/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) RFCMatchBoundsTRSProof [EQUIVALENT, 19 ms] (2) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(x1)))))))))) 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(x1))))))))))))) Q is empty. ---------------------------------------- (1) RFCMatchBoundsTRSProof (EQUIVALENT) Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R. The following rules were used to construct the certificate: 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(x1)))))))))) 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(x1))))))))))))) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 1, 2, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 89, 90, 91, 92, 93, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298 Node 1 is start node and node 2 is final node. Those nodes are connected through the following edges: * 1 to 5 labelled 1_1(0)* 1 to 14 labelled 1_1(0)* 2 to 2 labelled #_1(0)* 5 to 6 labelled 2_1(0)* 6 to 7 labelled 1_1(0)* 7 to 8 labelled 1_1(0)* 8 to 9 labelled 0_1(0)* 8 to 152 labelled 1_1(1)* 8 to 161 labelled 1_1(1)* 9 to 10 labelled 1_1(0)* 10 to 11 labelled 2_1(0)* 11 to 12 labelled 0_1(0)* 11 to 89 labelled 1_1(1)* 11 to 140 labelled 1_1(1)* 12 to 13 labelled 1_1(0)* 13 to 2 labelled 2_1(0)* 14 to 15 labelled 2_1(0)* 15 to 16 labelled 1_1(0)* 16 to 17 labelled 1_1(0)* 17 to 18 labelled 0_1(0)* 17 to 173 labelled 1_1(1)* 17 to 182 labelled 1_1(1)* 18 to 19 labelled 1_1(0)* 19 to 20 labelled 2_1(0)* 20 to 21 labelled 0_1(0)* 20 to 152 labelled 1_1(1)* 20 to 161 labelled 1_1(1)* 21 to 22 labelled 1_1(0)* 22 to 23 labelled 2_1(0)* 23 to 24 labelled 0_1(0)* 23 to 89 labelled 1_1(1)* 23 to 140 labelled 1_1(1)* 24 to 25 labelled 1_1(0)* 25 to 2 labelled 2_1(0)* 89 to 90 labelled 2_1(1)* 90 to 91 labelled 1_1(1)* 91 to 92 labelled 1_1(1)* 92 to 93 labelled 0_1(1)* 92 to 194 labelled 1_1(2)* 92 to 203 labelled 1_1(2)* 93 to 136 labelled 1_1(1)* 136 to 137 labelled 2_1(1)* 137 to 138 labelled 0_1(1)* 137 to 89 labelled 1_1(1)* 137 to 140 labelled 1_1(1)* 138 to 139 labelled 1_1(1)* 139 to 2 labelled 2_1(1)* 140 to 141 labelled 2_1(1)* 141 to 142 labelled 1_1(1)* 142 to 143 labelled 1_1(1)* 143 to 144 labelled 0_1(1)* 143 to 278 labelled 1_1(2)* 143 to 287 labelled 1_1(2)* 144 to 145 labelled 1_1(1)* 145 to 146 labelled 2_1(1)* 146 to 147 labelled 0_1(1)* 146 to 194 labelled 1_1(2)* 146 to 203 labelled 1_1(2)* 147 to 148 labelled 1_1(1)* 148 to 149 labelled 2_1(1)* 149 to 150 labelled 0_1(1)* 149 to 89 labelled 1_1(1)* 149 to 140 labelled 1_1(1)* 150 to 151 labelled 1_1(1)* 151 to 2 labelled 2_1(1)* 152 to 153 labelled 2_1(1)* 153 to 154 labelled 1_1(1)* 154 to 155 labelled 1_1(1)* 155 to 156 labelled 0_1(1)* 156 to 157 labelled 1_1(1)* 157 to 158 labelled 2_1(1)* 158 to 159 labelled 0_1(1)* 159 to 160 labelled 1_1(1)* 160 to 89 labelled 2_1(1)* 160 to 140 labelled 2_1(1)* 161 to 162 labelled 2_1(1)* 162 to 163 labelled 1_1(1)* 163 to 164 labelled 1_1(1)* 164 to 165 labelled 0_1(1)* 165 to 166 labelled 1_1(1)* 166 to 167 labelled 2_1(1)* 167 to 168 labelled 0_1(1)* 168 to 169 labelled 1_1(1)* 169 to 170 labelled 2_1(1)* 170 to 171 labelled 0_1(1)* 171 to 172 labelled 1_1(1)* 172 to 89 labelled 2_1(1)* 172 to 140 labelled 2_1(1)* 173 to 174 labelled 2_1(1)* 174 to 175 labelled 1_1(1)* 175 to 176 labelled 1_1(1)* 176 to 177 labelled 0_1(1)* 177 to 178 labelled 1_1(1)* 178 to 179 labelled 2_1(1)* 179 to 180 labelled 0_1(1)* 180 to 181 labelled 1_1(1)* 181 to 152 labelled 2_1(1)* 181 to 161 labelled 2_1(1)* 182 to 183 labelled 2_1(1)* 183 to 184 labelled 1_1(1)* 184 to 185 labelled 1_1(1)* 185 to 186 labelled 0_1(1)* 186 to 187 labelled 1_1(1)* 187 to 188 labelled 2_1(1)* 188 to 189 labelled 0_1(1)* 189 to 190 labelled 1_1(1)* 190 to 191 labelled 2_1(1)* 191 to 192 labelled 0_1(1)* 192 to 193 labelled 1_1(1)* 193 to 152 labelled 2_1(1)* 193 to 161 labelled 2_1(1)* 194 to 195 labelled 2_1(2)* 195 to 196 labelled 1_1(2)* 196 to 197 labelled 1_1(2)* 197 to 198 labelled 0_1(2)* 198 to 199 labelled 1_1(2)* 199 to 200 labelled 2_1(2)* 200 to 201 labelled 0_1(2)* 201 to 202 labelled 1_1(2)* 202 to 89 labelled 2_1(2)* 202 to 140 labelled 2_1(2)* 203 to 204 labelled 2_1(2)* 204 to 205 labelled 1_1(2)* 205 to 206 labelled 1_1(2)* 206 to 207 labelled 0_1(2)* 207 to 208 labelled 1_1(2)* 208 to 209 labelled 2_1(2)* 209 to 210 labelled 0_1(2)* 210 to 211 labelled 1_1(2)* 211 to 212 labelled 2_1(2)* 212 to 213 labelled 0_1(2)* 213 to 214 labelled 1_1(2)* 214 to 89 labelled 2_1(2)* 214 to 140 labelled 2_1(2)* 278 to 279 labelled 2_1(2)* 279 to 280 labelled 1_1(2)* 280 to 281 labelled 1_1(2)* 281 to 282 labelled 0_1(2)* 282 to 283 labelled 1_1(2)* 283 to 284 labelled 2_1(2)* 284 to 285 labelled 0_1(2)* 285 to 286 labelled 1_1(2)* 286 to 194 labelled 2_1(2)* 286 to 203 labelled 2_1(2)* 287 to 288 labelled 2_1(2)* 288 to 289 labelled 1_1(2)* 289 to 290 labelled 1_1(2)* 290 to 291 labelled 0_1(2)* 291 to 292 labelled 1_1(2)* 292 to 293 labelled 2_1(2)* 293 to 294 labelled 0_1(2)* 294 to 295 labelled 1_1(2)* 295 to 296 labelled 2_1(2)* 296 to 297 labelled 0_1(2)* 297 to 298 labelled 1_1(2)* 298 to 194 labelled 2_1(2)* 298 to 203 labelled 2_1(2) ---------------------------------------- (2) YES