MAYBE
* Step 1: Failure MAYBE
  + Considered Problem:
      - Strict TRS:
          0() -> n__0()
          U11(tt(),V1) -> U12(isNatList(activate(V1)))
          U12(tt()) -> tt()
          U21(tt(),V1) -> U22(isNat(activate(V1)))
          U22(tt()) -> tt()
          U31(tt(),V) -> U32(isNatList(activate(V)))
          U32(tt()) -> tt()
          U41(tt(),V1,V2) -> U42(isNat(activate(V1)),activate(V2))
          U42(tt(),V2) -> U43(isNatIList(activate(V2)))
          U43(tt()) -> tt()
          U51(tt(),V1,V2) -> U52(isNat(activate(V1)),activate(V2))
          U52(tt(),V2) -> U53(isNatList(activate(V2)))
          U53(tt()) -> tt()
          U61(tt(),V1,V2) -> U62(isNat(activate(V1)),activate(V2))
          U62(tt(),V2) -> U63(isNatIList(activate(V2)))
          U63(tt()) -> tt()
          U71(tt(),L) -> s(length(activate(L)))
          U81(tt()) -> nil()
          U91(tt(),IL,M,N) -> cons(activate(N),n__take(activate(M),activate(IL)))
          activate(X) -> X
          activate(n__0()) -> 0()
          activate(n__and(X1,X2)) -> and(activate(X1),X2)
          activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
          activate(n__isNat(X)) -> isNat(X)
          activate(n__isNatIListKind(X)) -> isNatIListKind(X)
          activate(n__isNatKind(X)) -> isNatKind(X)
          activate(n__length(X)) -> length(activate(X))
          activate(n__nil()) -> nil()
          activate(n__s(X)) -> s(activate(X))
          activate(n__take(X1,X2)) -> take(activate(X1),activate(X2))
          activate(n__zeros()) -> zeros()
          and(X1,X2) -> n__and(X1,X2)
          and(tt(),X) -> activate(X)
          cons(X1,X2) -> n__cons(X1,X2)
          isNat(X) -> n__isNat(X)
          isNat(n__0()) -> tt()
          isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)),activate(V1))
          isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1))
          isNatIList(V) -> U31(isNatIListKind(activate(V)),activate(V))
          isNatIList(n__cons(V1,V2)) -> U41(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2)))
                                           ,activate(V1)
                                           ,activate(V2))
          isNatIList(n__zeros()) -> tt()
          isNatIListKind(X) -> n__isNatIListKind(X)
          isNatIListKind(n__cons(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2)))
          isNatIListKind(n__nil()) -> tt()
          isNatIListKind(n__take(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2)))
          isNatIListKind(n__zeros()) -> tt()
          isNatKind(X) -> n__isNatKind(X)
          isNatKind(n__0()) -> tt()
          isNatKind(n__length(V1)) -> isNatIListKind(activate(V1))
          isNatKind(n__s(V1)) -> isNatKind(activate(V1))
          isNatList(n__cons(V1,V2)) -> U51(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2)))
                                          ,activate(V1)
                                          ,activate(V2))
          isNatList(n__nil()) -> tt()
          isNatList(n__take(V1,V2)) -> U61(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2)))
                                          ,activate(V1)
                                          ,activate(V2))
          length(X) -> n__length(X)
          length(cons(N,L)) -> U71(and(and(isNatList(activate(L)),n__isNatIListKind(activate(L)))
                                      ,n__and(n__isNat(N),n__isNatKind(N)))
                                  ,activate(L))
          length(nil()) -> 0()
          nil() -> n__nil()
          s(X) -> n__s(X)
          take(X1,X2) -> n__take(X1,X2)
          take(0(),IL) -> U81(and(isNatIList(IL),n__isNatIListKind(IL)))
          take(s(M),cons(N,IL)) -> U91(and(and(isNatIList(activate(IL)),n__isNatIListKind(activate(IL)))
                                          ,n__and(n__and(n__isNat(M),n__isNatKind(M))
                                                 ,n__and(n__isNat(N),n__isNatKind(N))))
                                      ,activate(IL)
                                      ,M
                                      ,N)
          zeros() -> cons(0(),n__zeros())
          zeros() -> n__zeros()
      - Signature:
          {0/0,U11/2,U12/1,U21/2,U22/1,U31/2,U32/1,U41/3,U42/2,U43/1,U51/3,U52/2,U53/1,U61/3,U62/2,U63/1,U71/2,U81/1
          ,U91/4,activate/1,and/2,cons/2,isNat/1,isNatIList/1,isNatIListKind/1,isNatKind/1,isNatList/1,length/1,nil/0
          ,s/1,take/2,zeros/0} / {n__0/0,n__and/2,n__cons/2,n__isNat/1,n__isNatIListKind/1,n__isNatKind/1,n__length/1
          ,n__nil/0,n__s/1,n__take/2,n__zeros/0,tt/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {0,U11,U12,U21,U22,U31,U32,U41,U42,U43,U51,U52,U53,U61,U62
          ,U63,U71,U81,U91,activate,and,cons,isNat,isNatIList,isNatIListKind,isNatKind,isNatList,length,nil,s,take
          ,zeros} and constructors {n__0,n__and,n__cons,n__isNat,n__isNatIListKind,n__isNatKind,n__length,n__nil,n__s
          ,n__take,n__zeros,tt}
  + Applied Processor:
      NaturalMI {miDimension = 3, miDegree = 3, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}
  + Details:
      Incompatible
MAYBE