* Step 1: Sum WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            active(cons(X1,X2)) -> cons(active(X1),X2)
            active(divides(X1,X2)) -> divides(X1,active(X2))
            active(divides(X1,X2)) -> divides(active(X1),X2)
            active(filter(X1,X2)) -> filter(X1,active(X2))
            active(filter(X1,X2)) -> filter(active(X1),X2)
            active(filter(s(s(X)),cons(Y,Z))) -> mark(if(divides(s(s(X)),Y)
                                                        ,filter(s(s(X)),Z)
                                                        ,cons(Y,filter(X,sieve(Y)))))
            active(from(X)) -> from(active(X))
            active(from(X)) -> mark(cons(X,from(s(X))))
            active(head(X)) -> head(active(X))
            active(head(cons(X,Y))) -> mark(X)
            active(if(X1,X2,X3)) -> if(active(X1),X2,X3)
            active(if(false(),X,Y)) -> mark(Y)
            active(if(true(),X,Y)) -> mark(X)
            active(primes()) -> mark(sieve(from(s(s(0())))))
            active(s(X)) -> s(active(X))
            active(sieve(X)) -> sieve(active(X))
            active(sieve(cons(X,Y))) -> mark(cons(X,filter(X,sieve(Y))))
            active(tail(X)) -> tail(active(X))
            active(tail(cons(X,Y))) -> mark(Y)
            cons(mark(X1),X2) -> mark(cons(X1,X2))
            cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
            divides(X1,mark(X2)) -> mark(divides(X1,X2))
            divides(mark(X1),X2) -> mark(divides(X1,X2))
            divides(ok(X1),ok(X2)) -> ok(divides(X1,X2))
            filter(X1,mark(X2)) -> mark(filter(X1,X2))
            filter(mark(X1),X2) -> mark(filter(X1,X2))
            filter(ok(X1),ok(X2)) -> ok(filter(X1,X2))
            from(mark(X)) -> mark(from(X))
            from(ok(X)) -> ok(from(X))
            head(mark(X)) -> mark(head(X))
            head(ok(X)) -> ok(head(X))
            if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
            if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
            proper(0()) -> ok(0())
            proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
            proper(divides(X1,X2)) -> divides(proper(X1),proper(X2))
            proper(false()) -> ok(false())
            proper(filter(X1,X2)) -> filter(proper(X1),proper(X2))
            proper(from(X)) -> from(proper(X))
            proper(head(X)) -> head(proper(X))
            proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3))
            proper(primes()) -> ok(primes())
            proper(s(X)) -> s(proper(X))
            proper(sieve(X)) -> sieve(proper(X))
            proper(tail(X)) -> tail(proper(X))
            proper(true()) -> ok(true())
            s(mark(X)) -> mark(s(X))
            s(ok(X)) -> ok(s(X))
            sieve(mark(X)) -> mark(sieve(X))
            sieve(ok(X)) -> ok(sieve(X))
            tail(mark(X)) -> mark(tail(X))
            tail(ok(X)) -> ok(tail(X))
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
        - Signature:
            {active/1,cons/2,divides/2,filter/2,from/1,head/1,if/3,proper/1,s/1,sieve/1,tail/1,top/1} / {0/0,false/0
            ,mark/1,ok/1,primes/0,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {active,cons,divides,filter,from,head,if,proper,s,sieve
            ,tail,top} and constructors {0,false,mark,ok,primes,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            active(cons(X1,X2)) -> cons(active(X1),X2)
            active(divides(X1,X2)) -> divides(X1,active(X2))
            active(divides(X1,X2)) -> divides(active(X1),X2)
            active(filter(X1,X2)) -> filter(X1,active(X2))
            active(filter(X1,X2)) -> filter(active(X1),X2)
            active(filter(s(s(X)),cons(Y,Z))) -> mark(if(divides(s(s(X)),Y)
                                                        ,filter(s(s(X)),Z)
                                                        ,cons(Y,filter(X,sieve(Y)))))
            active(from(X)) -> from(active(X))
            active(from(X)) -> mark(cons(X,from(s(X))))
            active(head(X)) -> head(active(X))
            active(head(cons(X,Y))) -> mark(X)
            active(if(X1,X2,X3)) -> if(active(X1),X2,X3)
            active(if(false(),X,Y)) -> mark(Y)
            active(if(true(),X,Y)) -> mark(X)
            active(primes()) -> mark(sieve(from(s(s(0())))))
            active(s(X)) -> s(active(X))
            active(sieve(X)) -> sieve(active(X))
            active(sieve(cons(X,Y))) -> mark(cons(X,filter(X,sieve(Y))))
            active(tail(X)) -> tail(active(X))
            active(tail(cons(X,Y))) -> mark(Y)
            cons(mark(X1),X2) -> mark(cons(X1,X2))
            cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
            divides(X1,mark(X2)) -> mark(divides(X1,X2))
            divides(mark(X1),X2) -> mark(divides(X1,X2))
            divides(ok(X1),ok(X2)) -> ok(divides(X1,X2))
            filter(X1,mark(X2)) -> mark(filter(X1,X2))
            filter(mark(X1),X2) -> mark(filter(X1,X2))
            filter(ok(X1),ok(X2)) -> ok(filter(X1,X2))
            from(mark(X)) -> mark(from(X))
            from(ok(X)) -> ok(from(X))
            head(mark(X)) -> mark(head(X))
            head(ok(X)) -> ok(head(X))
            if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
            if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
            proper(0()) -> ok(0())
            proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
            proper(divides(X1,X2)) -> divides(proper(X1),proper(X2))
            proper(false()) -> ok(false())
            proper(filter(X1,X2)) -> filter(proper(X1),proper(X2))
            proper(from(X)) -> from(proper(X))
            proper(head(X)) -> head(proper(X))
            proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3))
            proper(primes()) -> ok(primes())
            proper(s(X)) -> s(proper(X))
            proper(sieve(X)) -> sieve(proper(X))
            proper(tail(X)) -> tail(proper(X))
            proper(true()) -> ok(true())
            s(mark(X)) -> mark(s(X))
            s(ok(X)) -> ok(s(X))
            sieve(mark(X)) -> mark(sieve(X))
            sieve(ok(X)) -> ok(sieve(X))
            tail(mark(X)) -> mark(tail(X))
            tail(ok(X)) -> ok(tail(X))
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
        - Signature:
            {active/1,cons/2,divides/2,filter/2,from/1,head/1,if/3,proper/1,s/1,sieve/1,tail/1,top/1} / {0/0,false/0
            ,mark/1,ok/1,primes/0,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {active,cons,divides,filter,from,head,if,proper,s,sieve
            ,tail,top} and constructors {0,false,mark,ok,primes,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          cons(x,y){x -> mark(x)} =
            cons(mark(x),y) ->^+ mark(cons(x,y))
              = C[cons(x,y) = cons(x,y){}]

WORST_CASE(Omega(n^1),?)