TRS:
 {                 a__zeros() -> cons(0(), zeros()),
              a__U11(tt(), L) -> s(a__length(mark(L))),
                 a__U21(tt()) -> nil(),
       a__U31(tt(), IL, M, N) -> cons(mark(N), take(M, IL)),
              a__and(tt(), X) -> mark(X),
                a__isNat(0()) -> tt(),
         a__isNat(length(V1)) -> a__isNatList(V1),
              a__isNat(s(V1)) -> a__isNat(V1),
             a__isNatIList(V) -> a__isNatList(V),
       a__isNatIList(zeros()) -> tt(),
  a__isNatIList(cons(V1, V2)) -> a__and(a__isNat(V1), isNatIList(V2)),
          a__isNatList(nil()) -> tt(),
   a__isNatList(cons(V1, V2)) -> a__and(a__isNat(V1), isNatList(V2)),
   a__isNatList(take(V1, V2)) -> a__and(a__isNat(V1), isNatIList(V2)),
             a__length(nil()) -> 0(),
        a__length(cons(N, L)) -> a__U11(a__and(a__isNatList(L), isNat(N)), L),
             a__take(0(), IL) -> a__U21(a__isNatIList(IL)),
   a__take(s(M), cons(N, IL)) -> a__U31(a__and(a__isNatIList(IL), and(isNat(M), isNat(N))), IL, M, N),
                mark(zeros()) -> a__zeros(),
            mark(U11(X1, X2)) -> a__U11(mark(X1), X2),
              mark(length(X)) -> a__length(mark(X)),
                 mark(U21(X)) -> a__U21(mark(X)),
    mark(U31(X1, X2, X3, X4)) -> a__U31(mark(X1), X2, X3, X4),
           mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)),
            mark(and(X1, X2)) -> a__and(mark(X1), X2),
               mark(isNat(X)) -> a__isNat(X),
           mark(isNatList(X)) -> a__isNatList(X),
          mark(isNatIList(X)) -> a__isNatIList(X),
           mark(cons(X1, X2)) -> cons(mark(X1), X2),
                    mark(0()) -> 0(),
                   mark(tt()) -> tt(),
                   mark(s(X)) -> s(mark(X)),
                  mark(nil()) -> nil(),
                   a__zeros() -> zeros(),
               a__U11(X1, X2) -> U11(X1, X2),
                 a__length(X) -> length(X),
                    a__U21(X) -> U21(X),
       a__U31(X1, X2, X3, X4) -> U31(X1, X2, X3, X4),
              a__take(X1, X2) -> take(X1, X2),
               a__and(X1, X2) -> and(X1, X2),
                  a__isNat(X) -> isNat(X),
              a__isNatList(X) -> isNatList(X),
             a__isNatIList(X) -> isNatIList(X)}
 Fail