* Step 1: Sum WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            U101(mark(X1),X2) -> mark(U101(X1,X2))
            U101(ok(X1),ok(X2)) -> ok(U101(X1,X2))
            U102(mark(X)) -> mark(U102(X))
            U102(ok(X)) -> ok(U102(X))
            U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
            U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
            U111(mark(X)) -> mark(U111(X))
            U111(ok(X)) -> ok(U111(X))
            U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
            U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
            U121(mark(X)) -> mark(U121(X))
            U121(ok(X)) -> ok(U121(X))
            U131(mark(X1),X2) -> mark(U131(X1,X2))
            U131(ok(X1),ok(X2)) -> ok(U131(X1,X2))
            U132(mark(X)) -> mark(U132(X))
            U132(ok(X)) -> ok(U132(X))
            U141(mark(X1),X2) -> mark(U141(X1,X2))
            U141(ok(X1),ok(X2)) -> ok(U141(X1,X2))
            U142(mark(X)) -> mark(U142(X))
            U142(ok(X)) -> ok(U142(X))
            U151(mark(X1),X2) -> mark(U151(X1,X2))
            U151(ok(X1),ok(X2)) -> ok(U151(X1,X2))
            U152(mark(X)) -> mark(U152(X))
            U152(ok(X)) -> ok(U152(X))
            U161(mark(X1),X2) -> mark(U161(X1,X2))
            U161(ok(X1),ok(X2)) -> ok(U161(X1,X2))
            U171(mark(X1),X2,X3) -> mark(U171(X1,X2,X3))
            U171(ok(X1),ok(X2),ok(X3)) -> ok(U171(X1,X2,X3))
            U172(mark(X1),X2,X3) -> mark(U172(X1,X2,X3))
            U172(ok(X1),ok(X2),ok(X3)) -> ok(U172(X1,X2,X3))
            U181(mark(X1),X2) -> mark(U181(X1,X2))
            U181(ok(X1),ok(X2)) -> ok(U181(X1,X2))
            U182(mark(X1),X2) -> mark(U182(X1,X2))
            U182(ok(X1),ok(X2)) -> ok(U182(X1,X2))
            U191(mark(X1),X2) -> mark(U191(X1,X2))
            U191(ok(X1),ok(X2)) -> ok(U191(X1,X2))
            U201(mark(X1),X2,X3,X4) -> mark(U201(X1,X2,X3,X4))
            U201(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U201(X1,X2,X3,X4))
            U202(mark(X1),X2,X3,X4) -> mark(U202(X1,X2,X3,X4))
            U202(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U202(X1,X2,X3,X4))
            U203(mark(X1),X2,X3,X4) -> mark(U203(X1,X2,X3,X4))
            U203(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U203(X1,X2,X3,X4))
            U204(mark(X1),X2) -> mark(U204(X1,X2))
            U204(ok(X1),ok(X2)) -> ok(U204(X1,X2))
            U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
            U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
            U211(mark(X1),X2) -> mark(U211(X1,X2))
            U211(ok(X1),ok(X2)) -> ok(U211(X1,X2))
            U212(mark(X1),X2) -> mark(U212(X1,X2))
            U212(ok(X1),ok(X2)) -> ok(U212(X1,X2))
            U22(mark(X1),X2) -> mark(U22(X1,X2))
            U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
            U221(mark(X1),X2,X3) -> mark(U221(X1,X2,X3))
            U221(ok(X1),ok(X2),ok(X3)) -> ok(U221(X1,X2,X3))
            U222(mark(X1),X2,X3) -> mark(U222(X1,X2,X3))
            U222(ok(X1),ok(X2),ok(X3)) -> ok(U222(X1,X2,X3))
            U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3))
            U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3))
            U32(mark(X1),X2) -> mark(U32(X1,X2))
            U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
            U41(mark(X1),X2) -> mark(U41(X1,X2))
            U41(ok(X1),ok(X2)) -> ok(U41(X1,X2))
            U42(mark(X)) -> mark(U42(X))
            U42(ok(X)) -> ok(U42(X))
            U51(mark(X1),X2) -> mark(U51(X1,X2))
            U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
            U52(mark(X)) -> mark(U52(X))
            U52(ok(X)) -> ok(U52(X))
            U61(mark(X)) -> mark(U61(X))
            U61(ok(X)) -> ok(U61(X))
            U71(mark(X)) -> mark(U71(X))
            U71(ok(X)) -> ok(U71(X))
            U81(mark(X)) -> mark(U81(X))
            U81(ok(X)) -> ok(U81(X))
            U91(mark(X)) -> mark(U91(X))
            U91(ok(X)) -> ok(U91(X))
            active(U101(X1,X2)) -> U101(active(X1),X2)
            active(U101(tt(),V2)) -> mark(U102(isLNat(V2)))
            active(U102(X)) -> U102(active(X))
            active(U102(tt())) -> mark(tt())
