* Step 1: Sum WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            U11(mark(X1),X2,X3,X4) -> mark(U11(X1,X2,X3,X4))
            U11(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U11(X1,X2,X3,X4))
            U12(mark(X1),X2) -> mark(U12(X1,X2))
            U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
            active(U11(X1,X2,X3,X4)) -> U11(active(X1),X2,X3,X4)
            active(U11(tt(),N,X,XS)) -> mark(U12(splitAt(N,XS),X))
            active(U12(X1,X2)) -> U12(active(X1),X2)
            active(U12(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
            active(afterNth(N,XS)) -> mark(snd(splitAt(N,XS)))
            active(afterNth(X1,X2)) -> afterNth(X1,active(X2))
            active(afterNth(X1,X2)) -> afterNth(active(X1),X2)
            active(and(X1,X2)) -> and(active(X1),X2)
            active(and(tt(),X)) -> mark(X)
            active(cons(X1,X2)) -> cons(active(X1),X2)
            active(fst(X)) -> fst(active(X))
            active(fst(pair(X,Y))) -> mark(X)
            active(head(X)) -> head(active(X))
            active(head(cons(N,XS))) -> mark(N)
            active(natsFrom(N)) -> mark(cons(N,natsFrom(s(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(head(afterNth(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(Y)
            active(splitAt(X1,X2)) -> splitAt(X1,active(X2))
            active(splitAt(X1,X2)) -> splitAt(active(X1),X2)
            active(splitAt(0(),XS)) -> mark(pair(nil(),XS))
            active(splitAt(s(N),cons(X,XS))) -> mark(U11(tt(),N,X,XS))
            active(tail(X)) -> tail(active(X))
            active(tail(cons(N,XS))) -> mark(XS)
            active(take(N,XS)) -> mark(fst(splitAt(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))
            and(mark(X1),X2) -> mark(and(X1,X2))
            and(ok(X1),ok(X2)) -> ok(and(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))
            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(U11(X1,X2,X3,X4)) -> U11(proper(X1),proper(X2),proper(X3),proper(X4))
            proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
            proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2))
            proper(and(X1,X2)) -> and(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(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:
            {U11/4,U12/2,active/1,afterNth/2,and/2,cons/2,fst/1,head/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 {U11,U12,active,afterNth,and,cons,fst,head,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:
            U11(mark(X1),X2,X3,X4) -> mark(U11(X1,X2,X3,X4))
            U11(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U11(X1,X2,X3,X4))
            U12(mark(X1),X2) -> mark(U12(X1,X2))
            U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
            active(U11(X1,X2,X3,X4)) -> U11(active(X1),X2,X3,X4)
            active(U11(tt(),N,X,XS)) -> mark(U12(splitAt(N,XS),X))
            active(U12(X1,X2)) -> U12(active(X1),X2)
            active(U12(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
            active(afterNth(N,XS)) -> mark(snd(splitAt(N,XS)))
            active(afterNth(X1,X2)) -> afterNth(X1,active(X2))
            active(afterNth(X1,X2)) -> afterNth(active(X1),X2)
            active(and(X1,X2)) -> and(active(X1),X2)
            active(and(tt(),X)) -> mark(X)
            active(cons(X1,X2)) -> cons(active(X1),X2)
            active(fst(X)) -> fst(active(X))
            active(fst(pair(X,Y))) -> mark(X)
            active(head(X)) -> head(active(X))
            active(head(cons(N,XS))) -> mark(N)
            active(natsFrom(N)) -> mark(cons(N,natsFrom(s(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(head(afterNth(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(Y)
            active(splitAt(X1,X2)) -> splitAt(X1,active(X2))
            active(splitAt(X1,X2)) -> splitAt(active(X1),X2)
            active(splitAt(0(),XS)) -> mark(pair(nil(),XS))
            active(splitAt(s(N),cons(X,XS))) -> mark(U11(tt(),N,X,XS))
            active(tail(X)) -> tail(active(X))
            active(tail(cons(N,XS))) -> mark(XS)
            active(take(N,XS)) -> mark(fst(splitAt(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))
            and(mark(X1),X2) -> mark(and(X1,X2))
            and(ok(X1),ok(X2)) -> ok(and(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))
            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(U11(X1,X2,X3,X4)) -> U11(proper(X1),proper(X2),proper(X3),proper(X4))
            proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
            proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2))
            proper(and(X1,X2)) -> and(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(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:
            {U11/4,U12/2,active/1,afterNth/2,and/2,cons/2,fst/1,head/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 {U11,U12,active,afterNth,and,cons,fst,head,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:
          U11(x,y,z,u){x -> mark(x)} =
            U11(mark(x),y,z,u) ->^+ mark(U11(x,y,z,u))
              = C[U11(x,y,z,u) = U11(x,y,z,u){}]

WORST_CASE(Omega(n^1),?)