439 labelled b_1(0)* 439 to 440 labelled a_1(0)* 439 to 466 labelled b_1(1)* 440 to 441 labelled a_1(0)* 441 to 442 labelled a_1(0)* 441 to 455 labelled b_1(1)* 442 to 443 labelled a_1(0)* 443 to 432 labelled b_1(0)* 455 to 456 labelled a_1(1)* 456 to 457 labelled a_1(1)* 457 to 458 labelled a_1(1)* 458 to 459 labelled a_1(1)* 459 to 460 labelled b_1(1)* 460 to 461 labelled b_1(1)* 461 to 462 labelled a_1(1)* 461 to 477 labelled b_1(2)* 462 to 463 labelled a_1(1)* 463 to 464 labelled a_1(1)* 463 to 455 labelled b_1(1)* 464 to 465 labelled a_1(1)* 465 to 432 labelled b_1(1)* 466 to 467 labelled a_1(1)* 467 to 468 labelled a_1(1)* 468 to 469 labelled a_1(1)* 469 to 470 labelled a_1(1)* 470 to 471 labelled b_1(1)* 471 to 472 labelled b_1(1)* 472 to 473 labelled a_1(1)* 472 to 477 labelled b_1(2)* 473 to 474 labelled a_1(1)* 474 to 475 labelled a_1(1)* 474 to 455 labelled b_1(1)* 475 to 476 labelled a_1(1)* 476 to 461 labelled b_1(1)* 477 to 478 labelled a_1(2)* 478 to 479 labelled a_1(2)* 479 to 480 labelled a_1(2)* 480 to 481 labelled a_1(2)* 481 to 482 labelled b_1(2)* 482 to 483 labelled b_1(2)* 483 to 484 labelled a_1(2)* 483 to 477 labelled b_1(2)* 484 to 485 labelled a_1(2)* 485 to 486 labelled a_1(2)* 485 to 455 labelled b_1(1)* 486 to 487 labelled a_1(2)* 487 to 461 labelled b_1(2) ---------------------------------------- (6) YES