* Step 1: Sum WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            active(and(X1,X2)) -> and(X1,active(X2))
            active(and(X1,X2)) -> and(active(X1),X2)
            active(and(tt(),T)) -> mark(T)
            active(cons(X1,X2)) -> cons(active(X1),X2)
            active(isNat(0())) -> mark(tt())
            active(isNat(length(L))) -> mark(isNatList(L))
            active(isNat(s(N))) -> mark(isNat(N))
            active(isNatIList(IL)) -> mark(isNatList(IL))
            active(isNatIList(cons(N,IL))) -> mark(and(isNat(N),isNatIList(IL)))
            active(isNatIList(zeros())) -> mark(tt())
            active(isNatList(cons(N,L))) -> mark(and(isNat(N),isNatList(L)))
            active(isNatList(nil())) -> mark(tt())
            active(isNatList(take(N,IL))) -> mark(and(isNat(N),isNatIList(IL)))
            active(length(X)) -> length(active(X))
            active(length(cons(N,L))) -> mark(uLength(and(isNat(N),isNatList(L)),L))
            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(uTake1(isNatIList(IL)))
            active(take(s(M),cons(N,IL))) -> mark(uTake2(and(isNat(M),and(isNat(N),isNatIList(IL))),M,N,IL))
            active(uLength(X1,X2)) -> uLength(active(X1),X2)
            active(uLength(tt(),L)) -> mark(s(length(L)))
            active(uTake1(X)) -> uTake1(active(X))
            active(uTake1(tt())) -> mark(nil())
            active(uTake2(X1,X2,X3,X4)) -> uTake2(active(X1),X2,X3,X4)
            active(uTake2(tt(),M,N,IL)) -> mark(cons(N,take(M,IL)))
            active(zeros()) -> mark(cons(0(),zeros()))
            and(X1,mark(X2)) -> mark(and(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))
            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(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(uLength(X1,X2)) -> uLength(proper(X1),proper(X2))
            proper(uTake1(X)) -> uTake1(proper(X))
            proper(uTake2(X1,X2,X3,X4)) -> uTake2(proper(X1),proper(X2),proper(X3),proper(X4))
            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))
            uLength(mark(X1),X2) -> mark(uLength(X1,X2))
            uLength(ok(X1),ok(X2)) -> ok(uLength(X1,X2))
            uTake1(mark(X)) -> mark(uTake1(X))
            uTake1(ok(X)) -> ok(uTake1(X))
            uTake2(mark(X1),X2,X3,X4) -> mark(uTake2(X1,X2,X3,X4))
            uTake2(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(uTake2(X1,X2,X3,X4))
        - Signature:
            {active/1,and/2,cons/2,isNat/1,isNatIList/1,isNatList/1,length/1,proper/1,s/1,take/2,top/1,uLength/2
            ,uTake1/1,uTake2/4} / {0/0,mark/1,nil/0,ok/1,tt/0,zeros/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {active,and,cons,isNat,isNatIList,isNatList,length,proper
            ,s,take,top,uLength,uTake1,uTake2} 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:
            active(and(X1,X2)) -> and(X1,active(X2))
            active(and(X1,X2)) -> and(active(X1),X2)
            active(and(tt(),T)) -> mark(T)
            active(cons(X1,X2)) -> cons(active(X1),X2)
            active(isNat(0())) -> mark(tt())
            active(isNat(length(L))) -> mark(isNatList(L))
            active(isNat(s(N))) -> mark(isNat(N))
            active(isNatIList(IL)) -> mark(isNatList(IL))
            active(isNatIList(cons(N,IL))) -> mark(and(isNat(N),isNatIList(IL)))
            active(isNatIList(zeros())) -> mark(tt())
            active(isNatList(cons(N,L))) -> mark(and(isNat(N),isNatList(L)))
            active(isNatList(nil())) -> mark(tt())
            active(isNatList(take(N,IL))) -> mark(and(isNat(N),isNatIList(IL)))
            active(length(X)) -> length(active(X))
            active(length(cons(N,L))) -> mark(uLength(and(isNat(N),isNatList(L)),L))
            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(uTake1(isNatIList(IL)))
            active(take(s(M),cons(N,IL))) -> mark(uTake2(and(isNat(M),and(isNat(N),isNatIList(IL))),M,N,IL))
            active(uLength(X1,X2)) -> uLength(active(X1),X2)
            active(uLength(tt(),L)) -> mark(s(length(L)))
            active(uTake1(X)) -> uTake1(active(X))
            active(uTake1(tt())) -> mark(nil())
            active(uTake2(X1,X2,X3,X4)) -> uTake2(active(X1),X2,X3,X4)
            active(uTake2(tt(),M,N,IL)) -> mark(cons(N,take(M,IL)))
            active(zeros()) -> mark(cons(0(),zeros()))
            and(X1,mark(X2)) -> mark(and(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))
            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(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(uLength(X1,X2)) -> uLength(proper(X1),proper(X2))
            proper(uTake1(X)) -> uTake1(proper(X))
            proper(uTake2(X1,X2,X3,X4)) -> uTake2(proper(X1),proper(X2),proper(X3),proper(X4))
            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))
            uLength(mark(X1),X2) -> mark(uLength(X1,X2))
            uLength(ok(X1),ok(X2)) -> ok(uLength(X1,X2))
            uTake1(mark(X)) -> mark(uTake1(X))
            uTake1(ok(X)) -> ok(uTake1(X))
            uTake2(mark(X1),X2,X3,X4) -> mark(uTake2(X1,X2,X3,X4))
            uTake2(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(uTake2(X1,X2,X3,X4))
        - Signature:
            {active/1,and/2,cons/2,isNat/1,isNatIList/1,isNatList/1,length/1,proper/1,s/1,take/2,top/1,uLength/2
            ,uTake1/1,uTake2/4} / {0/0,mark/1,nil/0,ok/1,tt/0,zeros/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {active,and,cons,isNat,isNatIList,isNatList,length,proper
            ,s,take,top,uLength,uTake1,uTake2} and constructors {0,mark,nil,ok,tt,zeros}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          and(x,y){y -> mark(y)} =
            and(x,mark(y)) ->^+ mark(and(x,y))
              = C[and(x,y) = and(x,y){}]

WORST_CASE(Omega(n^1),?)