            active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
            active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
            active(U111(X)) -> U111(active(X))
            active(U111(tt())) -> mark(tt())
            active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
            active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
            active(U121(X)) -> U121(active(X))
            active(U121(tt())) -> mark(tt())
            active(U131(X1,X2)) -> U131(active(X1),X2)
            active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
            active(U132(X)) -> U132(active(X))
            active(U132(tt())) -> mark(tt())
            active(U141(X1,X2)) -> U141(active(X1),X2)
            active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
            active(U142(X)) -> U142(active(X))
            active(U142(tt())) -> mark(tt())
            active(U151(X1,X2)) -> U151(active(X1),X2)
            active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
            active(U152(X)) -> U152(active(X))
            active(U152(tt())) -> mark(tt())
            active(U161(X1,X2)) -> U161(active(X1),X2)
            active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
            active(U171(X1,X2,X3)) -> U171(active(X1),X2,X3)
            active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
            active(U172(X1,X2,X3)) -> U172(active(X1),X2,X3)
            active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
            active(U181(X1,X2)) -> U181(active(X1),X2)
            active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
            active(U182(X1,X2)) -> U182(active(X1),X2)
            active(U182(tt(),Y)) -> mark(Y)
            active(U191(X1,X2)) -> U191(active(X1),X2)
            active(U191(tt(),XS)) -> mark(pair(nil(),XS))
            active(U201(X1,X2,X3,X4)) -> U201(active(X1),X2,X3,X4)
            active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
            active(U202(X1,X2,X3,X4)) -> U202(active(X1),X2,X3,X4)
            active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
            active(U203(X1,X2,X3,X4)) -> U203(active(X1),X2,X3,X4)
            active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
            active(U204(X1,X2)) -> U204(active(X1),X2)
            active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
            active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
            active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
            active(U211(X1,X2)) -> U211(active(X1),X2)
            active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
            active(U212(X1,X2)) -> U212(active(X1),X2)
            active(U212(tt(),XS)) -> mark(XS)
            active(U22(X1,X2)) -> U22(active(X1),X2)
            active(U22(tt(),X)) -> mark(X)
            active(U221(X1,X2,X3)) -> U221(active(X1),X2,X3)
            active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
            active(U222(X1,X2,X3)) -> U222(active(X1),X2,X3)
            active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
            active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3)
            active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
            active(U32(X1,X2)) -> U32(active(X1),X2)
            active(U32(tt(),N)) -> mark(N)
            active(U41(X1,X2)) -> U41(active(X1),X2)
            active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
            active(U42(X)) -> U42(active(X))
            active(U42(tt())) -> mark(tt())
            active(U51(X1,X2)) -> U51(active(X1),X2)
            active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
            active(U52(X)) -> U52(active(X))
            active(U52(tt())) -> mark(tt())
            active(U61(X)) -> U61(active(X))
            active(U61(tt())) -> mark(tt())
            active(U71(X)) -> U71(active(X))
            active(U71(tt())) -> mark(tt())
            active(U81(X)) -> U81(active(X))
            active(U81(tt())) -> mark(tt())
            active(U91(X)) -> U91(active(X))
            active(U91(tt())) -> mark(tt())
            active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
