3.92/1.70 YES 3.92/1.71 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 3.92/1.71 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.92/1.71 3.92/1.71 3.92/1.71 Termination w.r.t. Q of the given QTRS could be proven: 3.92/1.71 3.92/1.71 (0) QTRS 3.92/1.71 (1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] 3.92/1.71 (2) YES 3.92/1.71 3.92/1.71 3.92/1.71 ---------------------------------------- 3.92/1.71 3.92/1.71 (0) 3.92/1.71 Obligation: 3.92/1.71 Q restricted rewrite system: 3.92/1.71 The TRS R consists of the following rules: 3.92/1.71 3.92/1.71 a(c(b(x1))) -> b(a(b(a(x1)))) 3.92/1.71 b(x1) -> c(a(c(x1))) 3.92/1.71 a(a(x1)) -> a(b(c(a(x1)))) 3.92/1.71 3.92/1.71 Q is empty. 3.92/1.71 3.92/1.71 ---------------------------------------- 3.92/1.71 3.92/1.71 (1) RFCMatchBoundsTRSProof (EQUIVALENT) 3.92/1.71 Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 4. This implies Q-termination of R. 3.92/1.71 The following rules were used to construct the certificate: 3.92/1.71 3.92/1.71 a(c(b(x1))) -> b(a(b(a(x1)))) 3.92/1.71 b(x1) -> c(a(c(x1))) 3.92/1.71 a(a(x1)) -> a(b(c(a(x1)))) 3.92/1.71 3.92/1.71 The certificate found is represented by the following graph. 3.92/1.71 The certificate consists of the following enumerated nodes: 3.92/1.71 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, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95 3.92/1.71 3.92/1.71 Node 1 is start node and node 2 is final node. 3.92/1.71 3.92/1.71 Those nodes are connected through the following edges: 3.92/1.71 3.92/1.71 * 1 to 3 labelled b_1(0)* 1 to 6 labelled c_1(0)* 1 to 8 labelled a_1(0)* 1 to 11 labelled c_1(1)* 2 to 2 labelled #_1(0)* 3 to 4 labelled a_1(0)* 3 to 39 labelled b_1(1)* 3 to 42 labelled c_1(2)* 4 to 5 labelled b_1(0)* 4 to 13 labelled c_1(1)* 5 to 2 labelled a_1(0)* 5 to 17 labelled b_1(1)* 5 to 20 labelled a_1(1)* 5 to 23 labelled c_1(2)* 6 to 7 labelled a_1(0)* 6 to 17 labelled b_1(1)* 6 to 23 labelled c_1(2)* 7 to 2 labelled c_1(0)* 8 to 9 labelled b_1(0)* 8 to 15 labelled c_1(1)* 9 to 10 labelled c_1(0)* 10 to 2 labelled a_1(0)* 10 to 17 labelled b_1(1)* 10 to 20 labelled a_1(1)* 10 to 23 labelled c_1(2)* 11 to 12 labelled a_1(1)* 11 to 51 labelled b_1(2)* 11 to 60 labelled c_1(3)* 12 to 3 labelled c_1(1)* 13 to 14 labelled a_1(1)* 13 to 29 labelled b_1(2)* 13 to 32 labelled c_1(3)* 14 to 5 labelled c_1(1)* 15 to 16 labelled a_1(1)* 16 to 9 labelled c_1(1)* 17 to 18 labelled a_1(1)* 17 to 54 labelled b_1(2)* 17 to 62 labelled c_1(3)* 18 to 19 labelled b_1(1)* 18 to 25 labelled c_1(2)* 19 to 2 labelled a_1(1)* 19 to 17 labelled b_1(1)* 19 to 20 labelled a_1(1)* 19 to 23 labelled c_1(2)* 20 to 21 labelled b_1(1)* 20 to 27 labelled c_1(2)* 21 to 22 labelled