Knuth–Bendix completion algorithm
Okay kiddo, let me try to explain the Knuth-Bendix completion algorithm in a way you can understand.
Imagine you have a bunch of letters - let's say A, B, and C. And you have some rules about how those letters can be combined. For example, if you have a B before a C, you can replace it with an A. So if you had "BC", you could change it to "AC".
Now imagine you have a really big list of rules like that, and you want to figure out all the possible ways you can combine those letters. It would take a really long time to go through every possibility by hand!
That's where the Knuth-Bendix completion algorithm comes in. It's a computer program that takes all those rules and tries to figure out all the possible combinations for you.
Here's how it works. First, it takes all the rules and puts them into a big list. Then, it starts trying out different combinations of letters and seeing if any of the rules apply.
If it finds a new combination, it adds it to the list of possible combinations. Then, it keeps going, trying out more and more combinations until it's sure it's found them all.
It's a really smart way to solve a big problem like this, because it saves a lot of time and effort. And it can be useful in all kinds of situations, not just with letters - anytime you have a bunch of rules and you want to figure out all the possibilities, the Knuth-Bendix completion algorithm can help!
Imagine you have a bunch of letters - let's say A, B, and C. And you have some rules about how those letters can be combined. For example, if you have a B before a C, you can replace it with an A. So if you had "BC", you could change it to "AC".
Now imagine you have a really big list of rules like that, and you want to figure out all the possible ways you can combine those letters. It would take a really long time to go through every possibility by hand!
That's where the Knuth-Bendix completion algorithm comes in. It's a computer program that takes all those rules and tries to figure out all the possible combinations for you.
Here's how it works. First, it takes all the rules and puts them into a big list. Then, it starts trying out different combinations of letters and seeing if any of the rules apply.
If it finds a new combination, it adds it to the list of possible combinations. Then, it keeps going, trying out more and more combinations until it's sure it's found them all.
It's a really smart way to solve a big problem like this, because it saves a lot of time and effort. And it can be useful in all kinds of situations, not just with letters - anytime you have a bunch of rules and you want to figure out all the possibilities, the Knuth-Bendix completion algorithm can help!