Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313446

details

property	value
status	complete
benchmark	LISTUTILITIES_nokinds_noand_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n167.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	293.105 seconds
cpu usage	1148.07
user time	1137.39
system time	10.6784
max virtual memory	1.8881408E7
max residence set size	1.4825064E7

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), ?)

output

1142.27/291.62	WORST_CASE(Omega(n^1), ?)
1147.66/293.03	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
1147.66/293.03	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
1147.66/293.03	
1147.66/293.03	
1147.66/293.03	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1147.66/293.03	
1147.66/293.03	(0) CpxTRS
1147.66/293.03	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
1147.66/293.03	(2) TRS for Loop Detection
1147.66/293.03	(3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
1147.66/293.03	(4) BEST
1147.66/293.03	    (5) proven lower bound
1147.66/293.03	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
1147.66/293.03	        (7) BOUNDS(n^1, INF)
1147.66/293.03	    (8) TRS for Loop Detection
1147.66/293.03	
1147.66/293.03	
1147.66/293.03	----------------------------------------
1147.66/293.03	
1147.66/293.03	(0)
1147.66/293.03	Obligation:
1147.66/293.03	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1147.66/293.03	
1147.66/293.03	
1147.66/293.03	The TRS R consists of the following rules:
1147.66/293.03	
1147.66/293.03	   a__U101(tt, V2) -> a__U102(a__isLNat(V2))
1147.66/293.03	   a__U102(tt) -> tt
1147.66/293.03	   a__U11(tt, N, XS) -> a__U12(a__isLNat(XS), N, XS)
1147.66/293.03	   a__U111(tt) -> tt
1147.66/293.03	   a__U12(tt, N, XS) -> a__snd(a__splitAt(mark(N), mark(XS)))
1147.66/293.03	   a__U121(tt) -> tt
1147.66/293.03	   a__U131(tt, V2) -> a__U132(a__isLNat(V2))
1147.66/293.03	   a__U132(tt) -> tt
1147.66/293.03	   a__U141(tt, V2) -> a__U142(a__isLNat(V2))
1147.66/293.03	   a__U142(tt) -> tt
1147.66/293.03	   a__U151(tt, V2) -> a__U152(a__isLNat(V2))
1147.66/293.03	   a__U152(tt) -> tt
1147.66/293.03	   a__U161(tt, N) -> cons(mark(N), natsFrom(s(N)))
1147.66/293.03	   a__U171(tt, N, XS) -> a__U172(a__isLNat(XS), N, XS)
1147.66/293.03	   a__U172(tt, N, XS) -> a__head(a__afterNth(mark(N), mark(XS)))
1147.66/293.03	   a__U181(tt, Y) -> a__U182(a__isLNat(Y), Y)
1147.66/293.03	   a__U182(tt, Y) -> mark(Y)
1147.66/293.03	   a__U191(tt, XS) -> pair(nil, mark(XS))
1147.66/293.03	   a__U201(tt, N, X, XS) -> a__U202(a__isNatural(X), N, X, XS)
1147.66/293.03	   a__U202(tt, N, X, XS) -> a__U203(a__isLNat(XS), N, X, XS)
1147.66/293.03	   a__U203(tt, N, X, XS) -> a__U204(a__splitAt(mark(N), mark(XS)), X)
1147.66/293.03	   a__U204(pair(YS, ZS), X) -> pair(cons(mark(X), YS), mark(ZS))
1147.66/293.03	   a__U21(tt, X, Y) -> a__U22(a__isLNat(Y), X)
1147.66/293.03	   a__U211(tt, XS) -> a__U212(a__isLNat(XS), XS)
1147.66/293.03	   a__U212(tt, XS) -> mark(XS)
1147.66/293.03	   a__U22(tt, X) -> mark(X)
