* Step 1: Sum WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            0() -> n__0()
            U101(tt(),V1,V2) -> U102(isNatKind(activate(V1)),activate(V1),activate(V2))
            U102(tt(),V1,V2) -> U103(isNatIListKind(activate(V2)),activate(V1),activate(V2))
            U103(tt(),V1,V2) -> U104(isNatIListKind(activate(V2)),activate(V1),activate(V2))
            U104(tt(),V1,V2) -> U105(isNat(activate(V1)),activate(V2))
            U105(tt(),V2) -> U106(isNatIList(activate(V2)))
            U106(tt()) -> tt()
            U11(tt(),V1) -> U12(isNatIListKind(activate(V1)),activate(V1))
            U111(tt(),L,N) -> U112(isNatIListKind(activate(L)),activate(L),activate(N))
            U112(tt(),L,N) -> U113(isNat(activate(N)),activate(L),activate(N))
            U113(tt(),L,N) -> U114(isNatKind(activate(N)),activate(L))
            U114(tt(),L) -> s(length(activate(L)))
            U12(tt(),V1) -> U13(isNatList(activate(V1)))
            U121(tt(),IL) -> U122(isNatIListKind(activate(IL)))
            U122(tt()) -> nil()
            U13(tt()) -> tt()
            U131(tt(),IL,M,N) -> U132(isNatIListKind(activate(IL)),activate(IL),activate(M),activate(N))
            U132(tt(),IL,M,N) -> U133(isNat(activate(M)),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)))
            U21(tt(),V1) -> U22(isNatKind(activate(V1)),activate(V1))
            U22(tt(),V1) -> U23(isNat(activate(V1)))
            U23(tt()) -> tt()
            U31(tt(),V) -> U32(isNatIListKind(activate(V)),activate(V))
            U32(tt(),V) -> U33(isNatList(activate(V)))
            U33(tt()) -> tt()
            U41(tt(),V1,V2) -> U42(isNatKind(activate(V1)),activate(V1),activate(V2))
            U42(tt(),V1,V2) -> U43(isNatIListKind(activate(V2)),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()
            U51(tt(),V2) -> U52(isNatIListKind(activate(V2)))
            U52(tt()) -> tt()
            U61(tt(),V2) -> U62(isNatIListKind(activate(V2)))
            U62(tt()) -> tt()
            U71(tt()) -> tt()
            U81(tt()) -> tt()
            U91(tt(),V1,V2) -> U92(isNatKind(activate(V1)),activate(V1),activate(V2))
            U92(tt(),V1,V2) -> U93(isNatIListKind(activate(V2)),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()
            activate(X) -> X
            activate(n__0()) -> 0()
            activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
            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()
            cons(X1,X2) -> n__cons(X1,X2)
            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(isNatKind(activate(V1)),activate(V1),activate(V2))
            isNatIList(n__zeros()) -> tt()
            isNatIListKind(n__cons(V1,V2)) -> U51(isNatKind(activate(V1)),activate(V2))
            isNatIListKind(n__nil()) -> tt()
            isNatIListKind(n__take(V1,V2)) -> U61(isNatKind(activate(V1)),activate(V2))
            isNatIListKind(n__zeros()) -> tt()
            isNatKind(n__0()) -> tt()
            isNatKind(n__length(V1)) -> U71(isNatIListKind(activate(V1)))
            isNatKind(n__s(V1)) -> U81(isNatKind(activate(V1)))
            isNatList(n__cons(V1,V2)) -> U91(isNatKind(activate(V1)),activate(V1),activate(V2))
            isNatList(n__nil()) -> tt()
            isNatList(n__take(V1,V2)) -> U101(isNatKind(activate(V1)),activate(V1),activate(V2))
            length(X) -> n__length(X)
            length(cons(N,L)) -> U111(isNatList(activate(L)),activate(L),N)
            length(nil()) -> 0()
            nil() -> n__nil()
            s(X) -> n__s(X)
            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)
            zeros() -> cons(0(),n__zeros())
            zeros() -> n__zeros()
        - Signature:
            {0/0,U101/3,U102/3,U103/3,U104/3,U105/2,U106/1,U11/2,U111/3,U112/3,U113/3,U114/2,U12/2,U121/2,U122/1,U13/1
            ,U131/4,U132/4,U133/4,U134/4,U135/4,U136/4,U21/2,U22/2,U23/1,U31/2,U32/2,U33/1,U41/3,U42/3,U43/3,U44/3,U45/2
            ,U46/1,U51/2,U52/1,U61/2,U62/1,U71/1,U81/1,U91/3,U92/3,U93/3,U94/3,U95/2,U96/1,activate/1,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__cons/2,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,U101,U102,U103,U104,U105,U106,U11,U111,U112,U113,U114
            ,U12,U121,U122,U13,U131,U132,U133,U134,U135,U136,U21,U22,U23,U31,U32,U33,U41,U42,U43,U44,U45,U46,U51,U52,U61
            ,U62,U71,U81,U91,U92,U93,U94,U95,U96,activate,cons,isNat,isNatIList,isNatIListKind,isNatKind,isNatList
            ,length,nil,s,take,zeros} and constructors {n__0,n__cons,n__length,n__nil,n__s,n__take,n__zeros,tt}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            0() -> n__0()
