/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) Strip Symbols Proof [SOUND, 0 ms] (4) QTRS (5) RFCMatchBoundsTRSProof [EQUIVALENT, 6 ms] (6) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(b(a(b(a(a(b(a(b(a(b(a(x1)))))))))))) -> a(a(b(a(b(a(b(a(a(b(a(b(a(b(x1)))))))))))))) Q is empty. ---------------------------------------- (1) QTRS Reverse (EQUIVALENT) We applied the QTRS Reverse Processor [REVERSE]. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(b(a(b(a(b(a(a(b(a(b(a(x1)))))))))))) -> b(a(b(a(b(a(a(b(a(b(a(b(a(a(x1)))))))))))))) Q is empty. ---------------------------------------- (3) Strip Symbols Proof (SOUND) We were given the following TRS: a(b(a(b(a(b(a(a(b(a(b(a(x1)))))))))))) -> b(a(b(a(b(a(a(b(a(b(a(b(a(a(x1)))))))))))))) By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: a(b(a(b(a(b(a(a(b(a(b(x))))))))))) -> b(a(b(a(b(a(a(b(a(b(a(b(a(x))))))))))))) ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(b(a(b(a(b(a(a(b(a(b(x))))))))))) -> b(a(b(a(b(a(a(b(a(b(a(b(a(x))))))))))))) Q is empty. ---------------------------------------- (5) 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: a(b(a(b(a(b(a(a(b(a(b(x))))))))))) -> b(a(b(a(b(a(a(b(a(b(a(b(a(x))))))))))))) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 444, 445, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455 Node 283 is start node and node 284 is final node. Those nodes are connected through the following edges: * 283 to 285 labelled b_1(0)* 284 to 284 labelled #_1(0)* 285 to 286 labelled a_1(0)* 286 to 287 labelled b_1(0)* 287 to 288 labelled a_1(0)* 288 to 289 labelled b_1(0)* 289 to 290 labelled a_1(0)* 289 to 360 labelled b_1(1)* 290 to 291 labelled a_1(0)* 290 to 297 labelled b_1(1)* 291 to 292 labelled b_1(0)* 292 to 293 labelled a_1(0)* 292 to 297 labelled b_1(1)* 293 to 294 labelled b_1(0)* 294 to 295 labelled a_1(0)* 294 to 297 labelled b_1(1)* 295 to 296 labelled b_1(0)* 296 to 284 labelled a_1(0)* 296 to 297 labelled b_1(1)* 297 to 298 labelled a_1(1)* 298 to 299 labelled b_1(1)* 299 to 300 labelled a_1(1)* 300 to 301 labelled b_1(1)* 301 to 302 labelled a_1(1)* 301 to 444 labelled b_1(2)* 302 to 303 labelled a_1(1)* 302 to 297 labelled b_1(1)* 303 to 304 labelled b_1(1)* 304 to 305 labelled a_1(1)* 304 to 297 labelled b_1(1)* 305 to 306 labelled b_1(1)* 306 to 307 labelled a_1(1)* 306 to 297 labelled b_1(1)* 307 to 308 labelled b_1(1)* 308 to 284 labelled a_1(1)* 308 to 297 labelled b_1(1)* 360 to 361 labelled a_1(1)* 361 to 362 labelled b_1(1)* 362 to 363 labelled a_1(1)* 363 to 364 labelled b_1(1)* 364 to 365 labelled a_1(1)* 364 to 444 labelled b_1(2)* 365 to 366 labelled a_1(1)* 365 to 297 labelled b_1(1)* 366 to 367 labelled b_1(1)* 367 to 368 labelled a_1(1)* 368 to 369 labelled b_1(1)* 369 to 370 labelled a_1(1)* 370 to 371 labelled b_1(1)* 371 to 306 labelled a_1(1)* 371 to 444 labelled b_1(2)* 444 to 445 labelled a_1(2)* 445 to 446 labelled b_1(2)* 446 to 447 labelled a_1(2)* 447 to 448 labelled b_1(2)* 448 to 449 labelled a_1(2)* 448 to 444 labelled b_1(2)* 449 to 450 labelled a_1(2)* 449 to 297 labelled b_1(1)* 450 to 451 labelled b_1(2)* 451 to 452 labelled a_1(2)* 452 to 453 labelled b_1(2)* 453 to 454 labelled a_1(2)* 454 to 455 labelled b_1(2)* 455 to 306 labelled a_1(2)* 455 to 444 labelled b_1(2) ---------------------------------------- (6) YES