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SRS Standard pair #516974716
details
property
value
status
complete
benchmark
size-12-alpha-3-num-350.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n028.star.cs.uiowa.edu
space
Waldmann_07_size12
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
6.21101903915 seconds
cpu usage
21.20690718
max memory
1.367998464E9
stage attributes
key
value
output-size
6342
starexec-result
YES
output
/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 0 ms] (4) QDP (5) QDPOrderProof [EQUIVALENT, 131 ms] (6) QDP (7) QDPOrderProof [EQUIVALENT, 48 ms] (8) QDP (9) DependencyGraphProof [EQUIVALENT, 0 ms] (10) QDP (11) UsableRulesProof [EQUIVALENT, 0 ms] (12) QDP (13) QDPSizeChangeProof [EQUIVALENT, 0 ms] (14) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(x1) -> b(x1) a(b(x1)) -> b(a(c(x1))) b(b(x1)) -> x1 c(c(x1)) -> a(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(x1) -> b(x1) b(a(x1)) -> c(a(b(x1))) b(b(x1)) -> x1 c(c(x1)) -> a(x1) Q is empty. ---------------------------------------- (3) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: A(x1) -> B(x1) B(a(x1)) -> C(a(b(x1))) B(a(x1)) -> A(b(x1)) B(a(x1)) -> B(x1) C(c(x1)) -> A(x1) The TRS R consists of the following rules: a(x1) -> b(x1) b(a(x1)) -> c(a(b(x1))) b(b(x1)) -> x1 c(c(x1)) -> a(x1) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (5) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. B(a(x1)) -> A(b(x1)) The remaining pairs can at least be oriented weakly. Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]:
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