TRS:
 {             a__and(tt(), T) -> mark(T),
             a__isNatIList(IL) -> a__isNatList(IL),
                 a__isNat(0()) -> tt(),
                a__isNat(s(N)) -> a__isNat(N),
           a__isNat(length(L)) -> a__isNatList(L),
        a__isNatIList(zeros()) -> tt(),
    a__isNatIList(cons(N, IL)) -> a__and(a__isNat(N), a__isNatIList(IL)),
           a__isNatList(nil()) -> tt(),
      a__isNatList(cons(N, L)) -> a__and(a__isNat(N), a__isNatList(L)),
     a__isNatList(take(N, IL)) -> a__and(a__isNat(N), a__isNatIList(IL)),
                    a__zeros() -> cons(0(), zeros()),
              a__take(0(), IL) -> a__uTake1(a__isNatIList(IL)),
               a__uTake1(tt()) -> nil(),
    a__take(s(M), cons(N, IL)) -> a__uTake2(a__and(a__isNat(M), a__and(a__isNat(N), a__isNatIList(IL))), M, N, IL),
     a__uTake2(tt(), M, N, IL) -> cons(mark(N), take(M, IL)),
         a__length(cons(N, L)) -> a__uLength(a__and(a__isNat(N), a__isNatList(L)), L),
           a__uLength(tt(), L) -> s(a__length(mark(L))),
             mark(and(X1, X2)) -> a__and(mark(X1), mark(X2)),
           mark(isNatIList(X)) -> a__isNatIList(X),
            mark(isNatList(X)) -> a__isNatList(X),
                mark(isNat(X)) -> a__isNat(X),
               mark(length(X)) -> a__length(mark(X)),
                 mark(zeros()) -> a__zeros(),
            mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)),
               mark(uTake1(X)) -> a__uTake1(mark(X)),
  mark(uTake2(X1, X2, X3, X4)) -> a__uTake2(mark(X1), X2, X3, X4),
         mark(uLength(X1, X2)) -> a__uLength(mark(X1), X2),
                    mark(tt()) -> tt(),
                     mark(0()) -> 0(),
                    mark(s(X)) -> s(mark(X)),
            mark(cons(X1, X2)) -> cons(mark(X1), X2),
                   mark(nil()) -> nil(),
                a__and(X1, X2) -> and(X1, X2),
              a__isNatIList(X) -> isNatIList(X),
               a__isNatList(X) -> isNatList(X),
                   a__isNat(X) -> isNat(X),
                  a__length(X) -> length(X),
                    a__zeros() -> zeros(),
               a__take(X1, X2) -> take(X1, X2),
                  a__uTake1(X) -> uTake1(X),
     a__uTake2(X1, X2, X3, X4) -> uTake2(X1, X2, X3, X4),
            a__uLength(X1, X2) -> uLength(X1, X2)}
 Fail