3.81/1.71 YES 3.81/1.72 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 3.81/1.72 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.81/1.72 3.81/1.72 3.81/1.72 Termination w.r.t. Q of the given QTRS could be proven: 3.81/1.72 3.81/1.72 (0) QTRS 3.81/1.72 (1) RFCMatchBoundsTRSProof [EQUIVALENT, 38 ms] 3.81/1.72 (2) YES 3.81/1.72 3.81/1.72 3.81/1.72 ---------------------------------------- 3.81/1.72 3.81/1.72 (0) 3.81/1.72 Obligation: 3.81/1.72 Q restricted rewrite system: 3.81/1.72 The TRS R consists of the following rules: 3.81/1.72 3.81/1.72 a(b(a(a(b(x1))))) -> c(c(c(c(a(x1))))) 3.81/1.72 c(x1) -> b(a(a(b(x1)))) 3.81/1.72 3.81/1.72 Q is empty. 3.81/1.72 3.81/1.72 ---------------------------------------- 3.81/1.72 3.81/1.72 (1) RFCMatchBoundsTRSProof (EQUIVALENT) 3.81/1.72 Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 4. This implies Q-termination of R. 3.81/1.72 The following rules were used to construct the certificate: 3.81/1.72 3.81/1.72 a(b(a(a(b(x1))))) -> c(c(c(c(a(x1))))) 3.81/1.72 c(x1) -> b(a(a(b(x1)))) 3.81/1.72 3.81/1.72 The certificate found is represented by the following graph. 3.81/1.72 The certificate consists of the following enumerated nodes: 3.81/1.72 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, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254 3.81/1.72 3.81/1.72 Node 1 is start node and node 2 is final node. 3.81/1.72 3.81/1.72 Those nodes are connected through the following edges: 3.81/1.72 3.81/1.72 * 1 to 3 labelled c_1(0)* 1 to 7 labelled b_1(0)* 1 to 10 labelled b_1(1)* 2 to 2 labelled #_1(0)* 3 to 4 labelled c_1(0)* 3 to 13 labelled b_1(1)* 4 to 5 labelled c_1(0)* 4 to 16 labelled b_1(1)* 5 to 6 labelled c_1(0)* 5 to 19 labelled b_1(1)* 6 to 2 labelled a_1(0)* 6 to 22 labelled c_1(1)* 6 to 26 labelled b_1(2)* 7 to 8 labelled a_1(0)* 7 to 38 labelled c_1(1)* 7 to 42 labelled b_1(2)* 8 to 9 labelled a_1(0)* 8 to 22 labelled c_1(1)* 8 to 26 labelled b_1(2)* 9 to 2 labelled b_1(0)* 10 to 11 labelled a_1(1)* 11 to 12 labelled a_1(1)* 12 to 3 labelled b_1(1)* 13 to 14 labelled a_1(1)* 14 to 15 labelled a_1(1)* 15 to 4 labelled b_1(1)* 16 to 17 labelled a_1(1)* 17 to 18 labelled a_1(1)* 18 to 5 labelled b_1(1)* 19 to 20 labelled a_1(1)* 19 to 54 labelled c_1(2)* 19 to 62 labelled b_1(3)* 20 to 21 labelled a_1(1)* 20 to 22 labelled c_1(1)* 20 to 26 labelled b_1(2)* 21 to 6 labelled b_1(1)* 22 to 23 labelled c_1(1)* 22 to 29 labelled b_1(2)* 23 to 24 labelled c_1(1)* 23 to 32 labelled b_1(2)* 24 to 25 labelled c_1(1)* 24 to 35 labelled b_1(2)* 25 to 2 labelled a_1(1)* 25 to 22 labelled c_1(1)* 25 to 26 labelled b_1(2)* 26 to 27 labelled a_1(2)* 27 to 28 labelled a_1(2)* 28 to 22 labelled b_1(2)* 29 to 30 labelled a_1(2)* 30 to 31 labelled a_1(2)* 31 to 23 labelled b_1(2)* 32 to 33 labelled a_1(2)* 33 to 34 labelled a_1(2)* 34 to 24 labelled b_1(2)* 35 to 36 labelled a_1(2)* 35 to 86 labelled c_1(3)* 35 to 98 labelled b_1(4)* 36 to 37 labelled a_1(2)* 36 to 22 labelled c_1(1)* 36 to 26 labelled b_1(2)* 37 to 25 labelled b_1(2)* 38 to 39 labelled c_1(1)* 38 to 45 labelled b_1(2)* 39 to 40 labelled c_1(1)* 39 to 48 labelled b_1(2)* 40 to 41 labelled c_1(1)* 40 to 51 labelled b_1(2)* 41 to 22 labelled a_1(1)* 41 to 58 labelled c_1(2)* 41 to 65 labelled b_1(3)* 42 to 43 labelled a_1(2)* 43 to 44 labelled a_1(2)* 44 to 38 labelled b_1(2)* 45 to 46 labelled a_1(2)* 46 to 47 labelled a_1(2)* 47 to 39 labelled b_1(2)* 48 to 49 labelled a_1(2)* 49 to 50 labelled a_1(2)* 50 to 40 labelled b_1(2)* 51 to 52 labelled a_1(2)* 52 to 53 labelled a_1(2)* 53 to 41 labelled b_1(2)* 54 to 55 labelled