* Step 1: Sum WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            active(dbl(X)) -> dbl(active(X))
            active(dbl(0())) -> mark(0())
            active(dbl(s(X))) -> mark(s(s(dbl(X))))
            active(dbl1(X)) -> dbl1(active(X))
            active(dbl1(0())) -> mark(01())
            active(dbl1(s(X))) -> mark(s1(s1(dbl1(X))))
            active(dbls(X)) -> dbls(active(X))
            active(dbls(cons(X,Y))) -> mark(cons(dbl(X),dbls(Y)))
            active(dbls(nil())) -> mark(nil())
            active(from(X)) -> mark(cons(X,from(s(X))))
            active(indx(X1,X2)) -> indx(active(X1),X2)
            active(indx(cons(X,Y),Z)) -> mark(cons(sel(X,Z),indx(Y,Z)))
            active(indx(nil(),X)) -> mark(nil())
            active(quote(X)) -> quote(active(X))
            active(quote(0())) -> mark(01())
            active(quote(dbl(X))) -> mark(dbl1(X))
            active(quote(s(X))) -> mark(s1(quote(X)))
            active(quote(sel(X,Y))) -> mark(sel1(X,Y))
            active(s1(X)) -> s1(active(X))
            active(sel(X1,X2)) -> sel(X1,active(X2))
            active(sel(X1,X2)) -> sel(active(X1),X2)
            active(sel(0(),cons(X,Y))) -> mark(X)
            active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
            active(sel1(X1,X2)) -> sel1(X1,active(X2))
            active(sel1(X1,X2)) -> sel1(active(X1),X2)
            active(sel1(0(),cons(X,Y))) -> mark(X)
            active(sel1(s(X),cons(Y,Z))) -> mark(sel1(X,Z))
            cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
            dbl(mark(X)) -> mark(dbl(X))
            dbl(ok(X)) -> ok(dbl(X))
            dbl1(mark(X)) -> mark(dbl1(X))
            dbl1(ok(X)) -> ok(dbl1(X))
            dbls(mark(X)) -> mark(dbls(X))
            dbls(ok(X)) -> ok(dbls(X))
            from(ok(X)) -> ok(from(X))
            indx(mark(X1),X2) -> mark(indx(X1,X2))
            indx(ok(X1),ok(X2)) -> ok(indx(X1,X2))
            proper(0()) -> ok(0())
            proper(01()) -> ok(01())
            proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
            proper(dbl(X)) -> dbl(proper(X))
            proper(dbl1(X)) -> dbl1(proper(X))
            proper(dbls(X)) -> dbls(proper(X))
            proper(from(X)) -> from(proper(X))
            proper(indx(X1,X2)) -> indx(proper(X1),proper(X2))
            proper(nil()) -> ok(nil())
            proper(quote(X)) -> quote(proper(X))
            proper(s(X)) -> s(proper(X))
            proper(s1(X)) -> s1(proper(X))
            proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
            proper(sel1(X1,X2)) -> sel1(proper(X1),proper(X2))
            quote(mark(X)) -> mark(quote(X))
            quote(ok(X)) -> ok(quote(X))
            s(ok(X)) -> ok(s(X))
            s1(mark(X)) -> mark(s1(X))
            s1(ok(X)) -> ok(s1(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))
            sel1(X1,mark(X2)) -> mark(sel1(X1,X2))
            sel1(mark(X1),X2) -> mark(sel1(X1,X2))
            sel1(ok(X1),ok(X2)) -> ok(sel1(X1,X2))
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
        - Signature:
            {active/1,cons/2,dbl/1,dbl1/1,dbls/1,from/1,indx/2,proper/1,quote/1,s/1,s1/1,sel/2,sel1/2,top/1} / {0/0,01/0
            ,mark/1,nil/0,ok/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {active,cons,dbl,dbl1,dbls,from,indx,proper,quote,s,s1,sel
            ,sel1,top} and constructors {0,01,mark,nil,ok}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            active(dbl(X)) -> dbl(active(X))
