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SRS Standard pair #516968854
details
property
value
status
complete
benchmark
z123.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n137.star.cs.uiowa.edu
space
Zantema_04
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
4.81698107719 seconds
cpu usage
15.942097122
max memory
1.234223104E9
stage attributes
key
value
output-size
6754
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 47 ms] (4) QTRS (5) DependencyPairsProof [EQUIVALENT, 0 ms] (6) QDP (7) DependencyGraphProof [EQUIVALENT, 0 ms] (8) QDP (9) MRRProof [EQUIVALENT, 27 ms] (10) QDP (11) QDPOrderProof [EQUIVALENT, 93 ms] (12) QDP (13) DependencyGraphProof [EQUIVALENT, 0 ms] (14) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(a(x1)) -> b(b(b(x1))) a(x1) -> d(c(d(x1))) b(b(b(x1))) -> a(f(x1)) b(b(x1)) -> c(c(c(x1))) c(c(x1)) -> d(d(d(x1))) c(d(d(x1))) -> f(x1) f(f(x1)) -> f(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(a(x1)) -> b(b(b(x1))) a(x1) -> d(c(d(x1))) b(b(b(x1))) -> f(a(x1)) b(b(x1)) -> c(c(c(x1))) c(c(x1)) -> d(d(d(x1))) d(d(c(x1))) -> f(x1) f(f(x1)) -> a(f(x1)) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(a(x_1)) = 39 + x_1 POL(b(x_1)) = 26 + x_1 POL(c(x_1)) = 17 + x_1 POL(d(x_1)) = 11 + x_1 POL(f(x_1)) = 39 + x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: b(b(x1)) -> c(c(c(x1))) c(c(x1)) -> d(d(d(x1))) ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(a(x1)) -> b(b(b(x1))) a(x1) -> d(c(d(x1))) b(b(b(x1))) -> f(a(x1)) d(d(c(x1))) -> f(x1) f(f(x1)) -> a(f(x1))
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