4.00/1.90 YES 4.38/1.91 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 4.38/1.91 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.38/1.91 4.38/1.91 4.38/1.91 Termination w.r.t. Q of the given QTRS could be proven: 4.38/1.91 4.38/1.91 (0) QTRS 4.38/1.91 (1) QTRS Reverse [EQUIVALENT, 0 ms] 4.38/1.91 (2) QTRS 4.38/1.91 (3) Strip Symbols Proof [SOUND, 0 ms] 4.38/1.91 (4) QTRS 4.38/1.91 (5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] 4.38/1.91 (6) YES 4.38/1.91 4.38/1.91 4.38/1.91 ---------------------------------------- 4.38/1.91 4.38/1.91 (0) 4.38/1.91 Obligation: 4.38/1.91 Q restricted rewrite system: 4.38/1.91 The TRS R consists of the following rules: 4.38/1.91 4.38/1.91 a(b(a(a(a(a(a(a(a(x1))))))))) -> a(a(a(a(a(a(a(a(b(a(a(b(x1)))))))))))) 4.38/1.91 4.38/1.91 Q is empty. 4.38/1.91 4.38/1.91 ---------------------------------------- 4.38/1.91 4.38/1.91 (1) QTRS Reverse (EQUIVALENT) 4.38/1.91 We applied the QTRS Reverse Processor [REVERSE]. 4.38/1.91 ---------------------------------------- 4.38/1.91 4.38/1.91 (2) 4.38/1.91 Obligation: 4.38/1.91 Q restricted rewrite system: 4.38/1.91 The TRS R consists of the following rules: 4.38/1.91 4.38/1.91 a(a(a(a(a(a(a(b(a(x1))))))))) -> b(a(a(b(a(a(a(a(a(a(a(a(x1)))))))))))) 4.38/1.91 4.38/1.91 Q is empty. 4.38/1.91 4.38/1.91 ---------------------------------------- 4.38/1.91 4.38/1.91 (3) Strip Symbols Proof (SOUND) 4.38/1.91 We were given the following TRS: 4.38/1.91 4.38/1.91 a(a(a(a(a(a(a(b(a(x1))))))))) -> b(a(a(b(a(a(a(a(a(a(a(a(x1)))))))))))) 4.38/1.91 4.38/1.91 By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 4.38/1.91 4.38/1.91 a(a(a(a(a(a(a(b(x)))))))) -> b(a(a(b(a(a(a(a(a(a(a(x))))))))))) 4.38/1.91 4.38/1.91 ---------------------------------------- 4.38/1.91 4.38/1.91 (4) 4.38/1.91 Obligation: 4.38/1.91 Q restricted rewrite system: 4.38/1.91 The TRS R consists of the following rules: 4.38/1.91 4.38/1.91 a(a(a(a(a(a(a(b(x)))))))) -> b(a(a(b(a(a(a(a(a(a(a(x))))))))))) 4.38/1.91 4.38/1.91 Q is empty. 4.38/1.91 4.38/1.91 ---------------------------------------- 4.38/1.91 4.38/1.91 (5) RFCMatchBoundsTRSProof (EQUIVALENT) 4.38/1.91 Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R. 4.38/1.91 The following rules were used to construct the certificate: 4.38/1.91 4.38/1.91 a(a(a(a(a(a(a(b(x)))))))) -> b(a(a(b(a(a(a(a(a(a(a(x))))))))))) 4.38/1.91 4.38/1.91 The certificate found is represented by the following graph. 4.38/1.91 The certificate consists of the following enumerated nodes: 4.38/1.91 475, 476, 477, 478, 479, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 490, 491, 492, 493, 494, 495, 496 4.38/1.91 4.38/1.91 Node 475 is start node and node 476 is final node. 4.38/1.91 4.38/1.91 Those nodes are connected through the following edges: 4.38/1.91 4.38/1.91 * 475 to 477 labelled b_1(0)* 476 to 476 labelled #_1(0)* 477 to 478 labelled a_1(0)* 478 to 479 labelled a_1(0)* 479 to 480 labelled b_1(0)* 480 to 481 labelled a_1(0)* 480 to 487 labelled b_1(1)* 481 to 482 labelled a_1(0)* 481 to 487 labelled b_1(1)* 482 to 483 labelled a_1(0)* 482 to 487 labelled b_1(1)* 483 to 484 labelled a_1(0)* 483 to 487 labelled b_1(1)* 484 to 485 labelled a_1(0)* 484 to 487 labelled b_1(1)* 485 to 486 labelled a_1(0)* 485 to 487 labelled b_1(1)* 486 to 476 labelled a_1(0)* 486 to 487 labelled b_1(1)* 487 to 488 labelled a_1(1)* 488 to 489 labelled a_1(1)* 489 to 490 labelled b_1(1)* 490 to 491 labelled a_1(1)* 490 to 487 labelled b_1(1)* 491 to 492 labelled a_1(1)* 491 to 487 labelled b_1(1)* 492 to 493 labelled a_1(1)* 492 to 487 labelled b_1(1)* 493 to 494 labelled a_1(1)* 493 to 487 labelled b_1(1)* 494 to 495 labelled a_1(1)* 494 to 487 labelled b_1(1)* 495 to 496 labelled a_1(1)* 495 to 487 labelled b_1(1)* 496 to 476 labelled a_1(1)* 496 to 487 labelled b_1(1) 4.38/1.91 4.38/1.91 4.38/1.91 ---------------------------------------- 4.38/1.91 4.38/1.91 (6) 4.38/1.91 YES 4.43/1.95 EOF