3.27/1.61 YES 3.27/1.61 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 3.27/1.61 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.27/1.61 3.27/1.61 3.27/1.61 Termination w.r.t. Q of the given QTRS could be proven: 3.27/1.61 3.27/1.61 (0) QTRS 3.27/1.61 (1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] 3.27/1.61 (2) YES 3.27/1.61 3.27/1.61 3.27/1.61 ---------------------------------------- 3.27/1.61 3.27/1.61 (0) 3.27/1.61 Obligation: 3.27/1.61 Q restricted rewrite system: 3.27/1.61 The TRS R consists of the following rules: 3.27/1.61 3.27/1.61 a(a(b(a(a(b(a(x1))))))) -> a(b(a(a(b(a(a(a(b(x1))))))))) 3.27/1.61 3.27/1.61 Q is empty. 3.27/1.61 3.27/1.61 ---------------------------------------- 3.27/1.61 3.27/1.61 (1) RFCMatchBoundsTRSProof (EQUIVALENT) 3.27/1.61 Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R. 3.27/1.61 The following rules were used to construct the certificate: 3.27/1.61 3.27/1.61 a(a(b(a(a(b(a(x1))))))) -> a(b(a(a(b(a(a(a(b(x1))))))))) 3.27/1.61 3.27/1.61 The certificate found is represented by the following graph. 3.27/1.61 The certificate consists of the following enumerated nodes: 3.27/1.61 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50 3.27/1.61 3.27/1.61 Node 1 is start node and node 2 is final node. 3.27/1.61 3.27/1.61 Those nodes are connected through the following edges: 3.27/1.61 3.27/1.61 * 1 to 3 labelled a_1(0)* 2 to 2 labelled #_1(0)* 3 to 4 labelled b_1(0)* 4 to 5 labelled a_1(0)* 4 to 19 labelled a_1(1)* 5 to 6 labelled a_1(0)* 6 to 7 labelled b_1(0)* 7 to 8 labelled a_1(0)* 7 to 27 labelled a_1(1)* 8 to 9 labelled a_1(0)* 8 to 11 labelled a_1(1)* 9 to 10 labelled a_1(0)* 10 to 2 labelled b_1(0)* 11 to 12 labelled b_1(1)* 12 to 13 labelled a_1(1)* 12 to 35 labelled a_1(2)* 13 to 14 labelled a_1(1)* 14 to 15 labelled b_1(1)* 15 to 16 labelled a_1(1)* 15 to 43 labelled a_1(2)* 16 to 17 labelled a_1(1)* 16 to 11 labelled a_1(1)* 17 to 18 labelled a_1(1)* 18 to 2 labelled b_1(1)* 19 to 20 labelled b_1(1)* 20 to 21 labelled a_1(1)* 21 to 22 labelled a_1(1)* 22 to 23 labelled b_1(1)* 23 to 24 labelled a_1(1)* 24 to 25 labelled a_1(1)* 25 to 26 labelled a_1(1)* 26 to 13 labelled b_1(1)* 26 to 35 labelled b_1(1)* 27 to 28 labelled b_1(1)* 28 to 29 labelled a_1(1)* 28 to 35 labelled a_1(2)* 29 to 30 labelled a_1(1)* 30 to 31 labelled b_1(1)* 31 to 32 labelled a_1(1)* 31 to 43 labelled a_1(2)* 32 to 33 labelled a_1(1)* 32 to 11 labelled a_1(1)* 33 to 34 labelled a_1(1)* 34 to 16 labelled b_1(1)* 34 to 43 labelled b_1(1)* 35 to 36 labelled b_1(2)* 36 to 37 labelled a_1(2)* 37 to 38 labelled a_1(2)* 38 to 39 labelled b_1(2)* 39 to 40 labelled a_1(2)* 40 to 41 labelled a_1(2)* 41 to 42 labelled a_1(2)* 42 to 13 labelled b_1(2)* 42 to 35 labelled b_1(2)* 43 to 44 labelled b_1(2)* 44 to 45 labelled a_1(2)* 44 to 35 labelled a_1(2)* 45 to 46 labelled a_1(2)* 46 to 47 labelled b_1(2)* 47 to 48 labelled a_1(2)* 47 to 43 labelled a_1(2)* 48 to 49 labelled a_1(2)* 48 to 11 labelled a_1(1)* 49 to 50 labelled a_1(2)* 50 to 16 labelled b_1(2)* 50 to 43 labelled b_1(2) 3.27/1.61 3.27/1.61 3.27/1.61 ---------------------------------------- 3.27/1.61 3.27/1.61 (2) 3.27/1.61 YES 3.50/1.65 EOF