            active(afterNth(X1,X2)) -> afterNth(X1,active(X2))
            active(afterNth(X1,X2)) -> afterNth(active(X1),X2)
            active(cons(X1,X2)) -> cons(active(X1),X2)
            active(fst(X)) -> fst(active(X))
            active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
            active(head(X)) -> head(active(X))
            active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
            active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
            active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
            active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
            active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
            active(isLNat(nil())) -> mark(tt())
            active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
            active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
            active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
            active(isNatural(0())) -> mark(tt())
            active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
            active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
            active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
            active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
            active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
            active(natsFrom(N)) -> mark(U161(isNatural(N),N))
            active(natsFrom(X)) -> natsFrom(active(X))
            active(pair(X1,X2)) -> pair(X1,active(X2))
            active(pair(X1,X2)) -> pair(active(X1),X2)
            active(s(X)) -> s(active(X))
            active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
            active(sel(X1,X2)) -> sel(X1,active(X2))
            active(sel(X1,X2)) -> sel(active(X1),X2)
            active(snd(X)) -> snd(active(X))
            active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
            active(splitAt(X1,X2)) -> splitAt(X1,active(X2))
            active(splitAt(X1,X2)) -> splitAt(active(X1),X2)
            active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
            active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
            active(tail(X)) -> tail(active(X))
            active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
            active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
            active(take(X1,X2)) -> take(X1,active(X2))
            active(take(X1,X2)) -> take(active(X1),X2)
            afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2))
            afterNth(mark(X1),X2) -> mark(afterNth(X1,X2))
            afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2))
            cons(mark(X1),X2) -> mark(cons(X1,X2))
            cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
            fst(mark(X)) -> mark(fst(X))
            fst(ok(X)) -> ok(fst(X))
            head(mark(X)) -> mark(head(X))
            head(ok(X)) -> ok(head(X))
            isLNat(ok(X)) -> ok(isLNat(X))
            isNatural(ok(X)) -> ok(isNatural(X))
            isPLNat(ok(X)) -> ok(isPLNat(X))
            natsFrom(mark(X)) -> mark(natsFrom(X))
            natsFrom(ok(X)) -> ok(natsFrom(X))
            pair(X1,mark(X2)) -> mark(pair(X1,X2))
            pair(mark(X1),X2) -> mark(pair(X1,X2))
            pair(ok(X1),ok(X2)) -> ok(pair(X1,X2))
            proper(0()) -> ok(0())
            proper(U101(X1,X2)) -> U101(proper(X1),proper(X2))
            proper(U102(X)) -> U102(proper(X))
            proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
            proper(U111(X)) -> U111(proper(X))
            proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
            proper(U121(X)) -> U121(proper(X))
            proper(U131(X1,X2)) -> U131(proper(X1),proper(X2))
            proper(U132(X)) -> U132(proper(X))
            proper(U141(X1,X2)) -> U141(proper(X1),proper(X2))
            proper(U142(X)) -> U142(proper(X))
            proper(U151(X1,X2)) -> U151(proper(X1),proper(X2))
            proper(U152(X)) -> U152(proper(X))
            proper(U161(X1,X2)) -> U161(proper(X1),proper(X2))
            proper(U171(X1,X2,X3)) -> U171(proper(X1),proper(X2),proper(X3))
            proper(U172(X1,X2,X3)) -> U172(proper(X1),proper(X2),proper(X3))
