/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) RFCMatchBoundsTRSProof [EQUIVALENT, 17 ms] (2) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(b(a(a(b(x1))))) -> c(c(c(c(a(x1))))) c(x1) -> b(a(a(b(x1)))) Q is empty. ---------------------------------------- (1) RFCMatchBoundsTRSProof (EQUIVALENT) Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 4. This implies Q-termination of R. The following rules were used to construct the certificate: a(b(a(a(b(x1))))) -> c(c(c(c(a(x1))))) c(x1) -> b(a(a(b(x1)))) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 1, 3, 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, 138, 139, 140, 142, 144, 146, 147, 148, 150, 153, 154, 156, 159, 160, 161, 162, 163, 165, 168, 169, 170, 171, 172, 173, 174, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254 Node 1 is start node and node 3 is final node. Those nodes are connected through the following edges: * 1 to 28 labelled c_1(0)* 1 to 32 labelled b_1(0)* 1 to 35 labelled b_1(1)* 3 to 3 labelled #_1(0)* 28 to 29 labelled c_1(0)* 28 to 38 labelled b_1(1)* 29 to 30 labelled c_1(0)* 29 to 41 labelled b_1(1)* 30 to 31 labelled c_1(0)* 30 to 44 labelled b_1(1)* 31 to 3 labelled a_1(0)* 31 to 47 labelled c_1(1)* 31 to 51 labelled b_1(2)* 32 to 33 labelled a_1(0)* 32 to 63 labelled c_1(1)* 32 to 67 labelled b_1(2)* 33 to 34 labelled a_1(0)* 33 to 47 labelled c_1(1)* 33 to 51 labelled b_1(2)* 34 to 3 labelled b_1(0)* 35 to 36 labelled a_1(1)* 36 to 37 labelled a_1(1)* 37 to 28 labelled b_1(1)* 38 to 39 labelled a_1(1)* 39 to 40 labelled a_1(1)* 40 to 29 labelled b_1(1)* 41 to 42 labelled a_1(1)* 42 to 43 labelled a_1(1)* 43 to 30 labelled b_1(1)* 44 to 45 labelled a_1(1)* 44 to 79 labelled c_1(2)* 44 to 87 labelled b_1(3)* 45 to 46 labelled a_1(1)* 45 to 47 labelled c_1(1)* 45 to 51 labelled b_1(2)* 46 to 31 labelled b_1(1)* 47 to 48 labelled c_1(1)* 47 to 54 labelled b_1(2)* 48 to 49 labelled c_1(1)* 48 to 57 labelled b_1(2)* 49 to 50 labelled c_1(1)* 49 to 60 labelled b_1(2)* 50 to 3 labelled a_1(1)* 50 to 47 labelled c_1(1)* 50 to 51 labelled b_1(2)* 51 to 52 labelled a_1(2)* 52 to 53 labelled a_1(2)* 53 to 47 labelled b_1(2)* 54 to 55 labelled a_1(2)* 55 to 56 labelled a_1(2)* 56 to 48 labelled b_1(2)* 57 to 58 labelled a_1(2)* 58 to 59 labelled a_1(2)* 59 to 49 labelled b_1(2)* 60 to 61 labelled a_1(2)* 60 to 111 labelled c_1(3)* 60 to 123 labelled b_1(4)* 61 to 62 labelled a_1(2)* 61 to 47 labelled c_1(1)* 61 to 51 labelled b_1(2)* 62 to 50 labelled b_1(2)* 63 to 64 labelled c_1(1)* 63 to 70 labelled b_1(2)* 64 to 65 labelled c_1(1)* 64 to 73 labelled b_1(2)* 65 to 66 labelled c_1(1)* 65 to 76 labelled b_1(2)* 66 to 47 labelled a_1(1)* 66 to 83 labelled c_1(2)* 66 to 90 labelled b_1(3)* 67 to 68 labelled a_1(2)* 68 to 69 labelled a_1(2)* 69 to 63 labelled b_1(2)* 70 to 71 labelled a_1(2)* 71 to 72 labelled a_1(2)* 72 to 64 labelled b_1(2)* 73 to 74 labelled a_1(2)* 74 to 75 labelled a_1(2)* 75 to 65 labelled b_1(2)* 76 to 77 labelled a_1(2)* 77 to 78 labelled a_1(2)* 78 to 66 labelled b_1(2)* 79 to 80 labelled c_1(2)* 79 to 93 labelled b_1(3)* 80 to 81 labelled c_1(2)* 80 to 96 labelled b_1(3)* 81 to 82 labelled c_1(2)* 81 to 99 labelled b_1(3)* 82 to 47 labelled a_1(2)* 82 to 115 labelled c_1(3)* 82 to 126 labelled b_1(4)* 83 to 84 labelled c_1(2)* 83 to 102 labelled b_1(3)* 