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SRS Standard pair #487090120
details
property
value
status
complete
benchmark
abbaaaabaa-abaaaabbaaaab.srs.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n141.star.cs.uiowa.edu
space
Wenzel_16
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.89492 seconds
cpu usage
4.4001
user time
4.18599
system time
0.214112
max virtual memory
1.9142144E7
max residence set size
419340.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) Strip Symbols Proof [SOUND, 0 ms] (4) QTRS (5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(b(b(a(a(a(a(b(a(a(x1)))))))))) -> a(b(a(a(a(a(b(b(a(a(a(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(a(b(a(a(a(a(b(b(a(x1)))))))))) -> b(a(a(a(a(b(b(a(a(a(a(b(a(x1))))))))))))) Q is empty. ---------------------------------------- (3) Strip Symbols Proof (SOUND) We were given the following TRS: a(a(b(a(a(a(a(b(b(a(x1)))))))))) -> b(a(a(a(a(b(b(a(a(a(a(b(a(x1))))))))))))) By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: a(a(b(a(a(a(a(b(b(x))))))))) -> b(a(a(a(a(b(b(a(a(a(a(b(x)))))))))))) ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(a(b(a(a(a(a(b(b(x))))))))) -> b(a(a(a(a(b(b(a(a(a(a(b(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(a(b(a(a(a(a(b(b(x))))))))) -> b(a(a(a(a(b(b(a(a(a(a(b(x)))))))))))) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 443, 455, 456, 457, 458, 459, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 480, 481, 482, 483, 484, 485, 486, 487 Node 431 is start node and node 432 is final node. Those nodes are connected through the following edges: * 431 to 433 labelled b_1(0)* 432 to 432 labelled #_1(0)* 433 to 434 labelled a_1(0)* 434 to 435 labelled a_1(0)* 435 to 436 labelled a_1(0)* 436 to 437 labelled a_1(0)* 437 to 438 labelled b_1(0)* 438 to 439 labelled b_1(0)* 439 to 440 labelled a_1(0)* 439 to 466 labelled b_1(1)* 440 to 441 labelled a_1(0)* 441 to 442 labelled a_1(0)* 441 to 455 labelled b_1(1)* 442 to 443 labelled a_1(0)* 443 to 432 labelled b_1(0)* 455 to 456 labelled a_1(1)* 456 to 457 labelled a_1(1)* 457 to 458 labelled a_1(1)* 458 to 459 labelled a_1(1)* 459 to 460 labelled b_1(1)* 460 to 461 labelled b_1(1)* 461 to 462 labelled a_1(1)* 461 to 477 labelled b_1(2)* 462 to 463 labelled a_1(1)* 463 to 464 labelled a_1(1)* 463 to 455 labelled b_1(1)* 464 to 465 labelled a_1(1)* 465 to 432 labelled b_1(1)* 466 to 467 labelled a_1(1)* 467 to 468 labelled a_1(1)* 468 to 469 labelled a_1(1)* 469 to 470 labelled a_1(1)* 470 to 471 labelled b_1(1)* 471 to 472 labelled b_1(1)* 472 to 473 labelled a_1(1)* 472 to 477 labelled b_1(2)* 473 to 474 labelled a_1(1)* 474 to 475 labelled a_1(1)* 474 to 455 labelled b_1(1)* 475 to 476 labelled a_1(1)* 476 to 461 labelled b_1(1)* 477 to 478 labelled a_1(2)* 478 to 479 labelled a_1(2)* 479 to 480 labelled a_1(2)* 480 to 481 labelled a_1(2)* 481 to 482 labelled b_1(2)* 482 to 483 labelled b_1(2)* 483 to 484 labelled a_1(2)* 483 to 477 labelled b_1(2)* 484 to 485 labelled a_1(2)* 485 to 486 labelled a_1(2)* 485 to 455 labelled b_1(1)* 486 to 487 labelled a_1(2)* 487 to 461 labelled b_1(2) ---------------------------------------- (6) YES
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