            proper(U181(X1,X2)) -> U181(proper(X1),proper(X2))
            proper(U182(X1,X2)) -> U182(proper(X1),proper(X2))
            proper(U191(X1,X2)) -> U191(proper(X1),proper(X2))
            proper(U201(X1,X2,X3,X4)) -> U201(proper(X1),proper(X2),proper(X3),proper(X4))
            proper(U202(X1,X2,X3,X4)) -> U202(proper(X1),proper(X2),proper(X3),proper(X4))
            proper(U203(X1,X2,X3,X4)) -> U203(proper(X1),proper(X2),proper(X3),proper(X4))
            proper(U204(X1,X2)) -> U204(proper(X1),proper(X2))
            proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
            proper(U211(X1,X2)) -> U211(proper(X1),proper(X2))
            proper(U212(X1,X2)) -> U212(proper(X1),proper(X2))
            proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
            proper(U221(X1,X2,X3)) -> U221(proper(X1),proper(X2),proper(X3))
            proper(U222(X1,X2,X3)) -> U222(proper(X1),proper(X2),proper(X3))
            proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3))
            proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
            proper(U41(X1,X2)) -> U41(proper(X1),proper(X2))
            proper(U42(X)) -> U42(proper(X))
            proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
            proper(U52(X)) -> U52(proper(X))
            proper(U61(X)) -> U61(proper(X))
            proper(U71(X)) -> U71(proper(X))
            proper(U81(X)) -> U81(proper(X))
            proper(U91(X)) -> U91(proper(X))
            proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2))
            proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
            proper(fst(X)) -> fst(proper(X))
            proper(head(X)) -> head(proper(X))
            proper(isLNat(X)) -> isLNat(proper(X))
            proper(isNatural(X)) -> isNatural(proper(X))
            proper(isPLNat(X)) -> isPLNat(proper(X))
            proper(natsFrom(X)) -> natsFrom(proper(X))
            proper(nil()) -> ok(nil())
            proper(pair(X1,X2)) -> pair(proper(X1),proper(X2))
            proper(s(X)) -> s(proper(X))
            proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
            proper(snd(X)) -> snd(proper(X))
            proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2))
            proper(tail(X)) -> tail(proper(X))
            proper(take(X1,X2)) -> take(proper(X1),proper(X2))
            proper(tt()) -> ok(tt())
            s(mark(X)) -> mark(s(X))
            s(ok(X)) -> ok(s(X))
            sel(X1,mark(X2)) -> mark(sel(X1,X2))
            sel(mark(X1),X2) -> mark(sel(X1,X2))
            sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
            snd(mark(X)) -> mark(snd(X))
            snd(ok(X)) -> ok(snd(X))
            splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2))
            splitAt(mark(X1),X2) -> mark(splitAt(X1,X2))
            splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2))
            tail(mark(X)) -> mark(tail(X))
            tail(ok(X)) -> ok(tail(X))
            take(X1,mark(X2)) -> mark(take(X1,X2))
            take(mark(X1),X2) -> mark(take(X1,X2))
            take(ok(X1),ok(X2)) -> ok(take(X1,X2))
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
        - Signature:
            {U101/2,U102/1,U11/3,U111/1,U12/3,U121/1,U131/2,U132/1,U141/2,U142/1,U151/2,U152/1,U161/2,U171/3,U172/3
            ,U181/2,U182/2,U191/2,U201/4,U202/4,U203/4,U204/2,U21/3,U211/2,U212/2,U22/2,U221/3,U222/3,U31/3,U32/2,U41/2
            ,U42/1,U51/2,U52/1,U61/1,U71/1,U81/1,U91/1,active/1,afterNth/2,cons/2,fst/1,head/1,isLNat/1,isNatural/1
            ,isPLNat/1,natsFrom/1,pair/2,proper/1,s/1,sel/2,snd/1,splitAt/2,tail/1,take/2,top/1} / {0/0,mark/1,nil/0
            ,ok/1,tt/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {U101,U102,U11,U111,U12,U121,U131,U132,U141,U142,U151,U152
            ,U161,U171,U172,U181,U182,U191,U201,U202,U203,U204,U21,U211,U212,U22,U221,U222,U31,U32,U41,U42,U51,U52,U61
            ,U71,U81,U91,active,afterNth,cons,fst,head,isLNat,isNatural,isPLNat,natsFrom,pair,proper,s,sel,snd,splitAt
            ,tail,take,top} and constructors {0,mark,nil,ok,tt}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            U101(mark(X1),X2) -> mark(U101(X1,X2))
