* Step 1: Sum WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            U11(mark(X1),X2) -> mark(U11(X1,X2))
            U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
            U21(mark(X)) -> mark(U21(X))
            U21(ok(X)) -> ok(U21(X))
            U31(mark(X1),X2,X3,X4) -> mark(U31(X1,X2,X3,X4))
            U31(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U31(X1,X2,X3,X4))
            active(U11(X1,X2)) -> U11(active(X1),X2)
            active(U11(tt(),L)) -> mark(s(length(L)))
            active(U21(X)) -> U21(active(X))
            active(U21(tt())) -> mark(nil())
            active(U31(X1,X2,X3,X4)) -> U31(active(X1),X2,X3,X4)
            active(U31(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
            active(and(X1,X2)) -> and(active(X1),X2)
            active(and(tt(),X)) -> mark(X)
            active(cons(X1,X2)) -> cons(active(X1),X2)
            active(isNat(0())) -> mark(tt())
            active(isNat(length(V1))) -> mark(isNatList(V1))
            active(isNat(s(V1))) -> mark(isNat(V1))
            active(isNatIList(V)) -> mark(isNatList(V))
            active(isNatIList(cons(V1,V2))) -> mark(and(isNat(V1),isNatIList(V2)))
            active(isNatIList(zeros())) -> mark(tt())
            active(isNatList(cons(V1,V2))) -> mark(and(isNat(V1),isNatList(V2)))
            active(isNatList(nil())) -> mark(tt())
            active(isNatList(take(V1,V2))) -> mark(and(isNat(V1),isNatIList(V2)))
            active(length(X)) -> length(active(X))
            active(length(cons(N,L))) -> mark(U11(and(isNatList(L),isNat(N)),L))
            active(length(nil())) -> mark(0())
            active(s(X)) -> s(active(X))
            active(take(X1,X2)) -> take(X1,active(X2))
            active(take(X1,X2)) -> take(active(X1),X2)
            active(take(0(),IL)) -> mark(U21(isNatIList(IL)))
            active(take(s(M),cons(N,IL))) -> mark(U31(and(isNatIList(IL),and(isNat(M),isNat(N))),IL,M,N))
            active(zeros()) -> mark(cons(0(),zeros()))
            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))
            isNat(ok(X)) -> ok(isNat(X))
            isNatIList(ok(X)) -> ok(isNatIList(X))
            isNatList(ok(X)) -> ok(isNatList(X))
            length(mark(X)) -> mark(length(X))
            length(ok(X)) -> ok(length(X))
            proper(0()) -> ok(0())
            proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
            proper(U21(X)) -> U21(proper(X))
            proper(U31(X1,X2,X3,X4)) -> U31(proper(X1),proper(X2),proper(X3),proper(X4))
            proper(and(X1,X2)) -> and(proper(X1),proper(X2))
            proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
            proper(isNat(X)) -> isNat(proper(X))
            proper(isNatIList(X)) -> isNatIList(proper(X))
            proper(isNatList(X)) -> isNatList(proper(X))
            proper(length(X)) -> length(proper(X))
            proper(nil()) -> ok(nil())
            proper(s(X)) -> s(proper(X))
            proper(take(X1,X2)) -> take(proper(X1),proper(X2))
            proper(tt()) -> ok(tt())
            proper(zeros()) -> ok(zeros())
            s(mark(X)) -> mark(s(X))
            s(ok(X)) -> ok(s(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:
            {U11/2,U21/1,U31/4,active/1,and/2,cons/2,isNat/1,isNatIList/1,isNatList/1,length/1,proper/1,s/1,take/2
            ,top/1} / {0/0,mark/1,nil/0,ok/1,tt/0,zeros/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {U11,U21,U31,active,and,cons,isNat,isNatIList,isNatList
            ,length,proper,s,take,top} and constructors {0,mark,nil,ok,tt,zeros}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            U11(mark(X1),X2) -> mark(U11(X1,X2))
