3.54/1.65 YES 3.54/1.68 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 3.54/1.68 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.54/1.68 3.54/1.68 3.54/1.68 Termination w.r.t. Q of the given QTRS could be proven: 3.54/1.68 3.54/1.68 (0) QTRS 3.54/1.68 (1) QTRS Reverse [EQUIVALENT, 0 ms] 3.54/1.68 (2) QTRS 3.54/1.68 (3) Strip Symbols Proof [SOUND, 0 ms] 3.54/1.68 (4) QTRS 3.54/1.68 (5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] 3.54/1.68 (6) YES 3.54/1.68 3.54/1.68 3.54/1.68 ---------------------------------------- 3.54/1.68 3.54/1.68 (0) 3.54/1.68 Obligation: 3.54/1.68 Q restricted rewrite system: 3.54/1.68 The TRS R consists of the following rules: 3.54/1.68 3.54/1.68 a(b(c(c(a(a(a(a(x1)))))))) -> a(a(a(a(a(b(c(c(a(a(a(b(c(c(x1)))))))))))))) 3.54/1.68 3.54/1.68 Q is empty. 3.54/1.68 3.54/1.68 ---------------------------------------- 3.54/1.68 3.54/1.68 (1) QTRS Reverse (EQUIVALENT) 3.54/1.68 We applied the QTRS Reverse Processor [REVERSE]. 3.54/1.68 ---------------------------------------- 3.54/1.68 3.54/1.68 (2) 3.54/1.68 Obligation: 3.54/1.68 Q restricted rewrite system: 3.54/1.68 The TRS R consists of the following rules: 3.54/1.68 3.54/1.68 a(a(a(a(c(c(b(a(x1)))))))) -> c(c(b(a(a(a(c(c(b(a(a(a(a(a(x1)))))))))))))) 3.54/1.68 3.54/1.68 Q is empty. 3.54/1.68 3.54/1.68 ---------------------------------------- 3.54/1.68 3.54/1.68 (3) Strip Symbols Proof (SOUND) 3.54/1.68 We were given the following TRS: 3.54/1.68 3.54/1.68 a(a(a(a(c(c(b(a(x1)))))))) -> c(c(b(a(a(a(c(c(b(a(a(a(a(a(x1)))))))))))))) 3.54/1.68 3.54/1.68 By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 3.54/1.68 3.54/1.68 a(a(a(a(c(c(b(x))))))) -> c(c(b(a(a(a(c(c(b(a(a(a(a(x))))))))))))) 3.54/1.68 3.54/1.68 ---------------------------------------- 3.54/1.68 3.54/1.68 (4) 3.54/1.68 Obligation: 3.54/1.68 Q restricted rewrite system: 3.54/1.68 The TRS R consists of the following rules: 3.54/1.68 3.54/1.68 a(a(a(a(c(c(b(x))))))) -> c(c(b(a(a(a(c(c(b(a(a(a(a(x))))))))))))) 3.54/1.68 3.54/1.68 Q is empty. 3.54/1.68 3.54/1.68 ---------------------------------------- 3.54/1.68 3.54/1.68 (5) RFCMatchBoundsTRSProof (EQUIVALENT) 3.54/1.68 Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R. 3.54/1.68 The following rules were used to construct the certificate: 3.54/1.68 3.54/1.68 a(a(a(a(c(c(b(x))))))) -> c(c(b(a(a(a(c(c(b(a(a(a(a(x))))))))))))) 3.54/1.68 3.54/1.68 The certificate found is represented by the following graph. 3.54/1.68 The certificate consists of the following enumerated nodes: 3.54/1.68 474, 475, 489, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511, 512 3.54/1.68 3.54/1.68 Node 474 is start node and node 475 is final node. 3.54/1.68 3.54/1.68 Those nodes are connected through the following edges: 3.54/1.68 3.54/1.68 * 474 to 489 labelled c_1(0)* 475 to 475 labelled #_1(0)* 489 to 490 labelled c_1(0)* 490 to 491 labelled b_1(0)* 491 to 492 labelled a_1(0)* 492 to 493 labelled a_1(0)* 493 to 494 labelled a_1(0)* 494 to 495 labelled c_1(0)* 495 to 496 labelled c_1(0)* 496 to 497 labelled b_1(0)* 497 to 498 labelled a_1(0)* 497 to 501 labelled c_1(1)* 498 to 499 labelled a_1(0)* 498 to 501 labelled c_1(1)* 499 to 500 labelled a_1(0)* 499 to 501 labelled c_1(1)* 500 to 475 labelled a_1(0)* 500 to 501 labelled c_1(1)* 501 to 502 labelled c_1(1)* 502 to 503 labelled b_1(1)* 503 to 504 labelled a_1(1)* 504 to 505 labelled a_1(1)* 505 to 506 labelled a_1(1)* 506 to 507 labelled c_1(1)* 507 to 508 labelled c_1(1)* 508 to 509 labelled b_1(1)* 509 to 510 labelled a_1(1)* 509 to 501 labelled c_1(1)* 510 to 511 labelled a_1(1)* 510 to 501 labelled c_1(1)* 511 to 512 labelled a_1(1)* 511 to 501 labelled c_1(1)* 512 to 475 labelled a_1(1)* 512 to 501 labelled c_1(1) 3.54/1.68 3.54/1.68 3.54/1.68 ---------------------------------------- 3.54/1.68 3.54/1.68 (6) 3.54/1.68 YES 3.74/1.71 EOF