Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308197

details

property	value
status	complete
benchmark	LISTUTILITIES_nokinds-noand_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n007.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	45.9181 seconds
cpu usage	105.98
user time	104.38
system time	1.59976
max virtual memory	1.8277336E7
max residence set size	5111268.0

stage attributes

key	value
starexec-result	WORST_CASE(NON_POLY, ?)

output

105.90/45.88	WORST_CASE(NON_POLY, ?)
105.90/45.89	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
105.90/45.89	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
105.90/45.89	
105.90/45.89	
105.90/45.89	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
105.90/45.89	
105.90/45.89	(0) CpxTRS
105.90/45.89	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
105.90/45.89	(2) TRS for Loop Detection
105.90/45.89	(3) DecreasingLoopProof [LOWER BOUND(ID), 392 ms]
105.90/45.89	(4) BEST
105.90/45.89	    (5) proven lower bound
105.90/45.89	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
105.90/45.89	        (7) BOUNDS(n^1, INF)
105.90/45.89	    (8) TRS for Loop Detection
105.90/45.89	        (9) DecreasingLoopProof [FINISHED, 42.6 s]
105.90/45.89	        (10) BOUNDS(EXP, INF)
105.90/45.89	
105.90/45.89	
105.90/45.89	----------------------------------------
105.90/45.89	
105.90/45.89	(0)
105.90/45.89	Obligation:
105.90/45.89	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
105.90/45.89	
105.90/45.89	
105.90/45.89	The TRS R consists of the following rules:
105.90/45.89	
105.90/45.89	   U101(tt, V2) -> U102(isLNat(activate(V2)))
105.90/45.89	   U102(tt) -> tt
105.90/45.89	   U11(tt, N, XS) -> U12(isLNat(activate(XS)), activate(N), activate(XS))
105.90/45.89	   U111(tt) -> tt
105.90/45.89	   U12(tt, N, XS) -> snd(splitAt(activate(N), activate(XS)))
105.90/45.89	   U121(tt) -> tt
105.90/45.89	   U131(tt, V2) -> U132(isLNat(activate(V2)))
105.90/45.89	   U132(tt) -> tt
105.90/45.89	   U141(tt, V2) -> U142(isLNat(activate(V2)))
105.90/45.89	   U142(tt) -> tt
105.90/45.89	   U151(tt, V2) -> U152(isLNat(activate(V2)))
105.90/45.89	   U152(tt) -> tt
105.90/45.89	   U161(tt, N) -> cons(activate(N), n__natsFrom(s(activate(N))))
105.90/45.89	   U171(tt, N, XS) -> U172(isLNat(activate(XS)), activate(N), activate(XS))
105.90/45.89	   U172(tt, N, XS) -> head(afterNth(activate(N), activate(XS)))
105.90/45.89	   U181(tt, Y) -> U182(isLNat(activate(Y)), activate(Y))
105.90/45.89	   U182(tt, Y) -> activate(Y)
105.90/45.89	   U191(tt, XS) -> pair(nil, activate(XS))
105.90/45.89	   U201(tt, N, X, XS) -> U202(isNatural(activate(X)), activate(N), activate(X), activate(XS))
105.90/45.89	   U202(tt, N, X, XS) -> U203(isLNat(activate(XS)), activate(N), activate(X), activate(XS))
105.90/45.89	   U203(tt, N, X, XS) -> U204(splitAt(activate(N), activate(XS)), activate(X))
105.90/45.89	   U204(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS)
