MAYBE
MAYBE
TRS:
 {
               U12(tt()) -> snd(splitAt(N, XS)),
               U11(tt()) -> U12(tt()),
         snd(pair(X, Y)) -> U51(tt()),
        splitAt(0(), XS) -> pair(nil(), XS),
  splitAt(s(N), cons(X)) -> U61(tt()),
               U22(tt()) -> X,
               U21(tt()) -> U22(tt()),
               U32(tt()) -> N,
               U31(tt()) -> U32(tt()),
               U42(tt()) -> head(afterNth(N, XS)),
               U41(tt()) -> U42(tt()),
           head(cons(N)) -> U31(tt()),
         afterNth(N, XS) -> U11(tt()),
               U52(tt()) -> Y,
               U51(tt()) -> U52(tt()),
               U62(tt()) -> U63(tt()),
               U61(tt()) -> U62(tt()),
               U63(tt()) -> U64(splitAt(N, XS)),
       U64(pair(YS, ZS)) -> pair(cons(X), ZS),
               U72(tt()) -> XS,
               U71(tt()) -> U72(tt()),
               U82(tt()) -> fst(splitAt(N, XS)),
               U81(tt()) -> U82(tt()),
         fst(pair(X, Y)) -> U21(tt()),
             natsFrom(N) -> cons(N),
              sel(N, XS) -> U41(tt()),
           tail(cons(N)) -> U71(tt()),
             take(N, XS) -> U81(tt())
 }
 DUP: We consider a duplicating system.
  Trs:
   {
                 U12(tt()) -> snd(splitAt(N, XS)),
                 U11(tt()) -> U12(tt()),
           snd(pair(X, Y)) -> U51(tt()),
          splitAt(0(), XS) -> pair(nil(), XS),
    splitAt(s(N), cons(X)) -> U61(tt()),
                 U22(tt()) -> X,
                 U21(tt()) -> U22(tt()),
                 U32(tt()) -> N,
                 U31(tt()) -> U32(tt()),
                 U42(tt()) -> head(afterNth(N, XS)),
                 U41(tt()) -> U42(tt()),
             head(cons(N)) -> U31(tt()),
           afterNth(N, XS) -> U11(tt()),
                 U52(tt()) -> Y,
                 U51(tt()) -> U52(tt()),
                 U62(tt()) -> U63(tt()),
                 U61(tt()) -> U62(tt()),
                 U63(tt()) -> U64(splitAt(N, XS)),
         U64(pair(YS, ZS)) -> pair(cons(X), ZS),
                 U72(tt()) -> XS,
                 U71(tt()) -> U72(tt()),
                 U82(tt()) -> fst(splitAt(N, XS)),
                 U81(tt()) -> U82(tt()),
           fst(pair(X, Y)) -> U21(tt()),
               natsFrom(N) -> cons(N),
                sel(N, XS) -> U41(tt()),
             tail(cons(N)) -> U71(tt()),
               take(N, XS) -> U81(tt())
   }
  Fail