TRS:
 {         a__U101(tt(), N, XS) -> a__fst(a__splitAt(mark(N), mark(XS))),
            a__U11(tt(), N, XS) -> a__snd(a__splitAt(mark(N), mark(XS))),
                a__U21(tt(), X) -> mark(X),
                a__U31(tt(), N) -> mark(N),
                a__U41(tt(), N) -> cons(mark(N), natsFrom(s(N))),
            a__U51(tt(), N, XS) -> a__head(a__afterNth(mark(N), mark(XS))),
                a__U61(tt(), Y) -> mark(Y),
               a__U71(tt(), XS) -> pair(nil(), mark(XS)),
         a__U81(tt(), N, X, XS) -> a__U82(a__splitAt(mark(N), mark(XS)), X),
        a__U82(pair(YS, ZS), X) -> pair(cons(mark(X), YS), mark(ZS)),
               a__U91(tt(), XS) -> mark(XS),
             a__afterNth(N, XS) -> a__U11(a__and(a__isNatural(N), isLNat(XS)), N, XS),
                a__and(tt(), X) -> mark(X),
             a__fst(pair(X, Y)) -> a__U21(a__and(a__isLNat(X), isLNat(Y)), X),
           a__head(cons(N, XS)) -> a__U31(a__and(a__isNatural(N), isLNat(XS)), N),
               a__isLNat(nil()) -> tt(),
    a__isLNat(afterNth(V1, V2)) -> a__and(a__isNatural(V1), isLNat(V2)),
        a__isLNat(cons(V1, V2)) -> a__and(a__isNatural(V1), isLNat(V2)),
             a__isLNat(fst(V1)) -> a__isPLNat(V1),
        a__isLNat(natsFrom(V1)) -> a__isNatural(V1),
             a__isLNat(snd(V1)) -> a__isPLNat(V1),
            a__isLNat(tail(V1)) -> a__isLNat(V1),
        a__isLNat(take(V1, V2)) -> a__and(a__isNatural(V1), isLNat(V2)),
              a__isNatural(0()) -> tt(),
         a__isNatural(head(V1)) -> a__isLNat(V1),
            a__isNatural(s(V1)) -> a__isNatural(V1),
      a__isNatural(sel(V1, V2)) -> a__and(a__isNatural(V1), isLNat(V2)),
       a__isPLNat(pair(V1, V2)) -> a__and(a__isLNat(V1), isLNat(V2)),
    a__isPLNat(splitAt(V1, V2)) -> a__and(a__isNatural(V1), isLNat(V2)),
                 a__natsFrom(N) -> a__U41(a__isNatural(N), N),
                  a__sel(N, XS) -> a__U51(a__and(a__isNatural(N), isLNat(XS)), N, XS),
             a__snd(pair(X, Y)) -> a__U61(a__and(a__isLNat(X), isLNat(Y)), Y),
            a__splitAt(0(), XS) -> a__U71(a__isLNat(XS), XS),
  a__splitAt(s(N), cons(X, XS)) -> a__U81(a__and(a__isNatural(N), and(isNatural(X), isLNat(XS))), N, X, XS),
           a__tail(cons(N, XS)) -> a__U91(a__and(a__isNatural(N), isLNat(XS)), XS),
                 a__take(N, XS) -> a__U101(a__and(a__isNatural(N), isLNat(XS)), N, XS),
         mark(U101(X1, X2, X3)) -> a__U101(mark(X1), X2, X3),
                   mark(fst(X)) -> a__fst(mark(X)),
          mark(splitAt(X1, X2)) -> a__splitAt(mark(X1), mark(X2)),
          mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3),
                   mark(snd(X)) -> a__snd(mark(X)),
              mark(U21(X1, X2)) -> a__U21(mark(X1), X2),
              mark(U31(X1, X2)) -> a__U31(mark(X1), X2),
              mark(U41(X1, X2)) -> a__U41(mark(X1), X2),
              mark(natsFrom(X)) -> a__natsFrom(mark(X)),
          mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3),
                  mark(head(X)) -> a__head(mark(X)),
         mark(afterNth(X1, X2)) -> a__afterNth(mark(X1), mark(X2)),
              mark(U61(X1, X2)) -> a__U61(mark(X1), X2),
              mark(U71(X1, X2)) -> a__U71(mark(X1), X2),
      mark(U81(X1, X2, X3, X4)) -> a__U81(mark(X1), X2, X3, X4),
              mark(U82(X1, X2)) -> a__U82(mark(X1), X2),
              mark(U91(X1, X2)) -> a__U91(mark(X1), X2),
              mark(and(X1, X2)) -> a__and(mark(X1), X2),
             mark(isNatural(X)) -> a__isNatural(X),
                mark(isLNat(X)) -> a__isLNat(X),
               mark(isPLNat(X)) -> a__isPLNat(X),
                  mark(tail(X)) -> a__tail(mark(X)),
             mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)),
              mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)),
                     mark(tt()) -> tt(),
             mark(cons(X1, X2)) -> cons(mark(X1), X2),
                     mark(s(X)) -> s(mark(X)),
             mark(pair(X1, X2)) -> pair(mark(X1), mark(X2)),
                    mark(nil()) -> nil(),
                      mark(0()) -> 0(),
            a__U101(X1, X2, X3) -> U101(X1, X2, X3),
                      a__fst(X) -> fst(X),
             a__splitAt(X1, X2) -> splitAt(X1, X2),
             a__U11(X1, X2, X3) -> U11(X1, X2, X3),
                      a__snd(X) -> snd(X),
                 a__U21(X1, X2) -> U21(X1, X2),
                 a__U31(X1, X2) -> U31(X1, X2),
                 a__U41(X1, X2) -> U41(X1, X2),
                 a__natsFrom(X) -> natsFrom(X),
             a__U51(X1, X2, X3) -> U51(X1, X2, X3),
                     a__head(X) -> head(X),
            a__afterNth(X1, X2) -> afterNth(X1, X2),
                 a__U61(X1, X2) -> U61(X1, X2),
                 a__U71(X1, X2) -> U71(X1, X2),
         a__U81(X1, X2, X3, X4) -> U81(X1, X2, X3, X4),
                 a__U82(X1, X2) -> U82(X1, X2),
                 a__U91(X1, X2) -> U91(X1, X2),
                 a__and(X1, X2) -> and(X1, X2),
                a__isNatural(X) -> isNatural(X),
                   a__isLNat(X) -> isLNat(X),
                  a__isPLNat(X) -> isPLNat(X),
                     a__tail(X) -> tail(X),
                a__take(X1, X2) -> take(X1, X2),
                 a__sel(X1, X2) -> sel(X1, X2)}
 Fail