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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308249
details
property
value
status
complete
benchmark
OvConsOS_nokinds_noand_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n119.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.565 seconds
cpu usage
619.985
user time
613.853
system time
6.13156
max virtual memory
1.8277336E7
max residence set size
9833136.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
619.76/291.50 WORST_CASE(Omega(n^1), ?) 619.76/291.52 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 619.76/291.52 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 619.76/291.52 619.76/291.52 619.76/291.52 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 619.76/291.52 619.76/291.52 (0) CpxTRS 619.76/291.52 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 619.76/291.52 (2) TRS for Loop Detection 619.76/291.52 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 619.76/291.52 (4) BEST 619.76/291.52 (5) proven lower bound 619.76/291.52 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 619.76/291.52 (7) BOUNDS(n^1, INF) 619.76/291.52 (8) TRS for Loop Detection 619.76/291.52 619.76/291.52 619.76/291.52 ---------------------------------------- 619.76/291.52 619.76/291.52 (0) 619.76/291.52 Obligation: 619.76/291.52 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 619.76/291.52 619.76/291.52 619.76/291.52 The TRS R consists of the following rules: 619.76/291.52 619.76/291.52 a__zeros -> cons(0, zeros) 619.76/291.52 a__U11(tt) -> tt 619.76/291.52 a__U21(tt) -> tt 619.76/291.52 a__U31(tt) -> tt 619.76/291.52 a__U41(tt, V2) -> a__U42(a__isNatIList(V2)) 619.76/291.52 a__U42(tt) -> tt 619.76/291.52 a__U51(tt, V2) -> a__U52(a__isNatList(V2)) 619.76/291.52 a__U52(tt) -> tt 619.76/291.52 a__U61(tt, V2) -> a__U62(a__isNatIList(V2)) 619.76/291.52 a__U62(tt) -> tt 619.76/291.52 a__U71(tt, L, N) -> a__U72(a__isNat(N), L) 619.76/291.52 a__U72(tt, L) -> s(a__length(mark(L))) 619.76/291.52 a__U81(tt) -> nil 619.76/291.52 a__U91(tt, IL, M, N) -> a__U92(a__isNat(M), IL, M, N) 619.76/291.52 a__U92(tt, IL, M, N) -> a__U93(a__isNat(N), IL, M, N) 619.76/291.52 a__U93(tt, IL, M, N) -> cons(mark(N), take(M, IL)) 619.76/291.52 a__isNat(0) -> tt 619.76/291.52 a__isNat(length(V1)) -> a__U11(a__isNatList(V1)) 619.76/291.52 a__isNat(s(V1)) -> a__U21(a__isNat(V1)) 619.76/291.52 a__isNatIList(V) -> a__U31(a__isNatList(V)) 619.76/291.52 a__isNatIList(zeros) -> tt 619.76/291.52 a__isNatIList(cons(V1, V2)) -> a__U41(a__isNat(V1), V2) 619.76/291.52 a__isNatList(nil) -> tt 619.76/291.52 a__isNatList(cons(V1, V2)) -> a__U51(a__isNat(V1), V2) 619.76/291.52 a__isNatList(take(V1, V2)) -> a__U61(a__isNat(V1), V2) 619.76/291.52 a__length(nil) -> 0 619.76/291.52 a__length(cons(N, L)) -> a__U71(a__isNatList(L), L, N) 619.76/291.52 a__take(0, IL) -> a__U81(a__isNatIList(IL)) 619.76/291.52 a__take(s(M), cons(N, IL)) -> a__U91(a__isNatIList(IL), IL, M, N) 619.76/291.52 mark(zeros) -> a__zeros 619.76/291.52 mark(U11(X)) -> a__U11(mark(X)) 619.76/291.52 mark(U21(X)) -> a__U21(mark(X)) 619.76/291.52 mark(U31(X)) -> a__U31(mark(X)) 619.76/291.52 mark(U41(X1, X2)) -> a__U41(mark(X1), X2) 619.76/291.52 mark(U42(X)) -> a__U42(mark(X)) 619.76/291.52 mark(isNatIList(X)) -> a__isNatIList(X) 619.76/291.52 mark(U51(X1, X2)) -> a__U51(mark(X1), X2) 619.76/291.52 mark(U52(X)) -> a__U52(mark(X)) 619.76/291.52 mark(isNatList(X)) -> a__isNatList(X) 619.76/291.52 mark(U61(X1, X2)) -> a__U61(mark(X1), X2) 619.76/291.52 mark(U62(X)) -> a__U62(mark(X)) 619.76/291.52 mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3) 619.76/291.52 mark(U72(X1, X2)) -> a__U72(mark(X1), X2) 619.76/291.52 mark(isNat(X)) -> a__isNat(X) 619.76/291.52 mark(length(X)) -> a__length(mark(X)) 619.76/291.52 mark(U81(X)) -> a__U81(mark(X)) 619.76/291.52 mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4) 619.76/291.52 mark(U92(X1, X2, X3, X4)) -> a__U92(mark(X1), X2, X3, X4) 619.76/291.52 mark(U93(X1, X2, X3, X4)) -> a__U93(mark(X1), X2, X3, X4) 619.76/291.52 mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) 619.76/291.52 mark(cons(X1, X2)) -> cons(mark(X1), X2) 619.76/291.52 mark(0) -> 0 619.76/291.52 mark(tt) -> tt 619.76/291.52 mark(s(X)) -> s(mark(X)) 619.76/291.52 mark(nil) -> nil 619.76/291.52 a__zeros -> zeros 619.76/291.52 a__U11(X) -> U11(X) 619.76/291.52 a__U21(X) -> U21(X) 619.76/291.52 a__U31(X) -> U31(X) 619.76/291.52 a__U41(X1, X2) -> U41(X1, X2) 619.76/291.52 a__U42(X) -> U42(X) 619.76/291.52 a__isNatIList(X) -> isNatIList(X) 619.76/291.52 a__U51(X1, X2) -> U51(X1, X2) 619.76/291.52 a__U52(X) -> U52(X) 619.76/291.52 a__isNatList(X) -> isNatList(X) 619.76/291.52 a__U61(X1, X2) -> U61(X1, X2) 619.76/291.52 a__U62(X) -> U62(X) 619.76/291.52 a__U71(X1, X2, X3) -> U71(X1, X2, X3) 619.76/291.52 a__U72(X1, X2) -> U72(X1, X2) 619.76/291.52 a__isNat(X) -> isNat(X) 619.76/291.52 a__length(X) -> length(X) 619.76/291.52 a__U81(X) -> U81(X) 619.76/291.52 a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4)
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return to Runtime_Complexity_Full_Rewriting 2019-04-01 06.11