            U101(tt(),V1,V2) -> U102(isNatKind(activate(V1)),activate(V1),activate(V2))
            U102(tt(),V1,V2) -> U103(isNatIListKind(activate(V2)),activate(V1),activate(V2))
            U103(tt(),V1,V2) -> U104(isNatIListKind(activate(V2)),activate(V1),activate(V2))
            U104(tt(),V1,V2) -> U105(isNat(activate(V1)),activate(V2))
            U105(tt(),V2) -> U106(isNatIList(activate(V2)))
            U106(tt()) -> tt()
            U11(tt(),V1) -> U12(isNatIListKind(activate(V1)),activate(V1))
            U111(tt(),L,N) -> U112(isNatIListKind(activate(L)),activate(L),activate(N))
            U112(tt(),L,N) -> U113(isNat(activate(N)),activate(L),activate(N))
            U113(tt(),L,N) -> U114(isNatKind(activate(N)),activate(L))
            U114(tt(),L) -> s(length(activate(L)))
            U12(tt(),V1) -> U13(isNatList(activate(V1)))
            U121(tt(),IL) -> U122(isNatIListKind(activate(IL)))
            U122(tt()) -> nil()
            U13(tt()) -> tt()
            U131(tt(),IL,M,N) -> U132(isNatIListKind(activate(IL)),activate(IL),activate(M),activate(N))
            U132(tt(),IL,M,N) -> U133(isNat(activate(M)),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)))
            U21(tt(),V1) -> U22(isNatKind(activate(V1)),activate(V1))
            U22(tt(),V1) -> U23(isNat(activate(V1)))
            U23(tt()) -> tt()
            U31(tt(),V) -> U32(isNatIListKind(activate(V)),activate(V))
            U32(tt(),V) -> U33(isNatList(activate(V)))
            U33(tt()) -> tt()
            U41(tt(),V1,V2) -> U42(isNatKind(activate(V1)),activate(V1),activate(V2))
            U42(tt(),V1,V2) -> U43(isNatIListKind(activate(V2)),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()
            U51(tt(),V2) -> U52(isNatIListKind(activate(V2)))
            U52(tt()) -> tt()
            U61(tt(),V2) -> U62(isNatIListKind(activate(V2)))
            U62(tt()) -> tt()
            U71(tt()) -> tt()
            U81(tt()) -> tt()
            U91(tt(),V1,V2) -> U92(isNatKind(activate(V1)),activate(V1),activate(V2))
            U92(tt(),V1,V2) -> U93(isNatIListKind(activate(V2)),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()
            activate(X) -> X
            activate(n__0()) -> 0()
            activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
            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()
            cons(X1,X2) -> n__cons(X1,X2)
            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(isNatKind(activate(V1)),activate(V1),activate(V2))
            isNatIList(n__zeros()) -> tt()
            isNatIListKind(n__cons(V1,V2)) -> U51(isNatKind(activate(V1)),activate(V2))
            isNatIListKind(n__nil()) -> tt()
            isNatIListKind(n__take(V1,V2)) -> U61(isNatKind(activate(V1)),activate(V2))
            isNatIListKind(n__zeros()) -> tt()
            isNatKind(n__0()) -> tt()
            isNatKind(n__length(V1)) -> U71(isNatIListKind(activate(V1)))
            isNatKind(n__s(V1)) -> U81(isNatKind(activate(V1)))
            isNatList(n__cons(V1,V2)) -> U91(isNatKind(activate(V1)),activate(V1),activate(V2))
            isNatList(n__nil()) -> tt()
            isNatList(n__take(V1,V2)) -> U101(isNatKind(activate(V1)),activate(V1),activate(V2))
            length(X) -> n__length(X)
            length(cons(N,L)) -> U111(isNatList(activate(L)),activate(L),N)
            length(nil()) -> 0()
            nil() -> n__nil()
            s(X) -> n__s(X)
            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)
            zeros() -> cons(0(),n__zeros())
            zeros() -> n__zeros()
        - Signature:
            {0/0,U101/3,U102/3,U103/3,U104/3,U105/2,U106/1,U11/2,U111/3,U112/3,U113/3,U114/2,U12/2,U121/2,U122/1,U13/1
            ,U131/4,U132/4,U133/4,U134/4,U135/4,U136/4,U21/2,U22/2,U23/1,U31/2,U32/2,U33/1,U41/3,U42/3,U43/3,U44/3,U45/2
            ,U46/1,U51/2,U52/1,U61/2,U62/1,U71/1,U81/1,U91/3,U92/3,U93/3,U94/3,U95/2,U96/1,activate/1,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__cons/2,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,U101,U102,U103,U104,U105,U106,U11,U111,U112,U113,U114
            ,U12,U121,U122,U13,U131,U132,U133,U134,U135,U136,U21,U22,U23,U31,U32,U33,U41,U42,U43,U44,U45,U46,U51,U52,U61
            ,U62,U71,U81,U91,U92,U93,U94,U95,U96,activate,cons,isNat,isNatIList,isNatIListKind,isNatKind,isNatList
            ,length,nil,s,take,zeros} and constructors {n__0,n__cons,n__length,n__nil,n__s,n__take,n__zeros,tt}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          activate(x){x -> n__cons(x,y)} =
            activate(n__cons(x,y)) ->^+ cons(activate(x),y)
              = C[activate(x) = activate(x){}]

WORST_CASE(Omega(n^1),?)