MAYBE
MAYBE
TRS:
 {
                     cons(X1, X2) -> n__cons(X1, X2),
                              0() -> n__0(),
                          zeros() -> cons(0(), n__zeros()),
                          zeros() -> n__zeros(),
               U102(tt(), V1, V2) ->
  U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
                isNatKind(n__0()) -> tt(),
         isNatKind(n__length(V1)) -> U71(isNatIListKind(activate(V1))),
              isNatKind(n__s(V1)) -> U81(isNatKind(activate(V1))),
                      activate(X) -> X,
             activate(n__zeros()) -> zeros(),
        activate(n__take(X1, X2)) -> take(X1, X2),
                 activate(n__0()) -> 0(),
           activate(n__length(X)) -> length(X),
                activate(n__s(X)) -> s(X),
        activate(n__cons(X1, X2)) -> cons(X1, X2),
               activate(n__nil()) -> nil(),
               U101(tt(), V1, V2) ->
  U102(isNatKind(activate(V1)), activate(V1), activate(V2)),
               U103(tt(), V1, V2) ->
  U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
       isNatIListKind(n__zeros()) -> tt(),
  isNatIListKind(n__take(V1, V2)) ->
  U61(isNatKind(activate(V1)), activate(V2)),
  isNatIListKind(n__cons(V1, V2)) ->
  U51(isNatKind(activate(V1)), activate(V2)),
         isNatIListKind(n__nil()) -> tt(),
               U104(tt(), V1, V2) -> U105(isNat(activate(V1)), activate(V2)),
                   U105(tt(), V2) -> U106(isNatIList(activate(V2))),
                    isNat(n__0()) -> tt(),
             isNat(n__length(V1)) ->
  U11(isNatIListKind(activate(V1)), activate(V1)),
                  isNat(n__s(V1)) ->
  U21(isNatKind(activate(V1)), activate(V1)),
                       U106(tt()) -> tt(),
                    isNatIList(V) ->
  U31(isNatIListKind(activate(V)), activate(V)),
           isNatIList(n__zeros()) -> tt(),
      isNatIList(n__cons(V1, V2)) ->
  U41(isNatKind(activate(V1)), activate(V1), activate(V2)),
                    U12(tt(), V1) -> U13(isNatList(activate(V1))),
                    U11(tt(), V1) ->
  U12(isNatIListKind(activate(V1)), activate(V1)),
                 U112(tt(), L, N) ->
  U113(isNat(activate(N)), activate(L), activate(N)),
                 U111(tt(), L, N) ->
  U112(isNatIListKind(activate(L)), activate(L), activate(N)),
                 U113(tt(), L, N) ->
  U114(isNatKind(activate(N)), activate(L)),
                    U114(tt(), L) -> s(length(activate(L))),
                             s(X) -> n__s(X),
                        length(X) -> n__length(X),
               length(cons(N, L)) ->
  U111(isNatList(activate(L)), activate(L), N),
                    length(nil()) -> 0(),
                        U13(tt()) -> tt(),
       isNatList(n__take(V1, V2)) ->
  U101(isNatKind(activate(V1)), activate(V1), activate(V2)),
       isNatList(n__cons(V1, V2)) ->
  U91(isNatKind(activate(V1)), activate(V1), activate(V2)),
              isNatList(n__nil()) -> tt(),
                       U122(tt()) -> nil(),
                   U121(tt(), IL) -> U122(isNatIListKind(activate(IL))),
                            nil() -> n__nil(),
             U132(tt(), IL, M, N) ->
  U133(isNat(activate(M)), activate(IL), activate(M), activate(N)),
             U131(tt(), IL, M, N) ->
  U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)),
             U133(tt(), IL, M, N) ->
  U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)),
             U134(tt(), IL, M, N) ->
  U135(isNat(activate(N)), activate(IL), activate(M), activate(N)),
             U135(tt(), IL, M, N) ->
  U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)),
             U136(tt(), IL, M, N) ->
  cons(activate(N), n__take(activate(M), activate(IL))),
                    U22(tt(), V1) -> U23(isNat(activate(V1))),
                    U21(tt(), V1) ->
