3.38/1.63 YES 3.67/1.68 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 3.67/1.68 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.67/1.68 3.67/1.68 3.67/1.68 Termination w.r.t. Q of the given QTRS could be proven: 3.67/1.68 3.67/1.68 (0) QTRS 3.67/1.68 (1) QTRS Reverse [EQUIVALENT, 0 ms] 3.67/1.68 (2) QTRS 3.67/1.68 (3) Strip Symbols Proof [SOUND, 0 ms] 3.67/1.68 (4) QTRS 3.67/1.68 (5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] 3.67/1.68 (6) YES 3.67/1.68 3.67/1.68 3.67/1.68 ---------------------------------------- 3.67/1.68 3.67/1.68 (0) 3.67/1.68 Obligation: 3.67/1.68 Q restricted rewrite system: 3.67/1.68 The TRS R consists of the following rules: 3.67/1.68 3.67/1.68 a(b(c(b(a(a(a(a(x1)))))))) -> a(a(a(a(a(b(c(b(a(a(b(c(b(x1))))))))))))) 3.67/1.68 3.67/1.68 Q is empty. 3.67/1.68 3.67/1.68 ---------------------------------------- 3.67/1.68 3.67/1.68 (1) QTRS Reverse (EQUIVALENT) 3.67/1.68 We applied the QTRS Reverse Processor [REVERSE]. 3.67/1.68 ---------------------------------------- 3.67/1.68 3.67/1.68 (2) 3.67/1.68 Obligation: 3.67/1.68 Q restricted rewrite system: 3.67/1.68 The TRS R consists of the following rules: 3.67/1.68 3.67/1.68 a(a(a(a(b(c(b(a(x1)))))))) -> b(c(b(a(a(b(c(b(a(a(a(a(a(x1))))))))))))) 3.67/1.68 3.67/1.68 Q is empty. 3.67/1.68 3.67/1.68 ---------------------------------------- 3.67/1.68 3.67/1.68 (3) Strip Symbols Proof (SOUND) 3.67/1.68 We were given the following TRS: 3.67/1.68 3.67/1.68 a(a(a(a(b(c(b(a(x1)))))))) -> b(c(b(a(a(b(c(b(a(a(a(a(a(x1))))))))))))) 3.67/1.68 3.67/1.68 By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 3.67/1.68 3.67/1.68 a(a(a(a(b(c(b(x))))))) -> b(c(b(a(a(b(c(b(a(a(a(a(x)))))))))))) 3.67/1.68 3.67/1.68 ---------------------------------------- 3.67/1.68 3.67/1.68 (4) 3.67/1.68 Obligation: 3.67/1.68 Q restricted rewrite system: 3.67/1.68 The TRS R consists of the following rules: 3.67/1.68 3.67/1.68 a(a(a(a(b(c(b(x))))))) -> b(c(b(a(a(b(c(b(a(a(a(a(x)))))))))))) 3.67/1.68 3.67/1.68 Q is empty. 3.67/1.68 3.67/1.68 ---------------------------------------- 3.67/1.68 3.67/1.68 (5) RFCMatchBoundsTRSProof (EQUIVALENT) 3.67/1.68 Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R. 3.67/1.68 The following rules were used to construct the certificate: 3.67/1.68 3.67/1.68 a(a(a(a(b(c(b(x))))))) -> b(c(b(a(a(b(c(b(a(a(a(a(x)))))))))))) 3.67/1.68 3.67/1.68 The certificate found is represented by the following graph. 3.67/1.68 The certificate consists of the following enumerated nodes: 3.67/1.68 473, 474, 475, 476, 477, 478, 479, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 490, 491, 492, 493, 494, 495, 496 3.67/1.68 3.67/1.68 Node 473 is start node and node 474 is final node. 3.67/1.68 3.67/1.68 Those nodes are connected through the following edges: 3.67/1.68 3.67/1.68 * 473 to 475 labelled b_1(0)* 474 to 474 labelled #_1(0)* 475 to 476 labelled c_1(0)* 476 to 477 labelled b_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 c_1(0)* 481 to 482 labelled b_1(0)* 482 to 483 labelled a_1(0)* 482 to 486 labelled b_1(1)* 483 to 484 labelled a_1(0)* 483 to 486 labelled b_1(1)* 484 to 485 labelled a_1(0)* 484 to 486 labelled b_1(1)* 485 to 474 labelled a_1(0)* 485 to 486 labelled b_1(1)* 486 to 487 labelled c_1(1)* 487 to 488 labelled b_1(1)* 488 to 489 labelled a_1(1)* 489 to 490 labelled a_1(1)* 490 to 491 labelled b_1(1)* 491 to 492 labelled c_1(1)* 492 to 493 labelled b_1(1)* 493 to 494 labelled a_1(1)* 493 to 486 labelled b_1(1)* 494 to 495 labelled a_1(1)* 494 to 486 labelled b_1(1)* 495 to 496 labelled a_1(1)* 495 to 486 labelled b_1(1)* 496 to 474 labelled a_1(1)* 496 to 486 labelled b_1(1) 3.67/1.68 3.67/1.68 3.67/1.68 ---------------------------------------- 3.67/1.68 3.67/1.68 (6) 3.67/1.68 YES 3.86/1.73 EOF