            U101(ok(X1),ok(X2)) -> ok(U101(X1,X2))
            U102(mark(X)) -> mark(U102(X))
            U102(ok(X)) -> ok(U102(X))
            U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
            U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
            U111(mark(X)) -> mark(U111(X))
            U111(ok(X)) -> ok(U111(X))
            U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
            U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
            U121(mark(X)) -> mark(U121(X))
            U121(ok(X)) -> ok(U121(X))
            U131(mark(X1),X2) -> mark(U131(X1,X2))
            U131(ok(X1),ok(X2)) -> ok(U131(X1,X2))
            U132(mark(X)) -> mark(U132(X))
            U132(ok(X)) -> ok(U132(X))
            U141(mark(X1),X2) -> mark(U141(X1,X2))
            U141(ok(X1),ok(X2)) -> ok(U141(X1,X2))
            U142(mark(X)) -> mark(U142(X))
            U142(ok(X)) -> ok(U142(X))
            U151(mark(X1),X2) -> mark(U151(X1,X2))
            U151(ok(X1),ok(X2)) -> ok(U151(X1,X2))
            U152(mark(X)) -> mark(U152(X))
            U152(ok(X)) -> ok(U152(X))
            U161(mark(X1),X2) -> mark(U161(X1,X2))
            U161(ok(X1),ok(X2)) -> ok(U161(X1,X2))
            U171(mark(X1),X2,X3) -> mark(U171(X1,X2,X3))
            U171(ok(X1),ok(X2),ok(X3)) -> ok(U171(X1,X2,X3))
            U172(mark(X1),X2,X3) -> mark(U172(X1,X2,X3))
            U172(ok(X1),ok(X2),ok(X3)) -> ok(U172(X1,X2,X3))
            U181(mark(X1),X2) -> mark(U181(X1,X2))
            U181(ok(X1),ok(X2)) -> ok(U181(X1,X2))
            U182(mark(X1),X2) -> mark(U182(X1,X2))
            U182(ok(X1),ok(X2)) -> ok(U182(X1,X2))
            U191(mark(X1),X2) -> mark(U191(X1,X2))
            U191(ok(X1),ok(X2)) -> ok(U191(X1,X2))
            U201(mark(X1),X2,X3,X4) -> mark(U201(X1,X2,X3,X4))
            U201(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U201(X1,X2,X3,X4))
            U202(mark(X1),X2,X3,X4) -> mark(U202(X1,X2,X3,X4))
            U202(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U202(X1,X2,X3,X4))
            U203(mark(X1),X2,X3,X4) -> mark(U203(X1,X2,X3,X4))
            U203(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U203(X1,X2,X3,X4))
            U204(mark(X1),X2) -> mark(U204(X1,X2))
            U204(ok(X1),ok(X2)) -> ok(U204(X1,X2))
            U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
            U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
            U211(mark(X1),X2) -> mark(U211(X1,X2))
            U211(ok(X1),ok(X2)) -> ok(U211(X1,X2))
            U212(mark(X1),X2) -> mark(U212(X1,X2))
            U212(ok(X1),ok(X2)) -> ok(U212(X1,X2))
            U22(mark(X1),X2) -> mark(U22(X1,X2))
            U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
            U221(mark(X1),X2,X3) -> mark(U221(X1,X2,X3))
            U221(ok(X1),ok(X2),ok(X3)) -> ok(U221(X1,X2,X3))
            U222(mark(X1),X2,X3) -> mark(U222(X1,X2,X3))
            U222(ok(X1),ok(X2),ok(X3)) -> ok(U222(X1,X2,X3))
            U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3))
            U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3))
            U32(mark(X1),X2) -> mark(U32(X1,X2))
            U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
            U41(mark(X1),X2) -> mark(U41(X1,X2))
            U41(ok(X1),ok(X2)) -> ok(U41(X1,X2))
            U42(mark(X)) -> mark(U42(X))
            U42(ok(X)) -> ok(U42(X))
            U51(mark(X1),X2) -> mark(U51(X1,X2))
            U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
            U52(mark(X)) -> mark(U52(X))
            U52(ok(X)) -> ok(U52(X))
            U61(mark(X)) -> mark(U61(X))
            U61(ok(X)) -> ok(U61(X))
            U71(mark(X)) -> mark(U71(X))
            U71(ok(X)) -> ok(U71(X))
            U81(mark(X)) -> mark(U81(X))
            U81(ok(X)) -> ok(U81(X))
            U91(mark(X)) -> mark(U91(X))
            U91(ok(X)) -> ok(U91(X))
            active(U101(X1,X2)) -> U101(active(X1),X2)
            active(U101(tt(),V2)) -> mark(U102(isLNat(V2)))
            active(U102(X)) -> U102(active(X))
            active(U102(tt())) -> mark(tt())
            active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