  U22(isNatKind(activate(V1)), activate(V1)),
                        U23(tt()) -> tt(),
                     U32(tt(), V) -> U33(isNatList(activate(V))),
                     U31(tt(), V) ->
  U32(isNatIListKind(activate(V)), activate(V)),
                        U33(tt()) -> tt(),
                U42(tt(), V1, V2) ->
  U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
                U41(tt(), V1, V2) ->
  U42(isNatKind(activate(V1)), activate(V1), activate(V2)),
                U43(tt(), V1, V2) ->
  U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
                U44(tt(), V1, V2) -> U45(isNat(activate(V1)), activate(V2)),
                    U45(tt(), V2) -> U46(isNatIList(activate(V2))),
                        U46(tt()) -> tt(),
                        U52(tt()) -> tt(),
                    U51(tt(), V2) -> U52(isNatIListKind(activate(V2))),
                        U62(tt()) -> tt(),
                    U61(tt(), V2) -> U62(isNatIListKind(activate(V2))),
                        U71(tt()) -> tt(),
                        U81(tt()) -> tt(),
                U92(tt(), V1, V2) ->
  U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
                U91(tt(), V1, V2) ->
  U92(isNatKind(activate(V1)), activate(V1), activate(V2)),
                U93(tt(), V1, V2) ->
  U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
                U94(tt(), V1, V2) -> U95(isNat(activate(V1)), activate(V2)),
                    U95(tt(), V2) -> U96(isNatList(activate(V2))),
                        U96(tt()) -> tt(),
                     take(X1, X2) -> n__take(X1, X2),
                    take(0(), IL) -> U121(isNatIList(IL), IL),
          take(s(M), cons(N, IL)) ->
  U131(isNatIList(activate(IL)), activate(IL), M, N)
 }
 DUP: We consider a duplicating system.
  Trs:
   {
                       cons(X1, X2) -> n__cons(X1, X2),
                                0() -> n__0(),
                            zeros() -> cons(0(), n__zeros()),
                            zeros() -> n__zeros(),
                 U102(tt(), V1, V2) ->
    U103(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
                  isNatKind(n__0()) -> tt(),
           isNatKind(n__length(V1)) -> U71(isNatIListKind(activate(V1))),
                isNatKind(n__s(V1)) -> U81(isNatKind(activate(V1))),
                        activate(X) -> X,
               activate(n__zeros()) -> zeros(),
          activate(n__take(X1, X2)) -> take(X1, X2),
                   activate(n__0()) -> 0(),
             activate(n__length(X)) -> length(X),
                  activate(n__s(X)) -> s(X),
          activate(n__cons(X1, X2)) -> cons(X1, X2),
                 activate(n__nil()) -> nil(),
                 U101(tt(), V1, V2) ->
    U102(isNatKind(activate(V1)), activate(V1), activate(V2)),
                 U103(tt(), V1, V2) ->
    U104(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
         isNatIListKind(n__zeros()) -> tt(),
    isNatIListKind(n__take(V1, V2)) ->
    U61(isNatKind(activate(V1)), activate(V2)),
    isNatIListKind(n__cons(V1, V2)) ->
    U51(isNatKind(activate(V1)), activate(V2)),
           isNatIListKind(n__nil()) -> tt(),
                 U104(tt(), V1, V2) ->
    U105(isNat(activate(V1)), activate(V2)),
                     U105(tt(), V2) -> U106(isNatIList(activate(V2))),
                      isNat(n__0()) -> tt(),
               isNat(n__length(V1)) ->
    U11(isNatIListKind(activate(V1)), activate(V1)),
                    isNat(n__s(V1)) ->
    U21(isNatKind(activate(V1)), activate(V1)),
                         U106(tt()) -> tt(),
                      isNatIList(V) ->
    U31(isNatIListKind(activate(V)), activate(V)),
             isNatIList(n__zeros()) -> tt(),
        isNatIList(n__cons(V1, V2)) ->
    U41(isNatKind(activate(V1)), activate(V1), activate(V2)),
