/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) RFCMatchBoundsTRSProof [EQUIVALENT, 20 ms] (2) YES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, 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, 212, 213, 214, 218, 219, 220, 224, 225, 226, 230, 231, 232, 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, 299, 300, 301, 302, 303, 304, 305 Node 1 is start node and node 3 is final node. Those nodes are connected through the following edges: * 1 to 5 labelled c_1(0)* 1 to 9 labelled b_1(0)* 1 to 12 labelled b_1(1)* 3 to 3 labelled #_1(0)* 5 to 6 labelled c_1(0)* 5 to 15 labelled b_1(1)* 6 to 7 labelled c_1(0)* 6 to 18 labelled b_1(1)* 7 to 8 labelled c_1(0)* 7 to 21 labelled b_1(1)* 8 to 3 labelled a_1(0)* 8 to 24 labelled c_1(1)* 8 to 28 labelled b_1(2)* 9 to 10 labelled a_1(0)* 9 to 40 labelled c_1(1)* 9 to 44 labelled b_1(2)* 10 to 11 labelled a_1(0)* 10 to 24 labelled c_1(1)* 10 to 28 labelled b_1(2)* 11 to 3 labelled b_1(0)* 12 to 13 labelled a_1(1)* 13 to 14 labelled a_1(1)* 14 to 5 labelled b_1(1)* 15 to 16 labelled a_1(1)* 16 to 17 labelled a_1(1)* 17 to 6 labelled b_1(1)* 18 to 19 labelled a_1(1)* 19 to 20 labelled a_1(1)* 20 to 7 labelled b_1(1)* 21 to 22 labelled a_1(1)* 21 to 56 labelled c_1(2)* 21 to 64 labelled b_1(3)* 22 to 23 labelled a_1(1)* 22 to 24 labelled c_1(1)* 22 to 28 labelled b_1(2)* 23 to 8 labelled b_1(1)* 24 to 25 labelled c_1(1)* 24 to 31 labelled b_1(2)* 25 to 26 labelled c_1(1)* 25 to 34 labelled b_1(2)* 26 to 27 labelled c_1(1)* 26 to 37 labelled b_1(2)* 27 to 3 labelled a_1(1)* 27 to 24 labelled c_1(1)* 27 to 28 labelled b_1(2)* 28 to 29 labelled a_1(2)* 29 to 30 labelled a_1(2)* 30 to 24 labelled b_1(2)* 31 to 32 labelled a_1(2)* 32 to 33 labelled a_1(2)* 33 to 25 labelled b_1(2)* 34 to 35 labelled a_1(2)* 35 to 36 labelled a_1(2)* 36 to 26 labelled b_1(2)* 37 to 38 labelled a_1(2)* 37 to 242 labelled c_1(3)* 37 to 254 labelled b_1(4)* 38 to 39 labelled a_1(2)* 38 to 24 labelled c_1(1)* 38 to 28 labelled b_1(2)* 39 to 27 labelled b_1(2)* 40 to 41 labelled c_1(1)* 40 to 47 labelled b_1(2)* 41 to 42 labelled c_1(1)* 41 to 50 labelled b_1(2)* 42 to 43 labelled c_1(1)* 42 to 53 labelled b_1(2)* 43 to 24 labelled a_1(1)* 43 to 60 labelled c_1(2)* 43 to 67 labelled b_1(3)* 44 to 45 labelled a_1(2)* 45 to 46 labelled a_1(2)* 46 to 40 labelled b_1(2)* 47 to 48 labelled a_1(2)* 48 to 49 labelled a_1(2)* 49 to 41 labelled b_1(2)* 50 to 51 labelled a_1(2)* 51 to 52 labelled a_1(2)* 52 to 42 labelled b_1(2)* 53 to 54 labelled a_1(2)* 54 to 55 labelled a_1(2)* 55 to 43 labelled b_1(2)* 56 to 57 labelled c_1(2)* 56 to 212 labelled b_1(3)* 57 to 58 labelled c_1(2)* 57 to 218 labelled b_1(3)* 58 to 59 labelled c_1(2)* 58 to 224 labelled b_1(3)* 59 to 24 labelled a_1(2)* 59 to 246 labelled c_1(3)* 59 to 257 labelled b_1(4)* 60 to 61 labelled c_1(2)* 60 to 230 labelled b_1(3)* 61 to 62 labelled c_1(2)* 61 to 236 labelled b_1(3)* 62 to 63 labelled c_1(2)* 62 to 239 labelled b_1(3)* 63 to 25 labelled a_1(2)* 63 to 250 labelled c_1(3)* 63 to 260 labelled b_1(4)* 64 to 65 labelled a_1(3)* 65 to 66 labelled a_1(3)* 