            active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
            active(U111(X)) -> U111(active(X))
            active(U111(tt())) -> mark(tt())
            active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
            active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
            active(U121(X)) -> U121(active(X))
            active(U121(tt())) -> mark(tt())
            active(U131(X1,X2)) -> U131(active(X1),X2)
            active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
            active(U132(X)) -> U132(active(X))
            active(U132(tt())) -> mark(tt())
            active(U141(X1,X2)) -> U141(active(X1),X2)
            active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
            active(U142(X)) -> U142(active(X))
            active(U142(tt())) -> mark(tt())
            active(U151(X1,X2)) -> U151(active(X1),X2)
            active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
            active(U152(X)) -> U152(active(X))
            active(U152(tt())) -> mark(tt())
            active(U161(X1,X2)) -> U161(active(X1),X2)
            active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
            active(U171(X1,X2,X3)) -> U171(active(X1),X2,X3)
            active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
            active(U172(X1,X2,X3)) -> U172(active(X1),X2,X3)
            active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
            active(U181(X1,X2)) -> U181(active(X1),X2)
            active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
            active(U182(X1,X2)) -> U182(active(X1),X2)
            active(U182(tt(),Y)) -> mark(Y)
            active(U191(X1,X2)) -> U191(active(X1),X2)
            active(U191(tt(),XS)) -> mark(pair(nil(),XS))
            active(U201(X1,X2,X3,X4)) -> U201(active(X1),X2,X3,X4)
            active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
            active(U202(X1,X2,X3,X4)) -> U202(active(X1),X2,X3,X4)
            active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
            active(U203(X1,X2,X3,X4)) -> U203(active(X1),X2,X3,X4)
            active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
            active(U204(X1,X2)) -> U204(active(X1),X2)
            active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
            active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
            active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
            active(U211(X1,X2)) -> U211(active(X1),X2)
            active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
            active(U212(X1,X2)) -> U212(active(X1),X2)
            active(U212(tt(),XS)) -> mark(XS)
            active(U22(X1,X2)) -> U22(active(X1),X2)
            active(U22(tt(),X)) -> mark(X)
            active(U221(X1,X2,X3)) -> U221(active(X1),X2,X3)
            active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
            active(U222(X1,X2,X3)) -> U222(active(X1),X2,X3)
            active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
            active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3)
            active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
            active(U32(X1,X2)) -> U32(active(X1),X2)
            active(U32(tt(),N)) -> mark(N)
            active(U41(X1,X2)) -> U41(active(X1),X2)
            active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
            active(U42(X)) -> U42(active(X))
            active(U42(tt())) -> mark(tt())
            active(U51(X1,X2)) -> U51(active(X1),X2)
            active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
            active(U52(X)) -> U52(active(X))
            active(U52(tt())) -> mark(tt())
            active(U61(X)) -> U61(active(X))
            active(U61(tt())) -> mark(tt())
            active(U71(X)) -> U71(active(X))
            active(U71(tt())) -> mark(tt())
            active(U81(X)) -> U81(active(X))
            active(U81(tt())) -> mark(tt())
            active(U91(X)) -> U91(active(X))
            active(U91(tt())) -> mark(tt())
            active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
            active(afterNth(X1,X2)) -> afterNth(X1,active(X2))
            active(afterNth(X1,X2)) -> afterNth(active(X1),X2)
