NO

Problem:
 U101(tt()) -> fst(splitAt(N,XS))
 U11(tt()) -> snd(splitAt(N,XS))
 U21(tt()) -> X
 U31(tt()) -> N
 U41(tt()) -> cons(N)
 U51(tt()) -> head(afterNth(N,XS))
 U61(tt()) -> Y
 U71(tt()) -> pair(nil(),XS)
 U81(tt()) -> U82(splitAt(N,XS))
 U82(pair(YS,ZS)) -> pair(cons(X),ZS)
 U91(tt()) -> XS
 and(tt()) -> X
 afterNth(N,XS) -> U11(and(isNatural()))
 fst(pair(X,Y)) -> U21(and(isLNat()))
 head(cons(N)) -> U31(and(isNatural()))
 isLNat() -> tt()
 isLNat() -> and(isNatural())
 isLNat() -> isPLNat()
 isLNat() -> isNatural()
 isLNat() -> isLNat()
 isNatural() -> tt()
 isNatural() -> isLNat()
 isNatural() -> isNatural()
 isNatural() -> and(isNatural())
 isPLNat() -> and(isLNat())
 isPLNat() -> and(isNatural())
 natsFrom(N) -> U41(isNatural())
 sel(N,XS) -> U51(and(isNatural()))
 snd(pair(X,Y)) -> U61(and(isLNat()))
 splitAt(0(),XS) -> U71(isLNat())
 splitAt(s(N),cons(X)) -> U81(and(isNatural()))
 tail(cons(N)) -> U91(and(isNatural()))
 take(N,XS) -> U101(and(isNatural()))

Proof:
 Fresh Variable Processor:
  loop length: 1
  terms:
   U101(tt())
  context: fst(splitAt([],XS))
  substitution:
   N -> U101(tt())
  Qed