3.64/1.83 YES 3.98/1.84 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 3.98/1.84 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.98/1.84 3.98/1.84 3.98/1.84 Termination w.r.t. Q of the given QTRS could be proven: 3.98/1.84 3.98/1.84 (0) QTRS 3.98/1.84 (1) QTRS Reverse [EQUIVALENT, 0 ms] 3.98/1.84 (2) QTRS 3.98/1.84 (3) Strip Symbols Proof [SOUND, 0 ms] 3.98/1.84 (4) QTRS 3.98/1.84 (5) RFCMatchBoundsTRSProof [EQUIVALENT, 2 ms] 3.98/1.84 (6) YES 3.98/1.84 3.98/1.84 3.98/1.84 ---------------------------------------- 3.98/1.84 3.98/1.84 (0) 3.98/1.84 Obligation: 3.98/1.84 Q restricted rewrite system: 3.98/1.84 The TRS R consists of the following rules: 3.98/1.84 3.98/1.84 a(b(c(c(a(a(a(a(a(x1))))))))) -> a(a(a(a(a(a(b(c(c(a(b(c(c(x1))))))))))))) 3.98/1.84 3.98/1.84 Q is empty. 3.98/1.84 3.98/1.84 ---------------------------------------- 3.98/1.84 3.98/1.84 (1) QTRS Reverse (EQUIVALENT) 3.98/1.84 We applied the QTRS Reverse Processor [REVERSE]. 3.98/1.84 ---------------------------------------- 3.98/1.84 3.98/1.84 (2) 3.98/1.84 Obligation: 3.98/1.84 Q restricted rewrite system: 3.98/1.84 The TRS R consists of the following rules: 3.98/1.84 3.98/1.84 a(a(a(a(a(c(c(b(a(x1))))))))) -> c(c(b(a(c(c(b(a(a(a(a(a(a(x1))))))))))))) 3.98/1.84 3.98/1.84 Q is empty. 3.98/1.84 3.98/1.84 ---------------------------------------- 3.98/1.84 3.98/1.84 (3) Strip Symbols Proof (SOUND) 3.98/1.84 We were given the following TRS: 3.98/1.84 3.98/1.84 a(a(a(a(a(c(c(b(a(x1))))))))) -> c(c(b(a(c(c(b(a(a(a(a(a(a(x1))))))))))))) 3.98/1.84 3.98/1.84 By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 3.98/1.84 3.98/1.84 a(a(a(a(a(c(c(b(x)))))))) -> c(c(b(a(c(c(b(a(a(a(a(a(x)))))))))))) 3.98/1.84 3.98/1.84 ---------------------------------------- 3.98/1.84 3.98/1.84 (4) 3.98/1.84 Obligation: 3.98/1.84 Q restricted rewrite system: 3.98/1.84 The TRS R consists of the following rules: 3.98/1.84 3.98/1.84 a(a(a(a(a(c(c(b(x)))))))) -> c(c(b(a(c(c(b(a(a(a(a(a(x)))))))))))) 3.98/1.84 3.98/1.84 Q is empty. 3.98/1.84 3.98/1.84 ---------------------------------------- 3.98/1.84 3.98/1.84 (5) RFCMatchBoundsTRSProof (EQUIVALENT) 3.98/1.84 Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R. 3.98/1.84 The following rules were used to construct the certificate: 3.98/1.84 3.98/1.84 a(a(a(a(a(c(c(b(x)))))))) -> c(c(b(a(c(c(b(a(a(a(a(a(x)))))))))))) 3.98/1.84 3.98/1.84 The certificate found is represented by the following graph. 3.98/1.84 The certificate consists of the following enumerated nodes: 3.98/1.84 508, 509, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530, 531 3.98/1.84 3.98/1.84 Node 508 is start node and node 509 is final node. 3.98/1.84 3.98/1.84 Those nodes are connected through the following edges: 3.98/1.84 3.98/1.84 * 508 to 510 labelled c_1(0)* 509 to 509 labelled #_1(0)* 510 to 511 labelled c_1(0)* 511 to 512 labelled b_1(0)* 512 to 513 labelled a_1(0)* 513 to 514 labelled c_1(0)* 514 to 515 labelled c_1(0)* 515 to 516 labelled b_1(0)* 516 to 517 labelled a_1(0)* 516 to 521 labelled c_1(1)* 517 to 518 labelled a_1(0)* 517 to 521 labelled c_1(1)* 518 to 519 labelled a_1(0)* 518 to 521 labelled c_1(1)* 519 to 520 labelled a_1(0)* 519 to 521 labelled c_1(1)* 520 to 509 labelled a_1(0)* 520 to 521 labelled c_1(1)* 521 to 522 labelled c_1(1)* 522 to 523 labelled b_1(1)* 523 to 524 labelled a_1(1)* 524 to 525 labelled c_1(1)* 525 to 526 labelled c_1(1)* 526 to 527 labelled b_1(1)* 527 to 528 labelled a_1(1)* 527 to 521 labelled c_1(1)* 528 to 529 labelled a_1(1)* 528 to 521 labelled c_1(1)* 529 to 530 labelled a_1(1)* 529 to 521 labelled c_1(1)* 530 to 531 labelled a_1(1)* 530 to 521 labelled c_1(1)* 531 to 509 labelled a_1(1)* 531 to 521 labelled c_1(1) 3.98/1.84 3.98/1.84 3.98/1.84 ---------------------------------------- 3.98/1.84 3.98/1.84 (6) 3.98/1.84 YES 3.98/1.89 EOF