            active(cons(X1,X2)) -> cons(active(X1),X2)
            active(fst(X)) -> fst(active(X))
            active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
            active(head(X)) -> head(active(X))
            active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
            active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
            active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
            active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
            active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
            active(isLNat(nil())) -> mark(tt())
            active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
            active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
            active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
            active(isNatural(0())) -> mark(tt())
            active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
            active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
            active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
            active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
            active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
            active(natsFrom(N)) -> mark(U161(isNatural(N),N))
            active(natsFrom(X)) -> natsFrom(active(X))
            active(pair(X1,X2)) -> pair(X1,active(X2))
            active(pair(X1,X2)) -> pair(active(X1),X2)
            active(s(X)) -> s(active(X))
            active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
            active(sel(X1,X2)) -> sel(X1,active(X2))
            active(sel(X1,X2)) -> sel(active(X1),X2)
            active(snd(X)) -> snd(active(X))
            active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
            active(splitAt(X1,X2)) -> splitAt(X1,active(X2))
            active(splitAt(X1,X2)) -> splitAt(active(X1),X2)
            active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
            active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
            active(tail(X)) -> tail(active(X))
            active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
            active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
            active(take(X1,X2)) -> take(X1,active(X2))
            active(take(X1,X2)) -> take(active(X1),X2)
            afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2))
            afterNth(mark(X1),X2) -> mark(afterNth(X1,X2))
            afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2))
            cons(mark(X1),X2) -> mark(cons(X1,X2))
            cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
            fst(mark(X)) -> mark(fst(X))
            fst(ok(X)) -> ok(fst(X))
            head(mark(X)) -> mark(head(X))
            head(ok(X)) -> ok(head(X))
            isLNat(ok(X)) -> ok(isLNat(X))
            isNatural(ok(X)) -> ok(isNatural(X))
            isPLNat(ok(X)) -> ok(isPLNat(X))
            natsFrom(mark(X)) -> mark(natsFrom(X))
            natsFrom(ok(X)) -> ok(natsFrom(X))
            pair(X1,mark(X2)) -> mark(pair(X1,X2))
            pair(mark(X1),X2) -> mark(pair(X1,X2))
            pair(ok(X1),ok(X2)) -> ok(pair(X1,X2))
            proper(0()) -> ok(0())
            proper(U101(X1,X2)) -> U101(proper(X1),proper(X2))
            proper(U102(X)) -> U102(proper(X))
            proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
            proper(U111(X)) -> U111(proper(X))
            proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
            proper(U121(X)) -> U121(proper(X))
            proper(U131(X1,X2)) -> U131(proper(X1),proper(X2))
            proper(U132(X)) -> U132(proper(X))
            proper(U141(X1,X2)) -> U141(proper(X1),proper(X2))
            proper(U142(X)) -> U142(proper(X))
            proper(U151(X1,X2)) -> U151(proper(X1),proper(X2))
            proper(U152(X)) -> U152(proper(X))
            proper(U161(X1,X2)) -> U161(proper(X1),proper(X2))
            proper(U171(X1,X2,X3)) -> U171(proper(X1),proper(X2),proper(X3))
            proper(U172(X1,X2,X3)) -> U172(proper(X1),proper(X2),proper(X3))
            proper(U181(X1,X2)) -> U181(proper(X1),proper(X2))