66 to 56 labelled b_1(3)* 67 to 68 labelled a_1(3)* 68 to 69 labelled a_1(3)* 69 to 60 labelled b_1(3)* 212 to 213 labelled a_1(3)* 213 to 214 labelled a_1(3)* 214 to 57 labelled b_1(3)* 218 to 219 labelled a_1(3)* 219 to 220 labelled a_1(3)* 220 to 58 labelled b_1(3)* 224 to 225 labelled a_1(3)* 225 to 226 labelled a_1(3)* 226 to 59 labelled b_1(3)* 230 to 231 labelled a_1(3)* 231 to 232 labelled a_1(3)* 232 to 61 labelled b_1(3)* 236 to 237 labelled a_1(3)* 237 to 238 labelled a_1(3)* 238 to 62 labelled b_1(3)* 239 to 240 labelled a_1(3)* 240 to 241 labelled a_1(3)* 241 to 63 labelled b_1(3)* 242 to 243 labelled c_1(3)* 242 to 263 labelled b_1(4)* 243 to 244 labelled c_1(3)* 243 to 266 labelled b_1(4)* 244 to 245 labelled c_1(3)* 244 to 269 labelled b_1(4)* 245 to 24 labelled a_1(3)* 245 to 246 labelled c_1(3)* 245 to 257 labelled b_1(4)* 246 to 247 labelled c_1(3)* 246 to 272 labelled b_1(4)* 247 to 248 labelled c_1(3)* 247 to 275 labelled b_1(4)* 248 to 249 labelled c_1(3)* 248 to 278 labelled b_1(4)* 249 to 25 labelled a_1(3)* 249 to 250 labelled c_1(3)* 249 to 260 labelled b_1(4)* 250 to 251 labelled c_1(3)* 250 to 281 labelled b_1(4)* 251 to 252 labelled c_1(3)* 251 to 284 labelled b_1(4)* 252 to 253 labelled c_1(3)* 252 to 287 labelled b_1(4)* 253 to 26 labelled a_1(3)* 253 to 290 labelled c_1(3)* 253 to 294 labelled b_1(4)* 254 to 255 labelled a_1(4)* 255 to 256 labelled a_1(4)* 256 to 242 labelled b_1(4)* 257 to 258 labelled a_1(4)* 258 to 259 labelled a_1(4)* 259 to 246 labelled b_1(4)* 260 to 261 labelled a_1(4)* 261 to 262 labelled a_1(4)* 262 to 250 labelled b_1(4)* 263 to 264 labelled a_1(4)* 264 to 265 labelled a_1(4)* 265 to 243 labelled b_1(4)* 266 to 267 labelled a_1(4)* 267 to 268 labelled a_1(4)* 268 to 244 labelled b_1(4)* 269 to 270 labelled a_1(4)* 270 to 271 labelled a_1(4)* 271 to 245 labelled b_1(4)* 272 to 273 labelled a_1(4)* 273 to 274 labelled a_1(4)* 274 to 247 labelled b_1(4)* 275 to 276 labelled a_1(4)* 276 to 277 labelled a_1(4)* 277 to 248 labelled b_1(4)* 278 to 279 labelled a_1(4)* 279 to 280 labelled a_1(4)* 280 to 249 labelled b_1(4)* 281 to 282 labelled a_1(4)* 282 to 283 labelled a_1(4)* 283 to 251 labelled b_1(4)* 284 to 285 labelled a_1(4)* 285 to 286 labelled a_1(4)* 286 to 252 labelled b_1(4)* 287 to 288 labelled a_1(4)* 288 to 289 labelled a_1(4)* 289 to 253 labelled b_1(4)* 290 to 291 labelled c_1(3)* 290 to 297 labelled b_1(4)* 291 to 292 labelled c_1(3)* 291 to 300 labelled b_1(4)* 292 to 293 labelled c_1(3)* 292 to 303 labelled b_1(4)* 293 to 27 labelled a_1(3)* 293 to 242 labelled c_1(3)* 293 to 254 labelled b_1(4)* 294 to 295 labelled a_1(4)* 295 to 296 labelled a_1(4)* 296 to 290 labelled b_1(4)* 297 to 298 labelled a_1(4)* 298 to 299 labelled a_1(4)* 299 to 291 labelled b_1(4)* 300 to 301 labelled a_1(4)* 301 to 302 labelled a_1(4)* 302 to 292 labelled b_1(4)* 303 to 304 labelled a_1(4)* 303 to 242 labelled c_1(3)* 303 to 254 labelled b_1(4)* 304 to 305 labelled a_1(4)* 304 to 24 labelled c_1(1)* 304 to 28 labelled b_1(2)* 305 to 293 labelled b_1(4) ---------------------------------------- (2) YES