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SRS Standard pair #516977722
details
property
value
status
complete
benchmark
abaaaaa-aaaaaababaaaab.srs.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n067.star.cs.uiowa.edu
space
Wenzel_16
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.22577786446 seconds
cpu usage
6.100482022
max memory
5.68782848E8
stage attributes
key
value
output-size
3491
starexec-result
YES
output
/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) Strip Symbols Proof [SOUND, 0 ms] (4) QTRS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(a(a(a(a(a(x1))))))) -> a(a(a(a(a(a(b(a(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(a(a(a(b(a(x1))))))) -> b(a(a(a(a(b(a(b(a(a(a(a(a(a(x1)))))))))))))) Q is empty. ---------------------------------------- (3) Strip Symbols Proof (SOUND) We were given the following TRS: a(a(a(a(a(b(a(x1))))))) -> b(a(a(a(a(b(a(b(a(a(a(a(a(a(x1)))))))))))))) By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: a(a(a(a(a(b(x)))))) -> b(a(a(a(a(b(a(b(a(a(a(a(a(x))))))))))))) ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(a(a(a(a(b(x)))))) -> b(a(a(a(a(b(a(b(a(a(a(a(a(x))))))))))))) Q is empty. ---------------------------------------- (5) RFCMatchBoundsTRSProof (EQUIVALENT) Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R. The following rules were used to construct the certificate: a(a(a(a(a(b(x)))))) -> b(a(a(a(a(b(a(b(a(a(a(a(a(x))))))))))))) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 345, 346, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 430 Node 345 is start node and node 346 is final node. Those nodes are connected through the following edges: * 345 to 407 labelled b_1(0)* 346 to 346 labelled #_1(0)* 407 to 408 labelled a_1(0)* 408 to 409 labelled a_1(0)* 409 to 410 labelled a_1(0)* 410 to 411 labelled a_1(0)* 411 to 412 labelled b_1(0)* 412 to 413 labelled a_1(0)* 413 to 414 labelled b_1(0)* 414 to 415 labelled a_1(0)* 414 to 419 labelled b_1(1)* 415 to 416 labelled a_1(0)* 415 to 419 labelled b_1(1)* 416 to 417 labelled a_1(0)* 416 to 419 labelled b_1(1)* 417 to 418 labelled a_1(0)* 417 to 419 labelled b_1(1)* 418 to 346 labelled a_1(0)* 418 to 419 labelled b_1(1)* 419 to 420 labelled a_1(1)* 420 to 421 labelled a_1(1)* 421 to 422 labelled a_1(1)* 422 to 423 labelled a_1(1)* 423 to 424 labelled b_1(1)* 424 to 425 labelled a_1(1)* 425 to 426 labelled b_1(1)* 426 to 427 labelled a_1(1)* 426 to 419 labelled b_1(1)* 427 to 428 labelled a_1(1)* 427 to 419 labelled b_1(1)* 428 to 429 labelled a_1(1)* 428 to 419 labelled b_1(1)* 429 to 430 labelled a_1(1)* 429 to 419 labelled b_1(1)* 430 to 346 labelled a_1(1)* 430 to 419 labelled b_1(1) ---------------------------------------- (6) YES
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