            proper(U182(X1,X2)) -> U182(proper(X1),proper(X2))
            proper(U191(X1,X2)) -> U191(proper(X1),proper(X2))
            proper(U201(X1,X2,X3,X4)) -> U201(proper(X1),proper(X2),proper(X3),proper(X4))
            proper(U202(X1,X2,X3,X4)) -> U202(proper(X1),proper(X2),proper(X3),proper(X4))
            proper(U203(X1,X2,X3,X4)) -> U203(proper(X1),proper(X2),proper(X3),proper(X4))
            proper(U204(X1,X2)) -> U204(proper(X1),proper(X2))
            proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
            proper(U211(X1,X2)) -> U211(proper(X1),proper(X2))
            proper(U212(X1,X2)) -> U212(proper(X1),proper(X2))
            proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
            proper(U221(X1,X2,X3)) -> U221(proper(X1),proper(X2),proper(X3))
            proper(U222(X1,X2,X3)) -> U222(proper(X1),proper(X2),proper(X3))
            proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3))
            proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
            proper(U41(X1,X2)) -> U41(proper(X1),proper(X2))
            proper(U42(X)) -> U42(proper(X))
            proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
            proper(U52(X)) -> U52(proper(X))
            proper(U61(X)) -> U61(proper(X))
            proper(U71(X)) -> U71(proper(X))
            proper(U81(X)) -> U81(proper(X))
            proper(U91(X)) -> U91(proper(X))
            proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2))
            proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
            proper(fst(X)) -> fst(proper(X))
            proper(head(X)) -> head(proper(X))
            proper(isLNat(X)) -> isLNat(proper(X))
            proper(isNatural(X)) -> isNatural(proper(X))
            proper(isPLNat(X)) -> isPLNat(proper(X))
            proper(natsFrom(X)) -> natsFrom(proper(X))
            proper(nil()) -> ok(nil())
            proper(pair(X1,X2)) -> pair(proper(X1),proper(X2))
            proper(s(X)) -> s(proper(X))
            proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
            proper(snd(X)) -> snd(proper(X))
            proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2))
            proper(tail(X)) -> tail(proper(X))
            proper(take(X1,X2)) -> take(proper(X1),proper(X2))
            proper(tt()) -> ok(tt())
            s(mark(X)) -> mark(s(X))
            s(ok(X)) -> ok(s(X))
            sel(X1,mark(X2)) -> mark(sel(X1,X2))
            sel(mark(X1),X2) -> mark(sel(X1,X2))
            sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
            snd(mark(X)) -> mark(snd(X))
            snd(ok(X)) -> ok(snd(X))
            splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2))
            splitAt(mark(X1),X2) -> mark(splitAt(X1,X2))
            splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2))
            tail(mark(X)) -> mark(tail(X))
            tail(ok(X)) -> ok(tail(X))
            take(X1,mark(X2)) -> mark(take(X1,X2))
            take(mark(X1),X2) -> mark(take(X1,X2))
            take(ok(X1),ok(X2)) -> ok(take(X1,X2))
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
        - Signature:
            {U101/2,U102/1,U11/3,U111/1,U12/3,U121/1,U131/2,U132/1,U141/2,U142/1,U151/2,U152/1,U161/2,U171/3,U172/3
            ,U181/2,U182/2,U191/2,U201/4,U202/4,U203/4,U204/2,U21/3,U211/2,U212/2,U22/2,U221/3,U222/3,U31/3,U32/2,U41/2
            ,U42/1,U51/2,U52/1,U61/1,U71/1,U81/1,U91/1,active/1,afterNth/2,cons/2,fst/1,head/1,isLNat/1,isNatural/1
            ,isPLNat/1,natsFrom/1,pair/2,proper/1,s/1,sel/2,snd/1,splitAt/2,tail/1,take/2,top/1} / {0/0,mark/1,nil/0
            ,ok/1,tt/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {U101,U102,U11,U111,U12,U121,U131,U132,U141,U142,U151,U152
            ,U161,U171,U172,U181,U182,U191,U201,U202,U203,U204,U21,U211,U212,U22,U221,U222,U31,U32,U41,U42,U51,U52,U61
            ,U71,U81,U91,active,afterNth,cons,fst,head,isLNat,isNatural,isPLNat,natsFrom,pair,proper,s,sel,snd,splitAt
            ,tail,take,top} and constructors {0,mark,nil,ok,tt}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          U101(x,y){x -> mark(x)} =
            U101(mark(x),y) ->^+ mark(U101(x,y))
              = C[U101(x,y) = U101(x,y){}]

WORST_CASE(Omega(n^1),?)