c_1(1)* 22 to 2 labelled a_1(1)* 22 to 17 labelled b_1(1)* 22 to 20 labelled a_1(1)* 22 to 23 labelled c_1(2)* 23 to 24 labelled a_1(2)* 23 to 80 labelled b_1(3)* 23 to 83 labelled c_1(4)* 24 to 17 labelled c_1(2)* 25 to 26 labelled a_1(2)* 25 to 29 labelled b_1(2)* 25 to 32 labelled c_1(3)* 26 to 19 labelled c_1(2)* 27 to 28 labelled a_1(2)* 28 to 21 labelled c_1(2)* 29 to 30 labelled a_1(2)* 30 to 31 labelled b_1(2)* 30 to 34 labelled c_1(3)* 31 to 17 labelled a_1(2)* 31 to 36 labelled a_1(2)* 32 to 33 labelled a_1(3)* 33 to 29 labelled c_1(3)* 34 to 35 labelled a_1(3)* 35 to 31 labelled c_1(3)* 36 to 37 labelled b_1(2)* 36 to 44 labelled c_1(3)* 37 to 38 labelled c_1(2)* 38 to 18 labelled a_1(2)* 38 to 57 labelled b_1(3)* 38 to 64 labelled c_1(4)* 39 to 40 labelled a_1(1)* 40 to 41 labelled b_1(1)* 40 to 46 labelled c_1(2)* 41 to 29 labelled a_1(1)* 41 to 48 labelled a_1(2)* 42 to 43 labelled a_1(2)* 43 to 39 labelled c_1(2)* 44 to 45 labelled a_1(3)* 45 to 37 labelled c_1(3)* 46 to 47 labelled a_1(2)* 47 to 41 labelled c_1(2)* 48 to 49 labelled b_1(2)* 48 to 66 labelled c_1(3)* 49 to 50 labelled c_1(2)* 50 to 30 labelled a_1(2)* 51 to 52 labelled a_1(2)* 52 to 53 labelled b_1(2)* 52 to 68 labelled c_1(3)* 53 to 39 labelled a_1(2)* 53 to 77 labelled a_1(2)* 54 to 55 labelled a_1(2)* 55 to 56 labelled b_1(2)* 55 to 70 labelled c_1(3)* 56 to 29 labelled a_1(2)* 56 to 74 labelled a_1(3)* 57 to 58 labelled a_1(3)* 58 to 59 labelled b_1(3)* 58 to 72 labelled c_1(4)* 59 to 29 labelled a_1(3)* 59 to 74 labelled a_1(3)* 60 to 61 labelled a_1(3)* 61 to 51 labelled c_1(3)* 62 to 63 labelled a_1(3)* 63 to 54 labelled c_1(3)* 64 to 65 labelled a_1(4)* 65 to 57 labelled c_1(4)* 66 to 67 labelled a_1(3)* 67 to 49 labelled c_1(3)* 68 to 69 labelled a_1(3)* 69 to 53 labelled c_1(3)* 70 to 71 labelled a_1(3)* 71 to 56 labelled c_1(3)* 72 to 73 labelled a_1(4)* 73 to 59 labelled c_1(4)* 74 to 75 labelled b_1(3)* 74 to 85 labelled c_1(4)* 75 to 76 labelled c_1(3)* 76 to 30 labelled a_1(3)* 77 to 78 labelled b_1(2)* 77 to 87 labelled c_1(3)* 78 to 79 labelled c_1(2)* 79 to 40 labelled a_1(2)* 80 to 81 labelled a_1(3)* 81 to 82 labelled b_1(3)* 81 to 89 labelled c_1(4)* 82 to 54 labelled a_1(3)* 82 to 91 labelled a_1(3)* 83 to 84 labelled a_1(4)* 84 to 80 labelled c_1(4)* 85 to 86 labelled a_1(4)* 86 to 75 labelled c_1(4)* 87 to 88 labelled a_1(3)* 88 to 78 labelled c_1(3)* 89 to 90 labelled a_1(4)* 90 to 82 labelled c_1(4)* 91 to 92 labelled b_1(3)* 91 to 94 labelled c_1(4)* 92 to 93 labelled c_1(3)* 93 to 55 labelled a_1(3)* 94 to 95 labelled a_1(4)* 95 to 92 labelled c_1(4) 3.92/1.71 3.92/1.71 3.92/1.71 ---------------------------------------- 3.92/1.71 3.92/1.71 (2) 3.92/1.71 YES 4.05/1.75 EOF