NO
0.08/0.19	NO
0.08/0.19	
0.08/0.19	Problem:
0.08/0.19	 U101(tt()) -> fst(splitAt(N,XS))
0.08/0.19	 U11(tt()) -> snd(splitAt(N,XS))
0.08/0.19	 U21(tt()) -> X
0.08/0.19	 U31(tt()) -> N
0.08/0.19	 U41(tt()) -> cons(N)
0.08/0.19	 U51(tt()) -> head(afterNth(N,XS))
0.08/0.19	 U61(tt()) -> Y
0.08/0.19	 U71(tt()) -> pair(nil(),XS)
0.08/0.19	 U81(tt()) -> U82(splitAt(N,XS))
0.08/0.19	 U82(pair(YS,ZS)) -> pair(cons(X),ZS)
0.08/0.19	 U91(tt()) -> XS
0.08/0.19	 and(tt()) -> X
0.08/0.19	 afterNth(N,XS) -> U11(and(isNatural()))
0.08/0.19	 fst(pair(X,Y)) -> U21(and(isLNat()))
0.08/0.19	 head(cons(N)) -> U31(and(isNatural()))
0.08/0.19	 isLNat() -> tt()
0.08/0.19	 isLNat() -> and(isNatural())
0.08/0.19	 isLNat() -> isPLNat()
0.08/0.19	 isLNat() -> isNatural()
0.08/0.19	 isLNat() -> isLNat()
0.08/0.19	 isNatural() -> tt()
0.08/0.19	 isNatural() -> isLNat()
0.08/0.19	 isNatural() -> isNatural()
0.08/0.19	 isNatural() -> and(isNatural())
0.08/0.19	 isPLNat() -> and(isLNat())
0.08/0.19	 isPLNat() -> and(isNatural())
0.08/0.19	 natsFrom(N) -> U41(isNatural())
0.08/0.19	 sel(N,XS) -> U51(and(isNatural()))
0.08/0.19	 snd(pair(X,Y)) -> U61(and(isLNat()))
0.08/0.19	 splitAt(0(),XS) -> U71(isLNat())
0.08/0.19	 splitAt(s(N),cons(X)) -> U81(and(isNatural()))
0.08/0.19	 tail(cons(N)) -> U91(and(isNatural()))
0.08/0.19	 take(N,XS) -> U101(and(isNatural()))
0.08/0.19	
0.08/0.19	Proof:
0.08/0.19	 Fresh Variable Processor:
0.08/0.19	  loop length: 1
0.08/0.19	  terms:
0.08/0.19	   U101(tt())
0.08/0.19	  context: fst(splitAt([],XS))
0.08/0.19	  substitution:
0.08/0.19	   N -> U101(tt())
0.08/0.19	  Qed
0.08/0.20	EOF