/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) Strip Symbols Proof [SOUND, 0 ms] (4) QTRS (5) RFCMatchBoundsTRSProof [EQUIVALENT, 1 ms] (6) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: b(b(b(a(b(a(b(b(a(b(x1)))))))))) -> b(b(a(b(a(b(b(b(a(b(a(b(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: b(a(b(b(a(b(a(b(b(b(x1)))))))))) -> b(b(a(b(a(b(b(b(a(b(a(b(b(x1))))))))))))) Q is empty. ---------------------------------------- (3) Strip Symbols Proof (SOUND) We were given the following TRS: b(a(b(b(a(b(a(b(b(b(x1)))))))))) -> b(b(a(b(a(b(b(b(a(b(a(b(b(x1))))))))))))) By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: a(b(b(a(b(a(b(b(b(x1))))))))) -> b(a(b(a(b(b(b(a(b(a(b(b(x1)))))))))))) ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(b(b(a(b(a(b(b(b(x1))))))))) -> b(a(b(a(b(b(b(a(b(a(b(b(x1)))))))))))) 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(b(a(b(a(b(b(b(x1))))))))) -> b(a(b(a(b(b(b(a(b(a(b(b(x1)))))))))))) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380, 381 Node 228 is start node and node 229 is final node. Those nodes are connected through the following edges: * 228 to 230 labelled b_1(0)* 229 to 229 labelled #_1(0)* 230 to 231 labelled a_1(0)* 231 to 232 labelled b_1(0)* 232 to 233 labelled a_1(0)* 233 to 234 labelled b_1(0)* 234 to 235 labelled b_1(0)* 235 to 236 labelled b_1(0)* 236 to 237 labelled a_1(0)* 236 to 360 labelled b_1(1)* 237 to 238 labelled b_1(0)* 238 to 239 labelled a_1(0)* 238 to 349 labelled b_1(1)* 239 to 240 labelled b_1(0)* 240 to 229 labelled b_1(0)* 349 to 350 labelled a_1(1)* 350 to 351 labelled b_1(1)* 351 to 352 labelled a_1(1)* 352 to 353 labelled b_1(1)* 353 to 354 labelled b_1(1)* 354 to 355 labelled b_1(1)* 355 to 356 labelled a_1(1)* 355 to 371 labelled b_1(2)* 356 to 357 labelled b_1(1)* 357 to 358 labelled a_1(1)* 357 to 349 labelled b_1(1)* 358 to 359 labelled b_1(1)* 359 to 229 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 b_1(1)* 365 to 366 labelled b_1(1)* 366 to 367 labelled a_1(1)* 366 to 371 labelled b_1(2)* 367 to 368 labelled b_1(1)* 368 to 369 labelled a_1(1)* 368 to 349 labelled b_1(1)* 369 to 370 labelled b_1(1)* 370 to 355 labelled b_1(1)* 371 to 372 labelled a_1(2)* 372 to 373 labelled b_1(2)* 373 to 374 labelled a_1(2)* 374 to 375 labelled b_1(2)* 375 to 376 labelled b_1(2)* 376 to 377 labelled b_1(2)* 377 to 378 labelled a_1(2)* 377 to 371 labelled b_1(2)* 378 to 379 labelled b_1(2)* 379 to 380 labelled a_1(2)* 379 to 349 labelled b_1(1)* 380 to 381 labelled b_1(2)* 381 to 355 labelled b_1(2) ---------------------------------------- (6) YES