84 to 85 labelled c_1(2)* 84 to 105 labelled b_1(3)* 85 to 86 labelled c_1(2)* 85 to 108 labelled b_1(3)* 86 to 48 labelled a_1(2)* 86 to 119 labelled c_1(3)* 86 to 129 labelled b_1(4)* 87 to 88 labelled a_1(3)* 88 to 89 labelled a_1(3)* 89 to 79 labelled b_1(3)* 90 to 91 labelled a_1(3)* 91 to 92 labelled a_1(3)* 92 to 83 labelled b_1(3)* 93 to 94 labelled a_1(3)* 94 to 95 labelled a_1(3)* 95 to 80 labelled b_1(3)* 96 to 97 labelled a_1(3)* 97 to 98 labelled a_1(3)* 98 to 81 labelled b_1(3)* 99 to 100 labelled a_1(3)* 100 to 101 labelled a_1(3)* 101 to 82 labelled b_1(3)* 102 to 103 labelled a_1(3)* 103 to 104 labelled a_1(3)* 104 to 84 labelled b_1(3)* 105 to 106 labelled a_1(3)* 106 to 107 labelled a_1(3)* 107 to 85 labelled b_1(3)* 108 to 109 labelled a_1(3)* 109 to 110 labelled a_1(3)* 110 to 86 labelled b_1(3)* 111 to 112 labelled c_1(3)* 111 to 132 labelled b_1(4)* 112 to 113 labelled c_1(3)* 112 to 135 labelled b_1(4)* 113 to 114 labelled c_1(3)* 113 to 138 labelled b_1(4)* 114 to 47 labelled a_1(3)* 114 to 115 labelled c_1(3)* 114 to 126 labelled b_1(4)* 115 to 116 labelled c_1(3)* 115 to 142 labelled b_1(4)* 116 to 117 labelled c_1(3)* 116 to 147 labelled b_1(4)* 117 to 118 labelled c_1(3)* 117 to 153 labelled b_1(4)* 118 to 48 labelled a_1(3)* 118 to 119 labelled c_1(3)* 118 to 129 labelled b_1(4)* 119 to 120 labelled c_1(3)* 119 to 159 labelled b_1(4)* 120 to 121 labelled c_1(3)* 120 to 162 labelled b_1(4)* 121 to 122 labelled c_1(3)* 121 to 168 labelled b_1(4)* 122 to 49 labelled a_1(3)* 122 to 171 labelled c_1(3)* 122 to 243 labelled b_1(4)* 123 to 124 labelled a_1(4)* 124 to 125 labelled a_1(4)* 125 to 111 labelled b_1(4)* 126 to 127 labelled a_1(4)* 127 to 128 labelled a_1(4)* 128 to 115 labelled b_1(4)* 129 to 130 labelled a_1(4)* 130 to 131 labelled a_1(4)* 131 to 119 labelled b_1(4)* 132 to 133 labelled a_1(4)* 133 to 134 labelled a_1(4)* 134 to 112 labelled b_1(4)* 135 to 136 labelled a_1(4)* 136 to 137 labelled a_1(4)* 137 to 113 labelled b_1(4)* 138 to 139 labelled a_1(4)* 139 to 140 labelled a_1(4)* 140 to 114 labelled b_1(4)* 142 to 144 labelled a_1(4)* 144 to 146 labelled a_1(4)* 146 to 116 labelled b_1(4)* 147 to 148 labelled a_1(4)* 148 to 150 labelled a_1(4)* 150 to 117 labelled b_1(4)* 153 to 154 labelled a_1(4)* 154 to 156 labelled a_1(4)* 156 to 118 labelled b_1(4)* 159 to 160 labelled a_1(4)* 160 to 161 labelled a_1(4)* 161 to 120 labelled b_1(4)* 162 to 163 labelled a_1(4)* 163 to 165 labelled a_1(4)* 165 to 121 labelled b_1(4)* 168 to 169 labelled a_1(4)* 169 to 170 labelled a_1(4)* 170 to 122 labelled b_1(4)* 171 to 172 labelled c_1(3)* 171 to 246 labelled b_1(4)* 172 to 173 labelled c_1(3)* 172 to 249 labelled b_1(4)* 173 to 174 labelled c_1(3)* 173 to 252 labelled b_1(4)* 174 to 50 labelled a_1(3)* 174 to 111 labelled c_1(3)* 174 to 123 labelled b_1(4)* 243 to 244 labelled a_1(4)* 244 to 245 labelled a_1(4)* 245 to 171 labelled b_1(4)* 246 to 247 labelled a_1(4)* 247 to 248 labelled a_1(4)* 248 to 172 labelled b_1(4)* 249 to 250 labelled a_1(4)* 250 to 251 labelled a_1(4)* 251 to 173 labelled b_1(4)* 252 to 253 labelled a_1(4)* 252 to 111 labelled c_1(3)* 252 to 123 labelled b_1(4)* 253 to 254 labelled a_1(4)* 253 to 47 labelled c_1(1)* 253 to 51 labelled b_1(2)* 254 to 174 labelled b_1(4) ---------------------------------------- (2) YES