            active(dbl(0())) -> mark(0())
            active(dbl(s(X))) -> mark(s(s(dbl(X))))
            active(dbl1(X)) -> dbl1(active(X))
            active(dbl1(0())) -> mark(01())
            active(dbl1(s(X))) -> mark(s1(s1(dbl1(X))))
            active(dbls(X)) -> dbls(active(X))
            active(dbls(cons(X,Y))) -> mark(cons(dbl(X),dbls(Y)))
            active(dbls(nil())) -> mark(nil())
            active(from(X)) -> mark(cons(X,from(s(X))))
            active(indx(X1,X2)) -> indx(active(X1),X2)
            active(indx(cons(X,Y),Z)) -> mark(cons(sel(X,Z),indx(Y,Z)))
            active(indx(nil(),X)) -> mark(nil())
            active(quote(X)) -> quote(active(X))
            active(quote(0())) -> mark(01())
            active(quote(dbl(X))) -> mark(dbl1(X))
            active(quote(s(X))) -> mark(s1(quote(X)))
            active(quote(sel(X,Y))) -> mark(sel1(X,Y))
            active(s1(X)) -> s1(active(X))
            active(sel(X1,X2)) -> sel(X1,active(X2))
            active(sel(X1,X2)) -> sel(active(X1),X2)
            active(sel(0(),cons(X,Y))) -> mark(X)
            active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
            active(sel1(X1,X2)) -> sel1(X1,active(X2))
            active(sel1(X1,X2)) -> sel1(active(X1),X2)
            active(sel1(0(),cons(X,Y))) -> mark(X)
            active(sel1(s(X),cons(Y,Z))) -> mark(sel1(X,Z))
            cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
            dbl(mark(X)) -> mark(dbl(X))
            dbl(ok(X)) -> ok(dbl(X))
            dbl1(mark(X)) -> mark(dbl1(X))
            dbl1(ok(X)) -> ok(dbl1(X))
            dbls(mark(X)) -> mark(dbls(X))
            dbls(ok(X)) -> ok(dbls(X))
            from(ok(X)) -> ok(from(X))
            indx(mark(X1),X2) -> mark(indx(X1,X2))
            indx(ok(X1),ok(X2)) -> ok(indx(X1,X2))
            proper(0()) -> ok(0())
            proper(01()) -> ok(01())
            proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
            proper(dbl(X)) -> dbl(proper(X))
            proper(dbl1(X)) -> dbl1(proper(X))
            proper(dbls(X)) -> dbls(proper(X))
            proper(from(X)) -> from(proper(X))
            proper(indx(X1,X2)) -> indx(proper(X1),proper(X2))
            proper(nil()) -> ok(nil())
            proper(quote(X)) -> quote(proper(X))
            proper(s(X)) -> s(proper(X))
            proper(s1(X)) -> s1(proper(X))
            proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
            proper(sel1(X1,X2)) -> sel1(proper(X1),proper(X2))
            quote(mark(X)) -> mark(quote(X))
            quote(ok(X)) -> ok(quote(X))
            s(ok(X)) -> ok(s(X))
            s1(mark(X)) -> mark(s1(X))
            s1(ok(X)) -> ok(s1(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))
            sel1(X1,mark(X2)) -> mark(sel1(X1,X2))
            sel1(mark(X1),X2) -> mark(sel1(X1,X2))
            sel1(ok(X1),ok(X2)) -> ok(sel1(X1,X2))
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
        - Signature:
            {active/1,cons/2,dbl/1,dbl1/1,dbls/1,from/1,indx/2,proper/1,quote/1,s/1,s1/1,sel/2,sel1/2,top/1} / {0/0,01/0
            ,mark/1,nil/0,ok/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {active,cons,dbl,dbl1,dbls,from,indx,proper,quote,s,s1,sel
            ,sel1,top} and constructors {0,01,mark,nil,ok}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          cons(x,y){x -> ok(x),y -> ok(y)} =
            cons(ok(x),ok(y)) ->^+ ok(cons(x,y))
              = C[cons(x,y) = cons(x,y){}]

WORST_CASE(Omega(n^1),?)