Generalized star height problem

Okay, so imagine you have some shapes made out of blocks called "languages". Each language has its own set of rules about how to make the shapes out of blocks. The generalized star height problem is all about figuring out how many blocks you need to stack on top of each other to make these shapes.

Let's play a game to see how this problem works. Pretend we have a language that tells you how to make shapes out of blocks with stars and lines:

- A star by itself is a shape.
- A line by itself is a shape.
- If you put two shapes together next to each other, that's a new shape.
- If you put two shapes on top of each other, that's another new shape.

There are lots of different shapes you could make with this language. For example, you could make a shape that looks like this:

```
*
_
```

That shape has a star and a line, stacked on top of each other. We say that the "height" of this shape is 2, because there are two blocks stacked on top of each other.

Now, imagine we have a more complicated language that tells you how to make shapes out of many different types of blocks. Maybe it has stars, circles, rectangles, and triangles, and each type of block can be stacked on top of each other in different ways. The generalized star height problem is all about figuring out how many blocks you need to stack on top of each other to make the shapes for this language.

This problem can be really hard, because there are so many different languages and so many different ways you could stack the blocks. But computer scientists and mathematicians love to solve hard problems like this, because they're a fun challenge!