105.90/45.89	   U21(tt, X, Y) -> U22(isLNat(activate(Y)), activate(X))
105.90/45.89	   U211(tt, XS) -> U212(isLNat(activate(XS)), activate(XS))
105.90/45.89	   U212(tt, XS) -> activate(XS)
105.90/45.89	   U22(tt, X) -> activate(X)
105.90/45.89	   U221(tt, N, XS) -> U222(isLNat(activate(XS)), activate(N), activate(XS))
105.90/45.89	   U222(tt, N, XS) -> fst(splitAt(activate(N), activate(XS)))
105.90/45.89	   U31(tt, N, XS) -> U32(isLNat(activate(XS)), activate(N))
105.90/45.89	   U32(tt, N) -> activate(N)
105.90/45.89	   U41(tt, V2) -> U42(isLNat(activate(V2)))
105.90/45.89	   U42(tt) -> tt
105.90/45.89	   U51(tt, V2) -> U52(isLNat(activate(V2)))
105.90/45.89	   U52(tt) -> tt
105.90/45.89	   U61(tt) -> tt
105.90/45.89	   U71(tt) -> tt
105.90/45.89	   U81(tt) -> tt
105.90/45.89	   U91(tt) -> tt
105.90/45.89	   afterNth(N, XS) -> U11(isNatural(N), N, XS)
105.90/45.89	   fst(pair(X, Y)) -> U21(isLNat(X), X, Y)
105.90/45.89	   head(cons(N, XS)) -> U31(isNatural(N), N, activate(XS))
105.90/45.89	   isLNat(n__nil) -> tt
105.90/45.89	   isLNat(n__afterNth(V1, V2)) -> U41(isNatural(activate(V1)), activate(V2))
105.90/45.89	   isLNat(n__cons(V1, V2)) -> U51(isNatural(activate(V1)), activate(V2))
105.90/45.89	   isLNat(n__fst(V1)) -> U61(isPLNat(activate(V1)))
105.90/45.89	   isLNat(n__natsFrom(V1)) -> U71(isNatural(activate(V1)))
105.90/45.89	   isLNat(n__snd(V1)) -> U81(isPLNat(activate(V1)))
105.90/45.89	   isLNat(n__tail(V1)) -> U91(isLNat(activate(V1)))
105.90/45.89	   isLNat(n__take(V1, V2)) -> U101(isNatural(activate(V1)), activate(V2))
105.90/45.89	   isNatural(n__0) -> tt
105.90/45.89	   isNatural(n__head(V1)) -> U111(isLNat(activate(V1)))
105.90/45.89	   isNatural(n__s(V1)) -> U121(isNatural(activate(V1)))
105.90/45.89	   isNatural(n__sel(V1, V2)) -> U131(isNatural(activate(V1)), activate(V2))
105.90/45.89	   isPLNat(n__pair(V1, V2)) -> U141(isLNat(activate(V1)), activate(V2))
105.90/45.89	   isPLNat(n__splitAt(V1, V2)) -> U151(isNatural(activate(V1)), activate(V2))
105.90/45.89	   natsFrom(N) -> U161(isNatural(N), N)
105.90/45.89	   sel(N, XS) -> U171(isNatural(N), N, XS)
105.90/45.89	   snd(pair(X, Y)) -> U181(isLNat(X), Y)
105.90/45.89	   splitAt(0, XS) -> U191(isLNat(XS), XS)
105.90/45.89	   splitAt(s(N), cons(X, XS)) -> U201(isNatural(N), N, X, activate(XS))
105.90/45.89	   tail(cons(N, XS)) -> U211(isNatural(N), activate(XS))
105.90/45.89	   take(N, XS) -> U221(isNatural(N), N, XS)
105.90/45.89	   natsFrom(X) -> n__natsFrom(X)
105.90/45.89	   nil -> n__nil
105.90/45.89	   afterNth(X1, X2) -> n__afterNth(X1, X2)
105.90/45.89	   cons(X1, X2) -> n__cons(X1, X2)
105.90/45.89	   fst(X) -> n__fst(X)
105.90/45.89	   snd(X) -> n__snd(X)
105.90/45.89	   tail(X) -> n__tail(X)
105.90/45.89	   take(X1, X2) -> n__take(X1, X2)
105.90/45.89	   0 -> n__0

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actions all output return to Runtime_Complexity_Full_Rewriting 2019-04-01 06.11