/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) RFCMatchBoundsTRSProof [EQUIVALENT, 27 ms] (2) YES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, 3, 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, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 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 3 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)* 3 to 3 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 47 labelled 1_1(1)* 8 to 56 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 26 labelled 1_1(1)* 11 to 35 labelled 1_1(1)* 12 to 13 labelled 1_1(0)* 13 to 3 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 236 labelled 1_1(1)* 17 to 245 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 47 labelled 1_1(1)* 20 to 56 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 26 labelled 1_1(1)* 23 to 35 labelled 1_1(1)* 24 to 25 labelled 1_1(0)* 25 to 3 labelled 2_1(0)* 26 to 27 labelled 2_1(1)* 27 to 28 labelled 1_1(1)* 28 to 29 labelled 1_1(1)* 29 to 30 labelled 0_1(1)* 29 to 257 labelled 1_1(2)* 29 to 266 labelled 1_1(2)* 30 to 31 labelled 1_1(1)* 31 to 32 labelled 2_1(1)* 32 to 33 labelled 0_1(1)* 32 to 26 labelled 1_1(1)* 32 to 35 labelled 1_1(1)* 33 to 34 labelled 1_1(1)* 34 to 3 labelled 2_1(1)* 35 to 36 labelled 2_1(1)* 36 to 37 labelled 1_1(1)* 37 to 38 labelled 1_1(1)* 38 to 39 labelled 0_1(1)* 38 to 278 labelled 1_1(2)* 38 to 287 labelled 1_1(2)* 39 to 40 labelled 1_1(1)* 40 to 41 labelled 2_1(1)* 41 to 42 labelled 0_1(1)* 41 to 257 labelled 1_1(2)* 41 to 266 labelled 1_1(2)* 42 to 43 labelled 1_1(1)* 43 to 44 labelled 2_1(1)* 44 to 45 labelled 0_1(1)* 44 to 26 labelled 1_1(1)* 44 to 35 labelled 1_1(1)* 45 to 46 labelled 1_1(1)* 46 to 3 labelled 2_1(1)* 47 to 48 labelled 2_1(1)* 48 to 49 labelled 1_1(1)* 49 to 50 labelled 1_1(1)* 50 to 51 labelled 0_1(1)* 51 to 52 labelled 1_1(1)* 52 to 53 labelled 2_1(1)* 53 to 54 labelled 0_1(1)* 54 to 55 labelled 1_1(1)* 55 to 26 labelled 2_1(1)* 55 to 35 labelled 2_1(1)* 56 to 57 labelled 2_1(1)* 57 to 58 labelled 1_1(1)* 58 to 59 labelled 1_1(1)* 59 to 60 labelled 0_1(1)* 60 to 61 labelled 1_1(1)* 61 to 62 labelled 2_1(1)* 62 to 63 labelled 0_1(1)* 63 to 64 labelled 1_1(1)* 64 to 65 labelled 2_1(1)* 65 to 66 labelled 0_1(1)* 66 to 67 labelled 1_1(1)* 67 to 26 labelled 2_1(1)* 67 to 35 labelled 2_1(1)* 236 to 237 labelled 2_1(1)* 237 to 238 labelled 1_1(1)* 238 to 239 labelled 1_1(1)* 239 to 240 labelled 0_1(1)* 240 to 241 labelled 1_1(1)* 241 to 242 labelled 2_1(1)* 242 to 243 labelled 0_1(1)* 243 to 244 labelled 1_1(1)* 244 to 47 labelled 2_1(1)* 244 to 56 labelled 2_1(1)* 245 to 246 labelled 2_1(1)* 246 to 247 labelled 1_1(1)* 247 to 248 labelled 1_1(1)* 248 to 249 labelled 0_1(1)* 249 to 250 labelled 1_1(1)* 250 to 251 labelled 2_1(1)* 251 to 252 labelled 0_1(1)* 252 to 253 labelled 1_1(1)* 253 to 254 labelled 2_1(1)* 254 to 255 labelled 0_1(1)* 255 to 256 labelled 1_1(1)* 256 to 47 labelled 2_1(1)* 256 to 56 labelled 2_1(1)* 257 to 258 labelled 2_1(2)* 258 to 259 labelled 1_1(2)* 259 to 260 labelled 1_1(2)* 260 to 261 labelled 0_1(2)* 261 to 262 labelled 1_1(2)* 262 to 263 labelled 2_1(2)* 263 to 264 labelled 0_1(2)* 264 to 265 labelled 1_1(2)* 265 to 26 labelled 2_1(2)* 265 to 35 labelled 2_1(2)* 266 to 267 labelled 2_1(2)* 267 to 268 labelled 1_1(2)* 268 to 269 labelled 1_1(2)* 269 to 270 labelled 0_1(2)* 270 to 271 labelled 1_1(2)* 271 to 272 labelled 2_1(2)* 272 to 273 labelled 0_1(2)* 273 to 274 labelled 1_1(2)* 274 to 275 labelled 2_1(2)* 275 to 276 labelled 0_1(2)* 276 to 277 labelled 1_1(2)* 277 to 26 labelled 2_1(2)* 277 to 35 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 257 labelled 2_1(2)* 286 to 266 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 257 labelled 2_1(2)* 298 to 266 labelled 2_1(2) ---------------------------------------- (2) YES