3.39/1.71 YES 3.76/1.74 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 3.76/1.74 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.76/1.74 3.76/1.74 3.76/1.74 Termination w.r.t. Q of the given QTRS could be proven: 3.76/1.74 3.76/1.74 (0) QTRS 3.76/1.74 (1) QTRS Reverse [EQUIVALENT, 0 ms] 3.76/1.74 (2) QTRS 3.76/1.74 (3) Strip Symbols Proof [SOUND, 1 ms] 3.76/1.74 (4) QTRS 3.76/1.74 (5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] 3.76/1.74 (6) YES 3.76/1.74 3.76/1.74 3.76/1.74 ---------------------------------------- 3.76/1.74 3.76/1.74 (0) 3.76/1.74 Obligation: 3.76/1.74 Q restricted rewrite system: 3.76/1.74 The TRS R consists of the following rules: 3.76/1.74 3.76/1.74 a(b(a(a(a(a(a(a(x1)))))))) -> a(a(a(a(a(a(a(b(a(a(a(a(a(b(x1)))))))))))))) 3.76/1.74 3.76/1.74 Q is empty. 3.76/1.74 3.76/1.74 ---------------------------------------- 3.76/1.74 3.76/1.74 (1) QTRS Reverse (EQUIVALENT) 3.76/1.74 We applied the QTRS Reverse Processor [REVERSE]. 3.76/1.74 ---------------------------------------- 3.76/1.74 3.76/1.74 (2) 3.76/1.74 Obligation: 3.76/1.74 Q restricted rewrite system: 3.76/1.74 The TRS R consists of the following rules: 3.76/1.74 3.76/1.74 a(a(a(a(a(a(b(a(x1)))))))) -> b(a(a(a(a(a(b(a(a(a(a(a(a(a(x1)))))))))))))) 3.76/1.74 3.76/1.74 Q is empty. 3.76/1.74 3.76/1.74 ---------------------------------------- 3.76/1.74 3.76/1.74 (3) Strip Symbols Proof (SOUND) 3.76/1.74 We were given the following TRS: 3.76/1.74 3.76/1.74 a(a(a(a(a(a(b(a(x1)))))))) -> b(a(a(a(a(a(b(a(a(a(a(a(a(a(x1)))))))))))))) 3.76/1.74 3.76/1.74 By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 3.76/1.74 3.76/1.74 a(a(a(a(a(a(b(x))))))) -> b(a(a(a(a(a(b(a(a(a(a(a(a(x))))))))))))) 3.76/1.74 3.76/1.74 ---------------------------------------- 3.76/1.74 3.76/1.74 (4) 3.76/1.74 Obligation: 3.76/1.74 Q restricted rewrite system: 3.76/1.74 The TRS R consists of the following rules: 3.76/1.74 3.76/1.74 a(a(a(a(a(a(b(x))))))) -> b(a(a(a(a(a(b(a(a(a(a(a(a(x))))))))))))) 3.76/1.74 3.76/1.74 Q is empty. 3.76/1.74 3.76/1.74 ---------------------------------------- 3.76/1.74 3.76/1.74 (5) RFCMatchBoundsTRSProof (EQUIVALENT) 3.76/1.74 Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R. 3.76/1.74 The following rules were used to construct the certificate: 3.76/1.74 3.76/1.74 a(a(a(a(a(a(b(x))))))) -> b(a(a(a(a(a(b(a(a(a(a(a(a(x))))))))))))) 3.76/1.74 3.76/1.74 The certificate found is represented by the following graph. 3.76/1.74 The certificate consists of the following enumerated nodes: 3.76/1.74 3, 7, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44 3.76/1.74 3.76/1.74 Node 3 is start node and node 7 is final node. 3.76/1.74 3.76/1.74 Those nodes are connected through the following edges: 3.76/1.74 3.76/1.74 * 3 to 21 labelled b_1(0)* 7 to 7 labelled #_1(0)* 21 to 22 labelled a_1(0)* 22 to 23 labelled a_1(0)* 23 to 24 labelled a_1(0)* 24 to 25 labelled a_1(0)* 25 to 26 labelled a_1(0)* 26 to 27 labelled b_1(0)* 27 to 28 labelled a_1(0)* 27 to 33 labelled b_1(1)* 28 to 29 labelled a_1(0)* 28 to 33 labelled b_1(1)* 29 to 30 labelled a_1(0)* 29 to 33 labelled b_1(1)* 30 to 31 labelled a_1(0)* 30 to 33 labelled b_1(1)* 31 to 32 labelled a_1(0)* 31 to 33 labelled b_1(1)* 32 to 7 labelled a_1(0)* 32 to 33 labelled b_1(1)* 33 to 34 labelled a_1(1)* 34 to 35 labelled a_1(1)* 35 to 36 labelled a_1(1)* 36 to 37 labelled a_1(1)* 37 to 38 labelled a_1(1)* 38 to 39 labelled b_1(1)* 39 to 40 labelled a_1(1)* 39 to 33 labelled b_1(1)* 40 to 41 labelled a_1(1)* 40 to 33 labelled b_1(1)* 41 to 42 labelled a_1(1)* 41 to 33 labelled b_1(1)* 42 to 43 labelled a_1(1)* 42 to 33 labelled b_1(1)* 43 to 44 labelled a_1(1)* 43 to 33 labelled b_1(1)* 44 to 7 labelled a_1(1)* 44 to 33 labelled b_1(1) 3.76/1.74 3.76/1.74 3.76/1.74 ---------------------------------------- 3.76/1.74 3.76/1.74 (6) 3.76/1.74 YES 3.76/1.77 EOF