Charcoal, 28 bytes

≔⁰ηＦＸ²Ｌ諧≔θ籧θη≧⁻§θη绬§θη 

Try it online! Link is to verbose version of code. Outputs using Charcoal's default Boolean output, which is - for true and nothing for false. Explanation:

≔⁰η 

Initialise the instruction pointer.

ＦＸ²Ｌθ« 

Loop as many times as there are theoretically possible states.

§≔θ籧θη 

Negate the value at the instruction pointer.

≧⁻§θηη 

Subtract the new value from the instruction pointer. Charcoal's array accesses are cyclic so this automatically emulates Foo's circular tape.

»¬§θη 

At the end of the loop, output whether the program halted.