4.07/1.90 YES 4.07/1.90 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 4.07/1.90 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.07/1.90 4.07/1.90 4.07/1.90 Termination w.r.t. Q of the given QTRS could be proven: 4.07/1.90 4.07/1.90 (0) QTRS 4.07/1.90 (1) QTRS Reverse [EQUIVALENT, 0 ms] 4.07/1.90 (2) QTRS 4.07/1.90 (3) Strip Symbols Proof [SOUND, 0 ms] 4.07/1.90 (4) QTRS 4.07/1.90 (5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] 4.07/1.90 (6) YES 4.07/1.90 4.07/1.90 4.07/1.90 ---------------------------------------- 4.07/1.90 4.07/1.90 (0) 4.07/1.90 Obligation: 4.07/1.90 Q restricted rewrite system: 4.07/1.90 The TRS R consists of the following rules: 4.07/1.90 4.07/1.90 a(b(a(c(a(a(a(a(x1)))))))) -> a(a(a(a(a(b(a(c(a(a(a(b(a(c(x1)))))))))))))) 4.07/1.90 4.07/1.90 Q is empty. 4.07/1.90 4.07/1.90 ---------------------------------------- 4.07/1.90 4.07/1.90 (1) QTRS Reverse (EQUIVALENT) 4.07/1.90 We applied the QTRS Reverse Processor [REVERSE]. 4.07/1.90 ---------------------------------------- 4.07/1.90 4.07/1.90 (2) 4.07/1.90 Obligation: 4.07/1.90 Q restricted rewrite system: 4.07/1.90 The TRS R consists of the following rules: 4.07/1.90 4.07/1.90 a(a(a(a(c(a(b(a(x1)))))))) -> c(a(b(a(a(a(c(a(b(a(a(a(a(a(x1)))))))))))))) 4.07/1.90 4.07/1.90 Q is empty. 4.07/1.90 4.07/1.90 ---------------------------------------- 4.07/1.90 4.07/1.90 (3) Strip Symbols Proof (SOUND) 4.07/1.90 We were given the following TRS: 4.07/1.90 4.07/1.90 a(a(a(a(c(a(b(a(x1)))))))) -> c(a(b(a(a(a(c(a(b(a(a(a(a(a(x1)))))))))))))) 4.07/1.90 4.07/1.90 By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 4.07/1.90 4.07/1.90 a(a(a(a(c(a(b(x))))))) -> c(a(b(a(a(a(c(a(b(a(a(a(a(x))))))))))))) 4.07/1.90 4.07/1.90 ---------------------------------------- 4.07/1.90 4.07/1.90 (4) 4.07/1.90 Obligation: 4.07/1.90 Q restricted rewrite system: 4.07/1.90 The TRS R consists of the following rules: 4.07/1.90 4.07/1.90 a(a(a(a(c(a(b(x))))))) -> c(a(b(a(a(a(c(a(b(a(a(a(a(x))))))))))))) 4.07/1.90 4.07/1.90 Q is empty. 4.07/1.90 4.07/1.90 ---------------------------------------- 4.07/1.90 4.07/1.90 (5) RFCMatchBoundsTRSProof (EQUIVALENT) 4.07/1.90 Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R. 4.07/1.90 The following rules were used to construct the certificate: 4.07/1.90 4.07/1.90 a(a(a(a(c(a(b(x))))))) -> c(a(b(a(a(a(c(a(b(a(a(a(a(x))))))))))))) 4.07/1.90 4.07/1.90 The certificate found is represented by the following graph. 4.07/1.90 The certificate consists of the following enumerated nodes: 4.07/1.90 461, 462, 515, 516, 517, 518, 519, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 538 4.07/1.90 4.07/1.90 Node 461 is start node and node 462 is final node. 4.07/1.90 4.07/1.90 Those nodes are connected through the following edges: 4.07/1.90 4.07/1.90 * 461 to 515 labelled c_1(0)* 462 to 462 labelled #_1(0)* 515 to 516 labelled a_1(0)* 516 to 517 labelled b_1(0)* 517 to 518 labelled a_1(0)* 518 to 519 labelled a_1(0)* 519 to 520 labelled a_1(0)* 520 to 521 labelled c_1(0)* 521 to 522 labelled a_1(0)* 522 to 523 labelled b_1(0)* 523 to 524 labelled a_1(0)* 523 to 527 labelled c_1(1)* 524 to 525 labelled a_1(0)* 524 to 527 labelled c_1(1)* 525 to 526 labelled a_1(0)* 525 to 527 labelled c_1(1)* 526 to 462 labelled a_1(0)* 526 to 527 labelled c_1(1)* 527 to 528 labelled a_1(1)* 528 to 529 labelled b_1(1)* 529 to 530 labelled a_1(1)* 530 to 531 labelled a_1(1)* 531 to 532 labelled a_1(1)* 532 to 533 labelled c_1(1)* 533 to 534 labelled a_1(1)* 534 to 535 labelled b_1(1)* 535 to 536 labelled a_1(1)* 535 to 527 labelled c_1(1)* 536 to 537 labelled a_1(1)* 536 to 527 labelled c_1(1)* 537 to 538 labelled a_1(1)* 537 to 527 labelled c_1(1)* 538 to 462 labelled a_1(1)* 538 to 527 labelled c_1(1) 4.07/1.90 4.07/1.90 4.07/1.90 ---------------------------------------- 4.07/1.90 4.07/1.90 (6) 4.07/1.90 YES 4.38/1.94 EOF