Here's a simple example to illustrate how AMMs balance orders:

Let's say there's a cryptocurrency market with an AMM. The current price is $100. The order book looks like this:

Buy Orders:

- 100 units at $99

- 50 units at $98

- 20 units at $97

Sell Orders:

- 50 units at $101

- 30 units at $102

- 20 units at $103

In this scenario, there's an imbalance between buy and sell orders. The AMM adjusts the price to balance the orders. Let's say it raises the price to $100.5. Here's what happens:

- The buy order for 100 units at $99 is now less attractive, so it's partially filled (e.g., 50 units).

- The sell order for 50 units at $101 is now more attractive, so it's partially filled (e.g., 25 units).

- The other orders are adjusted accordingly.

By adjusting the price, the AMM has balanced the order book, ensuring that buy and sell orders are matched fairly and efficiently. This process is continuous, with the AMM constantly monitoring and adjusting prices to maintain a balanced order book.

This example illustrates how AMMs play a crucial role in maintaining market equilibrium, ensuring that prices reflect genuine market sentiment, and providing liquidity to traders.