2.89/1.59	WORST_CASE(NON_POLY, ?)
2.89/1.60	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.89/1.60	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.89/1.60	
2.89/1.60	
2.89/1.60	The Runtime Complexity  of the given Name of obligation not specified could be proven to be BOUNDS(INF, INF).
2.89/1.60	
2.89/1.60	(0) Name of obligation not specified
2.89/1.60	(1) ExtraVarProof [FINISHED, 0 ms]
2.89/1.60	(2) BOUNDS(INF, INF)
2.89/1.60	
2.89/1.60	
2.89/1.60	----------------------------------------
2.89/1.60	
2.89/1.60	(0)
2.89/1.60	Obligation:
2.89/1.60	The Runtime Complexity  of the given Name of obligation not specified could be proven to be BOUNDS(INF, INF).
2.89/1.60	
2.89/1.60	
2.89/1.60	The TRS R consists of the following rules:
2.89/1.60	
2.89/1.60	   U12(tt) -> snd(splitAt(N, XS))
2.89/1.60	   U161(tt) -> cons(N)
2.89/1.60	   U172(tt) -> head(afterNth(N, XS))
2.89/1.60	   U182(tt) -> Y
2.89/1.60	   U191(tt) -> pair(nil, XS)
2.89/1.60	   U203(tt) -> U204(splitAt(N, XS))
2.89/1.60	   U204(pair(YS, ZS)) -> pair(cons(X), ZS)
2.89/1.60	   U212(tt) -> XS
2.89/1.60	   U22(tt) -> X
2.89/1.60	   U222(tt) -> fst(splitAt(N, XS))
2.89/1.60	   U32(tt) -> N
2.89/1.60	   U101(tt) -> U102(isLNat)
2.89/1.60	   U102(tt) -> tt
2.89/1.60	   U11(tt) -> U12(isLNat)
2.89/1.60	   U111(tt) -> tt
2.89/1.60	   U121(tt) -> tt
2.89/1.60	   U131(tt) -> U132(isLNat)
2.89/1.60	   U132(tt) -> tt
2.89/1.60	   U141(tt) -> U142(isLNat)
2.89/1.60	   U142(tt) -> tt
2.89/1.60	   U151(tt) -> U152(isLNat)
2.89/1.60	   U152(tt) -> tt
2.89/1.60	   U171(tt) -> U172(isLNat)
2.89/1.60	   U181(tt) -> U182(isLNat)
2.89/1.60	   U201(tt) -> U202(isNatural)
2.89/1.60	   U202(tt) -> U203(isLNat)
2.89/1.60	   U21(tt) -> U22(isLNat)
2.89/1.60	   U211(tt) -> U212(isLNat)
2.89/1.60	   U221(tt) -> U222(isLNat)
2.89/1.60	   U31(tt) -> U32(isLNat)
2.89/1.60	   U41(tt) -> U42(isLNat)
2.89/1.60	   U42(tt) -> tt
2.89/1.60	   U51(tt) -> U52(isLNat)
2.89/1.60	   U52(tt) -> tt
2.89/1.60	   U61(tt) -> tt
2.89/1.60	   U71(tt) -> tt
2.89/1.60	   U81(tt) -> tt
2.89/1.60	   U91(tt) -> tt
2.89/1.60	   afterNth(N, XS) -> U11(isNatural)
2.89/1.60	   fst(pair(X, Y)) -> U21(isLNat)
2.89/1.60	   head(cons(N)) -> U31(isNatural)
2.89/1.60	   isLNat -> tt
2.89/1.60	   isLNat -> U41(isNatural)
2.89/1.60	   isLNat -> U51(isNatural)
2.89/1.60	   isLNat -> U61(isPLNat)
2.89/1.60	   isLNat -> U71(isNatural)
2.89/1.60	   isLNat -> U81(isPLNat)
2.89/1.60	   isLNat -> U91(isLNat)
2.89/1.60	   isLNat -> U101(isNatural)
2.89/1.60	   isNatural -> tt
2.89/1.60	   isNatural -> U111(isLNat)
2.89/1.60	   isNatural -> U121(isNatural)
2.89/1.60	   isNatural -> U131(isNatural)
2.89/1.60	   isPLNat -> U141(isLNat)
2.89/1.60	   isPLNat -> U151(isNatural)
2.89/1.60	   natsFrom(N) -> U161(isNatural)
2.89/1.60	   sel(N, XS) -> U171(isNatural)
2.89/1.60	   snd(pair(X, Y)) -> U181(isLNat)
2.89/1.60	   splitAt(0, XS) -> U191(isLNat)
2.89/1.60	   splitAt(s(N), cons(X)) -> U201(isNatural)
2.89/1.60	   tail(cons(N)) -> U211(isNatural)
2.89/1.60	   take(N, XS) -> U221(isNatural)
2.89/1.60	
2.89/1.60	
2.89/1.60	----------------------------------------
2.89/1.60	
2.89/1.60	(1) ExtraVarProof (FINISHED)
2.89/1.60	unbounded runtime complexity due to extra variable on rhs
2.89/1.60	----------------------------------------
2.89/1.60	
2.89/1.60	(2)
2.89/1.60	BOUNDS(INF, INF)
3.16/1.63	EOF