c_1(2)* 54 to 68 labelled b_1(3)* 55 to 56 labelled c_1(2)* 55 to 71 labelled b_1(3)* 56 to 57 labelled c_1(2)* 56 to 74 labelled b_1(3)* 57 to 22 labelled a_1(2)* 57 to 90 labelled c_1(3)* 57 to 101 labelled b_1(4)* 58 to 59 labelled c_1(2)* 58 to 77 labelled b_1(3)* 59 to 60 labelled c_1(2)* 59 to 80 labelled b_1(3)* 60 to 61 labelled c_1(2)* 60 to 83 labelled b_1(3)* 61 to 23 labelled a_1(2)* 61 to 94 labelled c_1(3)* 61 to 104 labelled b_1(4)* 62 to 63 labelled a_1(3)* 63 to 64 labelled a_1(3)* 64 to 54 labelled b_1(3)* 65 to 66 labelled a_1(3)* 66 to 67 labelled a_1(3)* 67 to 58 labelled b_1(3)* 68 to 69 labelled a_1(3)* 69 to 70 labelled a_1(3)* 70 to 55 labelled b_1(3)* 71 to 72 labelled a_1(3)* 72 to 73 labelled a_1(3)* 73 to 56 labelled b_1(3)* 74 to 75 labelled a_1(3)* 75 to 76 labelled a_1(3)* 76 to 57 labelled b_1(3)* 77 to 78 labelled a_1(3)* 78 to 79 labelled a_1(3)* 79 to 59 labelled b_1(3)* 80 to 81 labelled a_1(3)* 81 to 82 labelled a_1(3)* 82 to 60 labelled b_1(3)* 83 to 84 labelled a_1(3)* 84 to 85 labelled a_1(3)* 85 to 61 labelled b_1(3)* 86 to 87 labelled c_1(3)* 86 to 107 labelled b_1(4)* 87 to 88 labelled c_1(3)* 87 to 110 labelled b_1(4)* 88 to 89 labelled c_1(3)* 88 to 113 labelled b_1(4)* 89 to 22 labelled a_1(3)* 89 to 90 labelled c_1(3)* 89 to 101 labelled b_1(4)* 90 to 91 labelled c_1(3)* 90 to 116 labelled b_1(4)* 91 to 92 labelled c_1(3)* 91 to 119 labelled b_1(4)* 92 to 93 labelled c_1(3)* 92 to 122 labelled b_1(4)* 93 to 23 labelled a_1(3)* 93 to 94 labelled c_1(3)* 93 to 104 labelled b_1(4)* 94 to 95 labelled c_1(3)* 94 to 125 labelled b_1(4)* 95 to 96 labelled c_1(3)* 95 to 128 labelled b_1(4)* 96 to 97 labelled c_1(3)* 96 to 131 labelled b_1(4)* 97 to 24 labelled a_1(3)* 97 to 134 labelled c_1(3)* 97 to 243 labelled b_1(4)* 98 to 99 labelled a_1(4)* 99 to 100 labelled a_1(4)* 100 to 86 labelled b_1(4)* 101 to 102 labelled a_1(4)* 102 to 103 labelled a_1(4)* 103 to 90 labelled b_1(4)* 104 to 105 labelled a_1(4)* 105 to 106 labelled a_1(4)* 106 to 94 labelled b_1(4)* 107 to 108 labelled a_1(4)* 108 to 109 labelled a_1(4)* 109 to 87 labelled b_1(4)* 110 to 111 labelled a_1(4)* 111 to 112 labelled a_1(4)* 112 to 88 labelled b_1(4)* 113 to 114 labelled a_1(4)* 114 to 115 labelled a_1(4)* 115 to 89 labelled b_1(4)* 116 to 117 labelled a_1(4)* 117 to 118 labelled a_1(4)* 118 to 91 labelled b_1(4)* 119 to 120 labelled a_1(4)* 120 to 121 labelled a_1(4)* 121 to 92 labelled b_1(4)* 122 to 123 labelled a_1(4)* 123 to 124 labelled a_1(4)* 124 to 93 labelled b_1(4)* 125 to 126 labelled a_1(4)* 126 to 127 labelled a_1(4)* 127 to 95 labelled b_1(4)* 128 to 129 labelled a_1(4)* 129 to 130 labelled a_1(4)* 130 to 96 labelled b_1(4)* 131 to 132 labelled a_1(4)* 132 to 133 labelled a_1(4)* 133 to 97 labelled b_1(4)* 134 to 135 labelled c_1(3)* 134 to 246 labelled b_1(4)* 135 to 136 labelled c_1(3)* 135 to 249 labelled b_1(4)* 136 to 137 labelled c_1(3)* 136 to 252 labelled b_1(4)* 137 to 25 labelled a_1(3)* 137 to 86 labelled c_1(3)* 137 to 98 labelled b_1(4)* 243 to 244 labelled a_1(4)* 244 to 245 labelled a_1(4)* 245 to 134 labelled b_1(4)* 246 to 247 labelled a_1(4)* 247 to 248 labelled a_1(4)* 248 to 135 labelled b_1(4)* 249 to 250 labelled a_1(4)* 250 to 251 labelled a_1(4)* 251 to 136 labelled b_1(4)* 252 to 253 labelled a_1(4)* 252 to 86 labelled c_1(3)* 252 to 98 labelled b_1(4)* 253 to 254 labelled a_1(4)* 253 to 22 labelled c_1(1)* 253 to 26 labelled b_1(2)* 254 to 137 labelled b_1(4) 3.81/1.72 3.81/1.72 3.81/1.72 ---------------------------------------- 3.81/1.72 3.81/1.72 (2) 3.81/1.72 YES 3.81/1.75 EOF