There are a couple Mullers, too
.
Iwan is the one that Mr. Dibbs is mentioning. Our own SOTSDO wrote an
article on the Albert System here, which talks about Anton Mueller. (Forgive the lack of umlauts. Helen can fix, if she wants.) I *think* Terry just got the name wrong, though.
From what I read -- and I am NOT a clarinet scholar (I've just played clarinets) -- the I. Muller system is the basis upon which both the Oehler and Albert system were created. In any case,
a. Unless it's a really, really old clarinet, it's not going to be a straight "Muller System."
Call it between 1812 and 1847ish.
Here's a pic of an "actual" Muller. The upper joint is extremely similar on your horn, but the lower joint's got some very obvious differences.
b. The Oehler and Albert "systems" are essentially refinements and reworkings of the original design by Muller. If you look at
an Albert and Oehler fingering chart, you'll see that a lot of the "basic" fingerings are the same.
Oehler's just got a bunch more keys, so a bunch more alternate fingerings.
c. According to
this extremely good article (and elsewhere), Albert system horns are generally called "Simple system" horns in the UK. However, I think folks tend to think that an Albert system horn that has very few keys and alternate fingerings is more "simple," though.
Like this horn. As I mention above, your horn has an extra key on the lower joint and is missing one on the upper joint, from what I've seen on Albert system horns. That's not significant enough of a difference to say that the horn's not "Albert system" or has become an Oehler.
In other words, it's not completely incorrect to call it a "Muller System" or "Simple System." It's just not as accurate as "Albert System."