3.74/1.79 YES 3.74/1.82 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 3.74/1.82 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.74/1.82 3.74/1.82 3.74/1.82 Termination w.r.t. Q of the given QTRS could be proven: 3.74/1.82 3.74/1.82 (0) QTRS 3.74/1.82 (1) QTRS Reverse [EQUIVALENT, 0 ms] 3.74/1.82 (2) QTRS 3.74/1.82 (3) Strip Symbols Proof [SOUND, 0 ms] 3.74/1.82 (4) QTRS 3.74/1.82 (5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] 3.74/1.82 (6) YES 3.74/1.82 3.74/1.82 3.74/1.82 ---------------------------------------- 3.74/1.82 3.74/1.82 (0) 3.74/1.82 Obligation: 3.74/1.82 Q restricted rewrite system: 3.74/1.82 The TRS R consists of the following rules: 3.74/1.82 3.74/1.82 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)))))))))))))) 3.74/1.82 3.74/1.82 Q is empty. 3.74/1.82 3.74/1.82 ---------------------------------------- 3.74/1.82 3.74/1.82 (1) QTRS Reverse (EQUIVALENT) 3.74/1.82 We applied the QTRS Reverse Processor [REVERSE]. 3.74/1.82 ---------------------------------------- 3.74/1.82 3.74/1.82 (2) 3.74/1.82 Obligation: 3.74/1.82 Q restricted rewrite system: 3.74/1.82 The TRS R consists of the following rules: 3.74/1.82 3.74/1.82 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)))))))))))))) 3.74/1.82 3.74/1.82 Q is empty. 3.74/1.82 3.74/1.82 ---------------------------------------- 3.74/1.82 3.74/1.82 (3) Strip Symbols Proof (SOUND) 3.74/1.82 We were given the following TRS: 3.74/1.82 3.74/1.82 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)))))))))))))) 3.74/1.82 3.74/1.82 By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 3.74/1.82 3.74/1.82 a(a(b(a(a(a(a(a(b(x))))))))) -> b(a(a(a(a(a(b(a(b(a(a(a(a(x))))))))))))) 3.74/1.82 3.74/1.82 ---------------------------------------- 3.74/1.82 3.74/1.82 (4) 3.74/1.82 Obligation: 3.74/1.82 Q restricted rewrite system: 3.74/1.82 The TRS R consists of the following rules: 3.74/1.82 3.74/1.82 a(a(b(a(a(a(a(a(b(x))))))))) -> b(a(a(a(a(a(b(a(b(a(a(a(a(x))))))))))))) 3.74/1.82 3.74/1.82 Q is empty. 3.74/1.82 3.74/1.82 ---------------------------------------- 3.74/1.82 3.74/1.82 (5) RFCMatchBoundsTRSProof (EQUIVALENT) 3.74/1.82 Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R. 3.74/1.82 The following rules were used to construct the certificate: 3.74/1.82 3.74/1.82 a(a(b(a(a(a(a(a(b(x))))))))) -> b(a(a(a(a(a(b(a(b(a(a(a(a(x))))))))))))) 3.74/1.82 3.74/1.82 The certificate found is represented by the following graph. 3.74/1.82 The certificate consists of the following enumerated nodes: 3.74/1.82 539, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 580, 581, 582, 583, 584, 585, 586, 587, 588 3.74/1.82 3.74/1.82 Node 539 is start node and node 540 is final node. 3.74/1.82 3.74/1.82 Those nodes are connected through the following edges: 3.74/1.82 3.74/1.82 * 539 to 541 labelled b_1(0)* 540 to 540 labelled #_1(0)* 541 to 542 labelled a_1(0)* 542 to 543 labelled a_1(0)* 543 to 544 labelled a_1(0)* 544 to 545 labelled a_1(0)* 545 to 546 labelled a_1(0)* 546 to 547 labelled b_1(0)* 547 to 548 labelled a_1(0)* 548 to 549 labelled b_1(0)* 549 to 550 labelled a_1(0)* 549 to 565 labelled b_1(1)* 550 to 551 labelled a_1(0)* 550 to 565 labelled b_1(1)* 551 to 552 labelled a_1(0)* 551 to 553 labelled b_1(1)* 552 to 540 labelled a_1(0)* 552 to 553 labelled b_1(1)* 553 to 554 labelled a_1(1)* 554 to 555 labelled a_1(1)* 555 to 556 labelled a_1(1)* 556 to 557 labelled a_1(1)* 557 to 558 labelled a_1(1)* 558 to 559 labelled b_1(1)* 559 to 560 labelled a_1(1)* 560 to 561 labelled b_1(1)* 561 to 562 labelled a_1(1)* 561 to 577 labelled b_1(2)* 562 to 563 labelled a_1(1)* 562 to 577 labelled b_1(2)* 563 to 564 labelled a_1(1)* 563 to 553 labelled b_1(1)* 564 to 540 labelled a_1(1)* 564 to 553 labelled b_1(1)* 565 to 566 labelled a_1(1)* 566 to 567 labelled a_1(1)* 567 to 568 labelled a_1(1)* 568 to 569 labelled a_1(1)* 569 to 570 labelled a_1(1)* 570 to 571 labelled b_1(1)* 571 to 572 labelled a_1(1)* 572 to 573 labelled b_1(1)* 573 to 574 labelled a_1(1)* 574 to 575 labelled a_1(1)* 574 to 577 labelled b_1(2)* 575 to 576 labelled a_1(1)* 576 to 559 labelled a_1(1)* 576 to 553 labelled b_1(1)* 577 to 578 labelled a_1(2)* 578 to 579 labelled a_1(2)* 579 to 580 labelled a_1(2)* 580 to 581 labelled a_1(2)* 581 to 582 labelled a_1(2)* 582 to 583 labelled b_1(2)* 583 to 584 labelled a_1(2)* 584 to 585 labelled b_1(2)* 585 to 586 labelled a_1(2)* 586 to 587 labelled a_1(2)* 586 to 577 labelled b_1(2)* 587 to 588 labelled a_1(2)* 588 to 559 labelled a_1(2)* 588 to 553 labelled b_1(1) 3.74/1.82 3.74/1.82 3.74/1.82 ---------------------------------------- 3.74/1.82 3.74/1.82 (6) 3.74/1.82 YES 4.02/1.84 EOF