I would be inclined to agree with both of those ID's. And yeah, they are tough to get rid of. But if you keep pulling all the top growth as soon as it appears, you will eventually weaken the plant to the point where it will die off.

I am still struggling with these two...are there any herbicides that target these? Been pulling them out but they are definitely winning the war!

A broadleaf herbicide with trichlopyr. Not sure why Round-up didn't work...it is still the most commonly used herbicide for both houtynnia and artemisia. You do know it takes some weeks for its effects to be seen. And may require a couple of treatments at the right time of year. An effective trick is to cut the vegetation, allowing for vigorous regrowth...then spraying when foliage is in full growth.

What about the method I use for b*****d plants.

When I lived in Australia, one of my nemeses was Onion Weed, Nothoscordum spp. It took a while, and lots pf aluminium dishes, but I completely eliminated it in my garden.

Get a tub made from dense material, eg plastic or metal, and place over the plants and bury the first inch or two. If it sprouts from the rhizomes, either replace the original lid with a wider one or add a second one over the new shoots

You coulld also give them a GOOD spray of Roundup, or, even better, Glyphosate 360, before you put their "lid" on.

Works every time.