            U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
            U21(mark(X)) -> mark(U21(X))
            U21(ok(X)) -> ok(U21(X))
            U31(mark(X1),X2,X3,X4) -> mark(U31(X1,X2,X3,X4))
            U31(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U31(X1,X2,X3,X4))
            active(U11(X1,X2)) -> U11(active(X1),X2)
            active(U11(tt(),L)) -> mark(s(length(L)))
            active(U21(X)) -> U21(active(X))
            active(U21(tt())) -> mark(nil())
            active(U31(X1,X2,X3,X4)) -> U31(active(X1),X2,X3,X4)
            active(U31(tt(),IL,M,N)) -> mark(cons(N,take(M,IL)))
            active(and(X1,X2)) -> and(active(X1),X2)
            active(and(tt(),X)) -> mark(X)
            active(cons(X1,X2)) -> cons(active(X1),X2)
            active(isNat(0())) -> mark(tt())
            active(isNat(length(V1))) -> mark(isNatList(V1))
            active(isNat(s(V1))) -> mark(isNat(V1))
            active(isNatIList(V)) -> mark(isNatList(V))
            active(isNatIList(cons(V1,V2))) -> mark(and(isNat(V1),isNatIList(V2)))
            active(isNatIList(zeros())) -> mark(tt())
            active(isNatList(cons(V1,V2))) -> mark(and(isNat(V1),isNatList(V2)))
            active(isNatList(nil())) -> mark(tt())
            active(isNatList(take(V1,V2))) -> mark(and(isNat(V1),isNatIList(V2)))
            active(length(X)) -> length(active(X))
            active(length(cons(N,L))) -> mark(U11(and(isNatList(L),isNat(N)),L))
            active(length(nil())) -> mark(0())
            active(s(X)) -> s(active(X))
            active(take(X1,X2)) -> take(X1,active(X2))
            active(take(X1,X2)) -> take(active(X1),X2)
            active(take(0(),IL)) -> mark(U21(isNatIList(IL)))
            active(take(s(M),cons(N,IL))) -> mark(U31(and(isNatIList(IL),and(isNat(M),isNat(N))),IL,M,N))
            active(zeros()) -> mark(cons(0(),zeros()))
            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))
            isNat(ok(X)) -> ok(isNat(X))
            isNatIList(ok(X)) -> ok(isNatIList(X))
            isNatList(ok(X)) -> ok(isNatList(X))
            length(mark(X)) -> mark(length(X))
            length(ok(X)) -> ok(length(X))
            proper(0()) -> ok(0())
            proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
            proper(U21(X)) -> U21(proper(X))
            proper(U31(X1,X2,X3,X4)) -> U31(proper(X1),proper(X2),proper(X3),proper(X4))
            proper(and(X1,X2)) -> and(proper(X1),proper(X2))
            proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
            proper(isNat(X)) -> isNat(proper(X))
            proper(isNatIList(X)) -> isNatIList(proper(X))
            proper(isNatList(X)) -> isNatList(proper(X))
            proper(length(X)) -> length(proper(X))
            proper(nil()) -> ok(nil())
            proper(s(X)) -> s(proper(X))
            proper(take(X1,X2)) -> take(proper(X1),proper(X2))
            proper(tt()) -> ok(tt())
            proper(zeros()) -> ok(zeros())
            s(mark(X)) -> mark(s(X))
            s(ok(X)) -> ok(s(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:
            {U11/2,U21/1,U31/4,active/1,and/2,cons/2,isNat/1,isNatIList/1,isNatList/1,length/1,proper/1,s/1,take/2
            ,top/1} / {0/0,mark/1,nil/0,ok/1,tt/0,zeros/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {U11,U21,U31,active,and,cons,isNat,isNatIList,isNatList
            ,length,proper,s,take,top} and constructors {0,mark,nil,ok,tt,zeros}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          U11(x,y){x -> mark(x)} =
            U11(mark(x),y) ->^+ mark(U11(x,y))
              = C[U11(x,y) = U11(x,y){}]

WORST_CASE(Omega(n^1),?)