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TRS Relative pair #487081884
details
property
value
status
complete
benchmark
rt2-4.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
Relative_05
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.85492 seconds
cpu usage
4.24669
user time
4.02687
system time
0.219825
max virtual memory
1.9604664E7
max residence set size
331792.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRS Reverse [SOUND, 0 ms] (2) RelTRS (3) FlatCCProof [EQUIVALENT, 0 ms] (4) RelTRS (5) RootLabelingProof [EQUIVALENT, 0 ms] (6) RelTRS (7) RelTRSRRRProof [EQUIVALENT, 57 ms] (8) RelTRS (9) RIsEmptyProof [EQUIVALENT, 0 ms] (10) YES ---------------------------------------- (0) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: f(g(x)) -> x The relative TRS consists of the following S rules: a -> h(g(f(a))) ---------------------------------------- (1) RelTRS Reverse (SOUND) We have reversed the following relative TRS [REVERSE]: The set of rules R is f(g(x)) -> x The set of rules S is a -> h(g(f(a))) We have obtained the following relative TRS: The set of rules R is g(f(x)) -> x The set of rules S is a'(x) -> a'(f(g(h(x)))) ---------------------------------------- (2) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: g(f(x)) -> x The relative TRS consists of the following S rules: a'(x) -> a'(f(g(h(x)))) ---------------------------------------- (3) FlatCCProof (EQUIVALENT) We used flat context closure [ROOTLAB] ---------------------------------------- (4) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: g(g(f(x))) -> g(x) f(g(f(x))) -> f(x) a'(g(f(x))) -> a'(x) h(g(f(x))) -> h(x) The relative TRS consists of the following S rules: a'(x) -> a'(f(g(h(x)))) ---------------------------------------- (5) RootLabelingProof (EQUIVALENT) We used plain root labeling [ROOTLAB] with the following heuristic: LabelAll: All function symbols get labeled ---------------------------------------- (6) Obligation: Relative term rewrite system:
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