3.11/1.60	WORST_CASE(NON_POLY, ?)
3.11/1.61	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.11/1.61	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.11/1.61	
3.11/1.61	
3.11/1.61	The Runtime Complexity  of the given Name of obligation not specified could be proven to be BOUNDS(INF, INF).
3.11/1.61	
3.11/1.61	(0) Name of obligation not specified
3.11/1.61	(1) ExtraVarProof [FINISHED, 0 ms]
3.11/1.61	(2) BOUNDS(INF, INF)
3.11/1.61	
3.11/1.61	
3.11/1.61	----------------------------------------
3.11/1.61	
3.11/1.61	(0)
3.11/1.61	Obligation:
3.11/1.61	The Runtime Complexity  of the given Name of obligation not specified could be proven to be BOUNDS(INF, INF).
3.11/1.61	
3.11/1.61	
3.11/1.61	The TRS R consists of the following rules:
3.11/1.61	
3.11/1.61	   U11(tt) -> snd(splitAt(N, XS))
3.11/1.61	   U161(tt) -> cons(N)
3.11/1.61	   U171(tt) -> head(afterNth(N, XS))
3.11/1.61	   U181(tt) -> Y
3.11/1.61	   U191(tt) -> pair(nil, XS)
3.11/1.61	   U201(tt) -> U202(splitAt(N, XS))
3.11/1.61	   U202(pair(YS, ZS)) -> pair(cons(X), ZS)
3.11/1.61	   U21(tt) -> X
3.11/1.61	   U211(tt) -> XS
3.11/1.61	   U221(tt) -> fst(splitAt(N, XS))
3.11/1.61	   U31(tt) -> N
3.11/1.61	   and(tt) -> X
3.11/1.61	   U101(tt) -> U102(isNatural)
3.11/1.61	   U102(tt) -> U103(isLNat)
3.11/1.61	   U103(tt) -> tt
3.11/1.61	   U111(tt) -> U112(isLNat)
3.11/1.61	   U112(tt) -> tt
3.11/1.61	   U121(tt) -> U122(isNatural)
3.11/1.61	   U122(tt) -> tt
3.11/1.61	   U131(tt) -> U132(isNatural)
3.11/1.61	   U132(tt) -> U133(isLNat)
3.11/1.61	   U133(tt) -> tt
3.11/1.61	   U141(tt) -> U142(isLNat)
3.11/1.61	   U142(tt) -> U143(isLNat)
3.11/1.61	   U143(tt) -> tt
3.11/1.61	   U151(tt) -> U152(isNatural)
3.11/1.61	   U152(tt) -> U153(isLNat)
3.11/1.61	   U153(tt) -> tt
3.11/1.61	   U41(tt) -> U42(isNatural)
3.11/1.61	   U42(tt) -> U43(isLNat)
3.11/1.61	   U43(tt) -> tt
3.11/1.61	   U51(tt) -> U52(isNatural)
3.11/1.61	   U52(tt) -> U53(isLNat)
3.11/1.61	   U53(tt) -> tt
3.11/1.61	   U61(tt) -> U62(isPLNat)
3.11/1.61	   U62(tt) -> tt
3.11/1.61	   U71(tt) -> U72(isNatural)
3.11/1.61	   U72(tt) -> tt
3.11/1.61	   U81(tt) -> U82(isPLNat)
3.11/1.61	   U82(tt) -> tt
3.11/1.61	   U91(tt) -> U92(isLNat)
3.11/1.61	   U92(tt) -> tt
3.11/1.61	   afterNth(N, XS) -> U11(and(and(isNatural)))
3.11/1.61	   fst(pair(X, Y)) -> U21(and(and(isLNat)))
3.11/1.61	   head(cons(N)) -> U31(and(and(isNatural)))
3.11/1.61	   isLNat -> tt
3.11/1.61	   isLNat -> U41(and(isNaturalKind))
3.11/1.61	   isLNat -> U51(and(isNaturalKind))
3.11/1.61	   isLNat -> U61(isPLNatKind)
3.11/1.61	   isLNat -> U71(isNaturalKind)
3.11/1.61	   isLNat -> U81(isPLNatKind)
3.11/1.61	   isLNat -> U91(isLNatKind)
3.11/1.61	   isLNat -> U101(and(isNaturalKind))
3.11/1.61	   isLNatKind -> tt
3.11/1.61	   isLNatKind -> and(isNaturalKind)
3.11/1.61	   isLNatKind -> isPLNatKind
3.11/1.61	   isLNatKind -> isNaturalKind
3.11/1.61	   isLNatKind -> isLNatKind
3.11/1.61	   isNatural -> tt
3.11/1.61	   isNatural -> U111(isLNatKind)
3.11/1.61	   isNatural -> U121(isNaturalKind)
3.11/1.61	   isNatural -> U131(and(isNaturalKind))
3.11/1.61	   isNaturalKind -> tt
3.11/1.61	   isNaturalKind -> isLNatKind
3.11/1.61	   isNaturalKind -> isNaturalKind
3.11/1.61	   isNaturalKind -> and(isNaturalKind)
3.11/1.61	   isPLNat -> U141(and(isLNatKind))
3.11/1.61	   isPLNat -> U151(and(isNaturalKind))
3.11/1.61	   isPLNatKind -> and(isLNatKind)
3.11/1.61	   isPLNatKind -> and(isNaturalKind)
3.11/1.61	   natsFrom(N) -> U161(and(isNatural))
3.11/1.61	   sel(N, XS) -> U171(and(and(isNatural)))
3.11/1.61	   snd(pair(X, Y)) -> U181(and(and(isLNat)))
3.11/1.61	   splitAt(0, XS) -> U191(and(isLNat))
3.11/1.61	   splitAt(s(N), cons(X)) -> U201(and(and(isNatural)))
3.11/1.61	   tail(cons(N)) -> U211(and(and(isNatural)))
3.11/1.61	   take(N, XS) -> U221(and(and(isNatural)))
3.11/1.61	
3.11/1.61	
3.11/1.61	----------------------------------------
3.11/1.61	
3.11/1.61	(1) ExtraVarProof (FINISHED)
3.11/1.61	unbounded runtime complexity due to extra variable on rhs
3.11/1.61	----------------------------------------
3.11/1.61	
3.11/1.61	(2)
3.11/1.61	BOUNDS(INF, INF)
3.30/1.65	EOF