                      U12(tt(), V1) -> U13(isNatList(activate(V1))),
                      U11(tt(), V1) ->
    U12(isNatIListKind(activate(V1)), activate(V1)),
                   U112(tt(), L, N) ->
    U113(isNat(activate(N)), activate(L), activate(N)),
                   U111(tt(), L, N) ->
    U112(isNatIListKind(activate(L)), activate(L), activate(N)),
                   U113(tt(), L, N) ->
    U114(isNatKind(activate(N)), activate(L)),
                      U114(tt(), L) -> s(length(activate(L))),
                               s(X) -> n__s(X),
                          length(X) -> n__length(X),
                 length(cons(N, L)) ->
    U111(isNatList(activate(L)), activate(L), N),
                      length(nil()) -> 0(),
                          U13(tt()) -> tt(),
         isNatList(n__take(V1, V2)) ->
    U101(isNatKind(activate(V1)), activate(V1), activate(V2)),
         isNatList(n__cons(V1, V2)) ->
    U91(isNatKind(activate(V1)), activate(V1), activate(V2)),
                isNatList(n__nil()) -> tt(),
                         U122(tt()) -> nil(),
                     U121(tt(), IL) -> U122(isNatIListKind(activate(IL))),
                              nil() -> n__nil(),
               U132(tt(), IL, M, N) ->
    U133(isNat(activate(M)), activate(IL), activate(M), activate(N)),
               U131(tt(), IL, M, N) ->
    U132(isNatIListKind(activate(IL)), activate(IL), activate(M), activate(N)
    ),
               U133(tt(), IL, M, N) ->
    U134(isNatKind(activate(M)), activate(IL), activate(M), activate(N)),
               U134(tt(), IL, M, N) ->
    U135(isNat(activate(N)), activate(IL), activate(M), activate(N)),
               U135(tt(), IL, M, N) ->
    U136(isNatKind(activate(N)), activate(IL), activate(M), activate(N)),
               U136(tt(), IL, M, N) ->
    cons(activate(N), n__take(activate(M), activate(IL))),
                      U22(tt(), V1) -> U23(isNat(activate(V1))),
                      U21(tt(), V1) ->
    U22(isNatKind(activate(V1)), activate(V1)),
                          U23(tt()) -> tt(),
                       U32(tt(), V) -> U33(isNatList(activate(V))),
                       U31(tt(), V) ->
    U32(isNatIListKind(activate(V)), activate(V)),
                          U33(tt()) -> tt(),
                  U42(tt(), V1, V2) ->
    U43(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
                  U41(tt(), V1, V2) ->
    U42(isNatKind(activate(V1)), activate(V1), activate(V2)),
                  U43(tt(), V1, V2) ->
    U44(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
                  U44(tt(), V1, V2) -> U45(isNat(activate(V1)), activate(V2)),
                      U45(tt(), V2) -> U46(isNatIList(activate(V2))),
                          U46(tt()) -> tt(),
                          U52(tt()) -> tt(),
                      U51(tt(), V2) -> U52(isNatIListKind(activate(V2))),
                          U62(tt()) -> tt(),
                      U61(tt(), V2) -> U62(isNatIListKind(activate(V2))),
                          U71(tt()) -> tt(),
                          U81(tt()) -> tt(),
                  U92(tt(), V1, V2) ->
    U93(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
                  U91(tt(), V1, V2) ->
    U92(isNatKind(activate(V1)), activate(V1), activate(V2)),
                  U93(tt(), V1, V2) ->
    U94(isNatIListKind(activate(V2)), activate(V1), activate(V2)),
                  U94(tt(), V1, V2) -> U95(isNat(activate(V1)), activate(V2)),
                      U95(tt(), V2) -> U96(isNatList(activate(V2))),
                          U96(tt()) -> tt(),
                       take(X1, X2) -> n__take(X1, X2),
                      take(0(), IL) -> U121(isNatIList(IL), IL),
            take(s(M), cons(N, IL)) ->
    U131(isNatIList(activate(IL)), activate(IL), M, N)
   }
  Fail