MAYBE
MAYBE
TRS:
 {
         fst(pair(X, Y)) -> U21(and(isLNat())),
        splitAt(0(), XS) -> U71(isLNat()),
  splitAt(s(N), cons(X)) -> U81(and(isNatural())),
              U101(tt()) -> fst(splitAt(N, XS)),
         snd(pair(X, Y)) -> U61(and(isLNat())),
               U11(tt()) -> snd(splitAt(N, XS)),
               U21(tt()) -> X,
               U31(tt()) -> N,
               U41(tt()) -> cons(N),
           head(cons(N)) -> U31(and(isNatural())),
         afterNth(N, XS) -> U11(and(isNatural())),
               U51(tt()) -> head(afterNth(N, XS)),
               U61(tt()) -> Y,
               U71(tt()) -> pair(nil(), XS),
       U82(pair(YS, ZS)) -> pair(cons(X), ZS),
               U81(tt()) -> U82(splitAt(N, XS)),
               U91(tt()) -> XS,
               and(tt()) -> X,
             isNatural() -> tt(),
             isNatural() -> and(isNatural()),
             isNatural() -> isNatural(),
             isNatural() -> isLNat(),
                isLNat() -> tt(),
                isLNat() -> and(isNatural()),
                isLNat() -> isNatural(),
                isLNat() -> isLNat(),
                isLNat() -> isPLNat(),
               isPLNat() -> and(isNatural()),
               isPLNat() -> and(isLNat()),
             natsFrom(N) -> U41(isNatural()),
              sel(N, XS) -> U51(and(isNatural())),
           tail(cons(N)) -> U91(and(isNatural())),
             take(N, XS) -> U101(and(isNatural()))
 }
 DUP: We consider a duplicating system.
  Trs:
   {
           fst(pair(X, Y)) -> U21(and(isLNat())),
          splitAt(0(), XS) -> U71(isLNat()),
    splitAt(s(N), cons(X)) -> U81(and(isNatural())),
                U101(tt()) -> fst(splitAt(N, XS)),
           snd(pair(X, Y)) -> U61(and(isLNat())),
                 U11(tt()) -> snd(splitAt(N, XS)),
                 U21(tt()) -> X,
                 U31(tt()) -> N,
                 U41(tt()) -> cons(N),
             head(cons(N)) -> U31(and(isNatural())),
           afterNth(N, XS) -> U11(and(isNatural())),
                 U51(tt()) -> head(afterNth(N, XS)),
                 U61(tt()) -> Y,
                 U71(tt()) -> pair(nil(), XS),
         U82(pair(YS, ZS)) -> pair(cons(X), ZS),
                 U81(tt()) -> U82(splitAt(N, XS)),
                 U91(tt()) -> XS,
                 and(tt()) -> X,
               isNatural() -> tt(),
               isNatural() -> and(isNatural()),
               isNatural() -> isNatural(),
               isNatural() -> isLNat(),
                  isLNat() -> tt(),
                  isLNat() -> and(isNatural()),
                  isLNat() -> isNatural(),
                  isLNat() -> isLNat(),
                  isLNat() -> isPLNat(),
                 isPLNat() -> and(isNatural()),
                 isPLNat() -> and(isLNat()),
               natsFrom(N) -> U41(isNatural()),
                sel(N, XS) -> U51(and(isNatural())),
             tail(cons(N)) -> U91(and(isNatural())),
               take(N, XS) -> U101(and(isNatural()))
   }
  Fail