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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) Strip Symbols Proof [SOUND, 0 ms] (4)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(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: 451, 452, 453, 454, 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, 488, 489, 490, 491, 492, 493, 494, 495, 496 Node 451 is start node and node 452 is final node. Those nodes are connected through the following edges: * 451 to 453 labelled b_1(0)* 452 to 452 labelled #_1(0)* 453 to 454 labelled a_1(0)* 454 to 455 labelled a_1(0)* 455 to 456 labelled b_1(0)* 456 to 457 labelled b_1(0)* 457 to 458 labelled a_1(0)* 458 to 459 labelled a_1(0)* 459 to 460 labelled b_1(0)* 460 to 461 labelled b_1(0)* 461 to 462 labelled a_1(0)* 461 to 475 labelled b_1(1)* 462 to 463 labelled a_1(0)* 462 to 464 labelled b_1(1)* 463 to 452 labelled b_1(0)* 464 to 465 labelled a_1(1)* 465 to 466 labelled a_1(1)* 466 to 467 labelled b_1(1)* 467 to 468 labelled b_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 486 labelled b_1(2)* 473 to 474 labelled a_1(1)* 473 to 464 labelled b_1(1)* 474 to 452 labelled b_1(1)* 475 to 476 labelled a_1(1)* 476 to 477 labelled a_1(1)* 477 to 478 labelled b_1(1)* 478 to 479 labelled b_1(1)* 479 to 480 labelled a_1(1)* 480 to 481 labelled a_1(1)* 481 to 482 labelled b_1(1)* 482 to 483 labelled b_1(1)* 483 to 484 labelled a_1(1)* 483 to 486 labelled b_1(2)* 484 to 485 labelled a_1(1)* 484 to 464 labelled b_1(1)* 485 to 472 labelled b_1(1)* 486 to 487 labelled a_1(2)* 487 to 488 labelled a_1(2)* 488 to 489 labelled b_1(2)* 489 to 490 labelled b_1(2)* 490 to 491 labelled a_1(2)* 491 to 492 labelled a_1(2)* 492 to 493 labelled b_1(2)* 493 to 494 labelled b_1(2)* 494 to 495 labelled a_1(2)* 494 to 486 labelled b_1(2)* 495 to 496 labelled a_1(2)* 495 to 464 labelled b_1(1)* 496 to 472 labelled b_1(2) ---------------------------------------- (6) YES