TRS:
 {          a__U11(tt(), N, XS) -> a__U12(tt(), N, XS),
            a__U12(tt(), N, XS) -> a__snd(a__splitAt(mark(N), mark(XS))),
                a__U21(tt(), X) -> a__U22(tt(), X),
                a__U22(tt(), X) -> mark(X),
                a__U31(tt(), N) -> a__U32(tt(), N),
                a__U32(tt(), N) -> mark(N),
            a__U41(tt(), N, XS) -> a__U42(tt(), N, XS),
            a__U42(tt(), N, XS) -> a__head(a__afterNth(mark(N), mark(XS))),
                a__U51(tt(), Y) -> a__U52(tt(), Y),
                a__U52(tt(), Y) -> mark(Y),
         a__U61(tt(), N, X, XS) -> a__U62(tt(), N, X, XS),
         a__U62(tt(), N, X, XS) -> a__U63(tt(), N, X, XS),
         a__U63(tt(), N, X, XS) -> a__U64(a__splitAt(mark(N), mark(XS)), X),
        a__U64(pair(YS, ZS), X) -> pair(cons(mark(X), YS), mark(ZS)),
               a__U71(tt(), XS) -> a__U72(tt(), XS),
               a__U72(tt(), XS) -> mark(XS),
            a__U81(tt(), N, XS) -> a__U82(tt(), N, XS),
            a__U82(tt(), N, XS) -> a__fst(a__splitAt(mark(N), mark(XS))),
             a__afterNth(N, XS) -> a__U11(tt(), N, XS),
             a__fst(pair(X, Y)) -> a__U21(tt(), X),
           a__head(cons(N, XS)) -> a__U31(tt(), N),
                 a__natsFrom(N) -> cons(mark(N), natsFrom(s(N))),
                  a__sel(N, XS) -> a__U41(tt(), N, XS),
             a__snd(pair(X, Y)) -> a__U51(tt(), Y),
            a__splitAt(0(), XS) -> pair(nil(), mark(XS)),
  a__splitAt(s(N), cons(X, XS)) -> a__U61(tt(), N, X, XS),
           a__tail(cons(N, XS)) -> a__U71(tt(), XS),
                 a__take(N, XS) -> a__U81(tt(), N, XS),
          mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3),
          mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3),
                   mark(snd(X)) -> a__snd(mark(X)),
          mark(splitAt(X1, X2)) -> a__splitAt(mark(X1), mark(X2)),
              mark(U21(X1, X2)) -> a__U21(mark(X1), X2),
              mark(U22(X1, X2)) -> a__U22(mark(X1), X2),
              mark(U31(X1, X2)) -> a__U31(mark(X1), X2),
              mark(U32(X1, X2)) -> a__U32(mark(X1), X2),
          mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3),
          mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3),
                  mark(head(X)) -> a__head(mark(X)),
         mark(afterNth(X1, X2)) -> a__afterNth(mark(X1), mark(X2)),
              mark(U51(X1, X2)) -> a__U51(mark(X1), X2),
              mark(U52(X1, X2)) -> a__U52(mark(X1), X2),
      mark(U61(X1, X2, X3, X4)) -> a__U61(mark(X1), X2, X3, X4),
      mark(U62(X1, X2, X3, X4)) -> a__U62(mark(X1), X2, X3, X4),
      mark(U63(X1, X2, X3, X4)) -> a__U63(mark(X1), X2, X3, X4),
              mark(U64(X1, X2)) -> a__U64(mark(X1), X2),
              mark(U71(X1, X2)) -> a__U71(mark(X1), X2),
              mark(U72(X1, X2)) -> a__U72(mark(X1), X2),
          mark(U81(X1, X2, X3)) -> a__U81(mark(X1), X2, X3),
          mark(U82(X1, X2, X3)) -> a__U82(mark(X1), X2, X3),
                   mark(fst(X)) -> a__fst(mark(X)),
              mark(natsFrom(X)) -> a__natsFrom(mark(X)),
              mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)),
                  mark(tail(X)) -> a__tail(mark(X)),
             mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)),
                     mark(tt()) -> tt(),
             mark(pair(X1, X2)) -> pair(mark(X1), mark(X2)),
             mark(cons(X1, X2)) -> cons(mark(X1), X2),
                     mark(s(X)) -> s(mark(X)),
                      mark(0()) -> 0(),
                    mark(nil()) -> nil(),
             a__U11(X1, X2, X3) -> U11(X1, X2, X3),
             a__U12(X1, X2, X3) -> U12(X1, X2, X3),
                      a__snd(X) -> snd(X),
             a__splitAt(X1, X2) -> splitAt(X1, X2),
                 a__U21(X1, X2) -> U21(X1, X2),
                 a__U22(X1, X2) -> U22(X1, X2),
                 a__U31(X1, X2) -> U31(X1, X2),
                 a__U32(X1, X2) -> U32(X1, X2),
             a__U41(X1, X2, X3) -> U41(X1, X2, X3),
             a__U42(X1, X2, X3) -> U42(X1, X2, X3),
                     a__head(X) -> head(X),
            a__afterNth(X1, X2) -> afterNth(X1, X2),
                 a__U51(X1, X2) -> U51(X1, X2),
                 a__U52(X1, X2) -> U52(X1, X2),
         a__U61(X1, X2, X3, X4) -> U61(X1, X2, X3, X4),
         a__U62(X1, X2, X3, X4) -> U62(X1, X2, X3, X4),
         a__U63(X1, X2, X3, X4) -> U63(X1, X2, X3, X4),
                 a__U64(X1, X2) -> U64(X1, X2),
                 a__U71(X1, X2) -> U71(X1, X2),
                 a__U72(X1, X2) -> U72(X1, X2),
             a__U81(X1, X2, X3) -> U81(X1, X2, X3),
             a__U82(X1, X2, X3) -> U82(X1, X2, X3),
                      a__fst(X) -> fst(X),
                 a__natsFrom(X) -> natsFrom(X),
                 a__sel(X1, X2) -> sel(X1, X2),
                     a__tail(X) -> tail(X),
                a__take(X1, X2) -> take(X1, X2)}
 Fail