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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313491
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
n082.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
295.923 seconds
cpu usage
1159.09
user time
1147.15
system time
11.9471
max virtual memory
3.781714E7
max residence set size
1.5014212E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1158.87/295.83 WORST_CASE(Omega(n^1), ?) 1158.87/295.84 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1158.87/295.84 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1158.87/295.84 1158.87/295.84 1158.87/295.84 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1158.87/295.84 1158.87/295.84 (0) CpxTRS 1158.87/295.84 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1158.87/295.84 (2) TRS for Loop Detection 1158.87/295.84 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1158.87/295.84 (4) BEST 1158.87/295.84 (5) proven lower bound 1158.87/295.84 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1158.87/295.84 (7) BOUNDS(n^1, INF) 1158.87/295.84 (8) TRS for Loop Detection 1158.87/295.84 1158.87/295.84 1158.87/295.84 ---------------------------------------- 1158.87/295.84 1158.87/295.84 (0) 1158.87/295.84 Obligation: 1158.87/295.84 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1158.87/295.84 1158.87/295.84 1158.87/295.84 The TRS R consists of the following rules: 1158.87/295.84 1158.87/295.84 a__zeros -> cons(0, zeros) 1158.87/295.84 a__U11(tt) -> tt 1158.87/295.84 a__U21(tt) -> tt 1158.87/295.84 a__U31(tt) -> tt 1158.87/295.84 a__U41(tt, V2) -> a__U42(a__isNatIList(V2)) 1158.87/295.84 a__U42(tt) -> tt 1158.87/295.84 a__U51(tt, V2) -> a__U52(a__isNatList(V2)) 1158.87/295.84 a__U52(tt) -> tt 1158.87/295.84 a__U61(tt, V2) -> a__U62(a__isNatIList(V2)) 1158.87/295.84 a__U62(tt) -> tt 1158.87/295.84 a__U71(tt, L, N) -> a__U72(a__isNat(N), L) 1158.87/295.84 a__U72(tt, L) -> s(a__length(mark(L))) 1158.87/295.84 a__U81(tt) -> nil 1158.87/295.84 a__U91(tt, IL, M, N) -> a__U92(a__isNat(M), IL, M, N) 1158.87/295.84 a__U92(tt, IL, M, N) -> a__U93(a__isNat(N), IL, M, N) 1158.87/295.84 a__U93(tt, IL, M, N) -> cons(mark(N), take(M, IL)) 1158.87/295.84 a__isNat(0) -> tt 1158.87/295.84 a__isNat(length(V1)) -> a__U11(a__isNatList(V1)) 1158.87/295.84 a__isNat(s(V1)) -> a__U21(a__isNat(V1)) 1158.87/295.84 a__isNatIList(V) -> a__U31(a__isNatList(V)) 1158.87/295.84 a__isNatIList(zeros) -> tt 1158.87/295.84 a__isNatIList(cons(V1, V2)) -> a__U41(a__isNat(V1), V2) 1158.87/295.84 a__isNatList(nil) -> tt 1158.87/295.84 a__isNatList(cons(V1, V2)) -> a__U51(a__isNat(V1), V2) 1158.87/295.84 a__isNatList(take(V1, V2)) -> a__U61(a__isNat(V1), V2) 1158.87/295.84 a__length(nil) -> 0 1158.87/295.84 a__length(cons(N, L)) -> a__U71(a__isNatList(L), L, N) 1158.87/295.84 a__take(0, IL) -> a__U81(a__isNatIList(IL)) 1158.87/295.84 a__take(s(M), cons(N, IL)) -> a__U91(a__isNatIList(IL), IL, M, N) 1158.87/295.84 mark(zeros) -> a__zeros 1158.87/295.84 mark(U11(X)) -> a__U11(mark(X)) 1158.87/295.84 mark(U21(X)) -> a__U21(mark(X)) 1158.87/295.84 mark(U31(X)) -> a__U31(mark(X)) 1158.87/295.84 mark(U41(X1, X2)) -> a__U41(mark(X1), X2) 1158.87/295.84 mark(U42(X)) -> a__U42(mark(X)) 1158.87/295.84 mark(isNatIList(X)) -> a__isNatIList(X) 1158.87/295.84 mark(U51(X1, X2)) -> a__U51(mark(X1), X2) 1158.87/295.84 mark(U52(X)) -> a__U52(mark(X)) 1158.87/295.84 mark(isNatList(X)) -> a__isNatList(X) 1158.87/295.84 mark(U61(X1, X2)) -> a__U61(mark(X1), X2) 1158.87/295.84 mark(U62(X)) -> a__U62(mark(X)) 1158.87/295.84 mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3) 1158.87/295.84 mark(U72(X1, X2)) -> a__U72(mark(X1), X2) 1158.87/295.84 mark(isNat(X)) -> a__isNat(X) 1158.87/295.84 mark(length(X)) -> a__length(mark(X)) 1158.87/295.84 mark(U81(X)) -> a__U81(mark(X)) 1158.87/295.84 mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4) 1158.87/295.84 mark(U92(X1, X2, X3, X4)) -> a__U92(mark(X1), X2, X3, X4) 1158.87/295.84 mark(U93(X1, X2, X3, X4)) -> a__U93(mark(X1), X2, X3, X4) 1158.87/295.84 mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) 1158.87/295.84 mark(cons(X1, X2)) -> cons(mark(X1), X2) 1158.87/295.84 mark(0) -> 0 1158.87/295.84 mark(tt) -> tt 1158.87/295.84 mark(s(X)) -> s(mark(X)) 1158.87/295.84 mark(nil) -> nil 1158.87/295.84 a__zeros -> zeros 1158.87/295.84 a__U11(X) -> U11(X) 1158.87/295.84 a__U21(X) -> U21(X) 1158.87/295.84 a__U31(X) -> U31(X) 1158.87/295.84 a__U41(X1, X2) -> U41(X1, X2) 1158.87/295.84 a__U42(X) -> U42(X) 1158.87/295.84 a__isNatIList(X) -> isNatIList(X) 1158.87/295.84 a__U51(X1, X2) -> U51(X1, X2) 1158.87/295.84 a__U52(X) -> U52(X) 1158.87/295.84 a__isNatList(X) -> isNatList(X) 1158.87/295.84 a__U61(X1, X2) -> U61(X1, X2) 1158.87/295.84 a__U62(X) -> U62(X) 1158.87/295.84 a__U71(X1, X2, X3) -> U71(X1, X2, X3) 1158.87/295.84 a__U72(X1, X2) -> U72(X1, X2) 1158.87/295.84 a__isNat(X) -> isNat(X) 1158.87/295.84 a__length(X) -> length(X) 1158.87/295.84 a__U81(X) -> U81(X) 1158.87/295.84 a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4)
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return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40