4.15/1.77 YES 4.26/1.80 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 4.26/1.80 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.26/1.80 4.26/1.80 4.26/1.80 Termination w.r.t. Q of the given QTRS could be proven: 4.26/1.80 4.26/1.80 (0) QTRS 4.26/1.80 (1) QTRS Reverse [EQUIVALENT, 0 ms] 4.26/1.80 (2) QTRS 4.26/1.80 (3) Strip Symbols Proof [SOUND, 0 ms] 4.26/1.80 (4) QTRS 4.26/1.80 (5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] 4.26/1.80 (6) YES 4.26/1.80 4.26/1.80 4.26/1.80 ---------------------------------------- 4.26/1.80 4.26/1.80 (0) 4.26/1.80 Obligation: 4.26/1.80 Q restricted rewrite system: 4.26/1.80 The TRS R consists of the following rules: 4.26/1.80 4.26/1.80 a(b(b(a(a(a(a(x1))))))) -> a(a(a(a(a(b(b(a(b(b(a(a(b(b(x1)))))))))))))) 4.26/1.80 4.26/1.80 Q is empty. 4.26/1.80 4.26/1.80 ---------------------------------------- 4.26/1.80 4.26/1.80 (1) QTRS Reverse (EQUIVALENT) 4.26/1.80 We applied the QTRS Reverse Processor [REVERSE]. 4.26/1.80 ---------------------------------------- 4.26/1.80 4.26/1.80 (2) 4.26/1.80 Obligation: 4.26/1.80 Q restricted rewrite system: 4.26/1.80 The TRS R consists of the following rules: 4.26/1.80 4.26/1.80 a(a(a(a(b(b(a(x1))))))) -> b(b(a(a(b(b(a(b(b(a(a(a(a(a(x1)))))))))))))) 4.26/1.80 4.26/1.80 Q is empty. 4.26/1.80 4.26/1.80 ---------------------------------------- 4.26/1.80 4.26/1.80 (3) Strip Symbols Proof (SOUND) 4.26/1.80 We were given the following TRS: 4.26/1.80 4.26/1.80 a(a(a(a(b(b(a(x1))))))) -> b(b(a(a(b(b(a(b(b(a(a(a(a(a(x1)))))))))))))) 4.26/1.80 4.26/1.80 By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 4.26/1.80 4.26/1.80 a(a(a(a(b(b(x)))))) -> b(b(a(a(b(b(a(b(b(a(a(a(a(x))))))))))))) 4.26/1.80 4.26/1.80 ---------------------------------------- 4.26/1.80 4.26/1.80 (4) 4.26/1.80 Obligation: 4.26/1.80 Q restricted rewrite system: 4.26/1.80 The TRS R consists of the following rules: 4.26/1.80 4.26/1.80 a(a(a(a(b(b(x)))))) -> b(b(a(a(b(b(a(b(b(a(a(a(a(x))))))))))))) 4.26/1.80 4.26/1.80 Q is empty. 4.26/1.80 4.26/1.80 ---------------------------------------- 4.26/1.80 4.26/1.80 (5) RFCMatchBoundsTRSProof (EQUIVALENT) 4.26/1.80 Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R. 4.26/1.80 The following rules were used to construct the certificate: 4.26/1.80 4.26/1.80 a(a(a(a(b(b(x)))))) -> b(b(a(a(b(b(a(b(b(a(a(a(a(x))))))))))))) 4.26/1.80 4.26/1.80 The certificate found is represented by the following graph. 4.26/1.80 The certificate consists of the following enumerated nodes: 4.26/1.80 525, 526, 527, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 550 4.26/1.80 4.26/1.80 Node 525 is start node and node 526 is final node. 4.26/1.80 4.26/1.80 Those nodes are connected through the following edges: 4.26/1.80 4.26/1.80 * 525 to 527 labelled b_1(0)* 526 to 526 labelled #_1(0)* 527 to 528 labelled b_1(0)* 528 to 529 labelled a_1(0)* 529 to 530 labelled a_1(0)* 530 to 531 labelled b_1(0)* 531 to 532 labelled b_1(0)* 532 to 533 labelled a_1(0)* 533 to 534 labelled b_1(0)* 534 to 535 labelled b_1(0)* 535 to 536 labelled a_1(0)* 535 to 539 labelled b_1(1)* 536 to 537 labelled a_1(0)* 536 to 539 labelled b_1(1)* 537 to 538 labelled a_1(0)* 537 to 539 labelled b_1(1)* 538 to 526 labelled a_1(0)* 538 to 539 labelled b_1(1)* 539 to 540 labelled b_1(1)* 540 to 541 labelled a_1(1)* 541 to 542 labelled a_1(1)* 542 to 543 labelled b_1(1)* 543 to 544 labelled b_1(1)* 544 to 545 labelled a_1(1)* 545 to 546 labelled b_1(1)* 546 to 547 labelled b_1(1)* 547 to 548 labelled a_1(1)* 547 to 539 labelled b_1(1)* 548 to 549 labelled a_1(1)* 548 to 539 labelled b_1(1)* 549 to 550 labelled a_1(1)* 549 to 539 labelled b_1(1)* 550 to 526 labelled a_1(1)* 550 to 539 labelled b_1(1) 4.26/1.80 4.26/1.80 4.26/1.80 ---------------------------------------- 4.26/1.80 4.26/1.80 (6) 4.26/1.80 YES 4.30/1.84 EOF