Toy contract with an internal and external library

Incrementer.sol

// SPDX-License-Identifier: MIT

pragma solidity >=0.8.19;

library IncrementerLibExternal {
  function increment(uint256 x) external pure returns (uint256) {
      return x + 1;
  }
}

library IncrementerLibInternal {
  function increment(uint256 x) internal pure returns (uint256) {
      return x + 1;
  }
}

// By running solc --ir Incrementer.sol on this file and examining the output, you'll see that incrementExternal
// has a larger bytecode footprint than incrementInternal. 
contract Incremeneter {
  uint256 public counter = 0;

  function incrementExternal() external {
      counter = IncrementerLibExternal.increment(counter);
  }

  function intercrementInternal() external {
      counter = IncrementerLibInternal.increment(counter);
  }
}