TRS:
 {                     a__zeros() -> cons(0(), zeros()),
                 a__U11(tt(), V1) -> a__U12(a__isNatList(V1)),
                     a__U12(tt()) -> tt(),
                 a__U21(tt(), V1) -> a__U22(a__isNat(V1)),
                     a__U22(tt()) -> tt(),
                  a__U31(tt(), V) -> a__U32(a__isNatList(V)),
                     a__U32(tt()) -> tt(),
             a__U41(tt(), V1, V2) -> a__U42(a__isNat(V1), V2),
                 a__U42(tt(), V2) -> a__U43(a__isNatIList(V2)),
                     a__U43(tt()) -> tt(),
             a__U51(tt(), V1, V2) -> a__U52(a__isNat(V1), V2),
                 a__U52(tt(), V2) -> a__U53(a__isNatList(V2)),
                     a__U53(tt()) -> tt(),
             a__U61(tt(), V1, V2) -> a__U62(a__isNat(V1), V2),
                 a__U62(tt(), V2) -> a__U63(a__isNatIList(V2)),
                     a__U63(tt()) -> tt(),
                  a__U71(tt(), L) -> s(a__length(mark(L))),
                     a__U81(tt()) -> nil(),
           a__U91(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__U11(a__isNatIListKind(V1), V1),
                  a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1),
                 a__isNatIList(V) -> a__U31(a__isNatIListKind(V), V),
           a__isNatIList(zeros()) -> tt(),
      a__isNatIList(cons(V1, V2)) -> a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2),
         a__isNatIListKind(nil()) -> tt(),
       a__isNatIListKind(zeros()) -> tt(),
  a__isNatIListKind(cons(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2)),
  a__isNatIListKind(take(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2)),
                a__isNatKind(0()) -> tt(),
         a__isNatKind(length(V1)) -> a__isNatIListKind(V1),
              a__isNatKind(s(V1)) -> a__isNatKind(V1),
              a__isNatList(nil()) -> tt(),
       a__isNatList(cons(V1, V2)) -> a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2),
       a__isNatList(take(V1, V2)) -> a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2),
                 a__length(nil()) -> 0(),
            a__length(cons(N, L)) -> a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L),
                 a__take(0(), IL) -> a__U81(a__and(a__isNatIList(IL), isNatIListKind(IL))),
       a__take(s(M), cons(N, IL)) -> a__U91(a__and(a__and(a__isNatIList(IL), isNatIListKind(IL)), and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))), IL, M, N),
                    mark(zeros()) -> a__zeros(),
                mark(U11(X1, X2)) -> a__U11(mark(X1), X2),
                     mark(U12(X)) -> a__U12(mark(X)),
               mark(isNatList(X)) -> a__isNatList(X),
                mark(U21(X1, X2)) -> a__U21(mark(X1), X2),
                     mark(U22(X)) -> a__U22(mark(X)),
                   mark(isNat(X)) -> a__isNat(X),
                mark(U31(X1, X2)) -> a__U31(mark(X1), X2),
                     mark(U32(X)) -> a__U32(mark(X)),
            mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3),
                mark(U42(X1, X2)) -> a__U42(mark(X1), X2),
                     mark(U43(X)) -> a__U43(mark(X)),
              mark(isNatIList(X)) -> a__isNatIList(X),
            mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3),
                mark(U52(X1, X2)) -> a__U52(mark(X1), X2),
                     mark(U53(X)) -> a__U53(mark(X)),
            mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3),
                mark(U62(X1, X2)) -> a__U62(mark(X1), X2),
                     mark(U63(X)) -> a__U63(mark(X)),
                mark(U71(X1, X2)) -> a__U71(mark(X1), X2),
                  mark(length(X)) -> a__length(mark(X)),
                     mark(U81(X)) -> a__U81(mark(X)),
        mark(U91(X1, X2, X3, X4)) -> a__U91(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(isNatIListKind(X)) -> a__isNatIListKind(X),
               mark(isNatKind(X)) -> a__isNatKind(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__U12(X) -> U12(X),
                  a__isNatList(X) -> isNatList(X),
                   a__U21(X1, X2) -> U21(X1, X2),
                        a__U22(X) -> U22(X),
                      a__isNat(X) -> isNat(X),
                   a__U31(X1, X2) -> U31(X1, X2),
                        a__U32(X) -> U32(X),
               a__U41(X1, X2, X3) -> U41(X1, X2, X3),
                   a__U42(X1, X2) -> U42(X1, X2),
                        a__U43(X) -> U43(X),
                 a__isNatIList(X) -> isNatIList(X),
               a__U51(X1, X2, X3) -> U51(X1, X2, X3),
                   a__U52(X1, X2) -> U52(X1, X2),
                        a__U53(X) -> U53(X),
               a__U61(X1, X2, X3) -> U61(X1, X2, X3),
                   a__U62(X1, X2) -> U62(X1, X2),
                        a__U63(X) -> U63(X),
                   a__U71(X1, X2) -> U71(X1, X2),
                     a__length(X) -> length(X),
                        a__U81(X) -> U81(X),
           a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4),
                  a__take(X1, X2) -> take(X1, X2),
                   a__and(X1, X2) -> and(X1, X2),
             a__isNatIListKind(X) -> isNatIListKind(X),
                  a__isNatKind(X) -> isNatKind(X)}
 Fail