1147.66/293.03	   a__U221(tt, N, XS) -> a__U222(a__isLNat(XS), N, XS)
1147.66/293.03	   a__U222(tt, N, XS) -> a__fst(a__splitAt(mark(N), mark(XS)))
1147.66/293.03	   a__U31(tt, N, XS) -> a__U32(a__isLNat(XS), N)
1147.66/293.03	   a__U32(tt, N) -> mark(N)
1147.66/293.03	   a__U41(tt, V2) -> a__U42(a__isLNat(V2))
1147.66/293.03	   a__U42(tt) -> tt
1147.66/293.03	   a__U51(tt, V2) -> a__U52(a__isLNat(V2))
1147.66/293.03	   a__U52(tt) -> tt
1147.66/293.03	   a__U61(tt) -> tt
1147.66/293.03	   a__U71(tt) -> tt
1147.66/293.03	   a__U81(tt) -> tt
1147.66/293.03	   a__U91(tt) -> tt
1147.66/293.03	   a__afterNth(N, XS) -> a__U11(a__isNatural(N), N, XS)
1147.66/293.03	   a__fst(pair(X, Y)) -> a__U21(a__isLNat(X), X, Y)
1147.66/293.03	   a__head(cons(N, XS)) -> a__U31(a__isNatural(N), N, XS)
1147.66/293.03	   a__isLNat(nil) -> tt
1147.66/293.03	   a__isLNat(afterNth(V1, V2)) -> a__U41(a__isNatural(V1), V2)
1147.66/293.03	   a__isLNat(cons(V1, V2)) -> a__U51(a__isNatural(V1), V2)
1147.66/293.03	   a__isLNat(fst(V1)) -> a__U61(a__isPLNat(V1))
1147.66/293.03	   a__isLNat(natsFrom(V1)) -> a__U71(a__isNatural(V1))
1147.66/293.03	   a__isLNat(snd(V1)) -> a__U81(a__isPLNat(V1))
1147.66/293.03	   a__isLNat(tail(V1)) -> a__U91(a__isLNat(V1))
1147.66/293.03	   a__isLNat(take(V1, V2)) -> a__U101(a__isNatural(V1), V2)
1147.66/293.03	   a__isNatural(0) -> tt
1147.66/293.03	   a__isNatural(head(V1)) -> a__U111(a__isLNat(V1))
1147.66/293.03	   a__isNatural(s(V1)) -> a__U121(a__isNatural(V1))
1147.66/293.03	   a__isNatural(sel(V1, V2)) -> a__U131(a__isNatural(V1), V2)
1147.66/293.03	   a__isPLNat(pair(V1, V2)) -> a__U141(a__isLNat(V1), V2)
1147.66/293.03	   a__isPLNat(splitAt(V1, V2)) -> a__U151(a__isNatural(V1), V2)
1147.66/293.03	   a__natsFrom(N) -> a__U161(a__isNatural(N), N)
1147.66/293.03	   a__sel(N, XS) -> a__U171(a__isNatural(N), N, XS)
1147.66/293.03	   a__snd(pair(X, Y)) -> a__U181(a__isLNat(X), Y)
1147.66/293.03	   a__splitAt(0, XS) -> a__U191(a__isLNat(XS), XS)
1147.66/293.03	   a__splitAt(s(N), cons(X, XS)) -> a__U201(a__isNatural(N), N, X, XS)
1147.66/293.03	   a__tail(cons(N, XS)) -> a__U211(a__isNatural(N), XS)
1147.66/293.03	   a__take(N, XS) -> a__U221(a__isNatural(N), N, XS)
1147.66/293.03	   mark(U101(X1, X2)) -> a__U101(mark(X1), X2)
1147.66/293.03	   mark(U102(X)) -> a__U102(mark(X))
1147.66/293.03	   mark(isLNat(X)) -> a__isLNat(X)
1147.66/293.03	   mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
1147.66/293.03	   mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
1147.66/293.03	   mark(U111(X)) -> a__U111(mark(X))
1147.66/293.03	   mark(snd(X)) -> a__snd(mark(X))
1147.66/293.03	   mark(splitAt(X1, X2)) -> a__splitAt(mark(X1), mark(X2))
1147.66/293.03	   mark(U121(X)) -> a__U121(mark(X))
1147.66/293.03	   mark(U131(X1, X2)) -> a__U131(mark(X1), X2)
1147.66/293.03	   mark(U132(X)) -> a__U132(mark(X))

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actions all output return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40