While I was initialy convinced by the two previous answers, a colleague of mine showed me the light about this exercise.

He claims that the maximum value of the counter is $110$, not $20$.

As proof, consider the following execution :

• Thread $t$ reads $i = 0$; counter = 0
• Thread $u$ executes $10$ loops in total; counter = 10
• Thread $t$ writes $i = 1$;
• Thread $u$ tests if $i < 10$ and the test is satisfied
• Thread $u$ reads $i = 1$;
• Thread $t$ executes $10$ loops in total; counter = 20
• Thread $u$ writes $i = 2$;
• Thread $t$ tests if $i < 10$ and the test is satisfied
• Thread $t$ reads $i = 2$;
• Thread $u$ executes $9$ loops in total; counter = 29
• Thread $t$ writes $i = 3$;
• …
• Thread $t$ executes $1$ loop; counter = 110
• Both tests $i < 10$ are false and both threads exit.

The value $110$ is $10 + 10 + 9 + 9 + … + 1 + 1 = 10\times 11$.

While I was initialy convinced by the two previous answers, a colleague of mine showed me the light about this exercise.

He claims that the maximum value of the counter is $65$, not $20$.

As proof, consider the following execution :

• Thread $t$ reads $i = 0$; counter = 0
• Thread $u$ executes $10$ loops in total; counter = 10
• Thread $t$ writes $i = 1$;
• Thread $u$ enters the loop and reads $i = 1$;
• Thread $t$ executes $10$ loops in total; counter = 20
• Thread $u$ writes $i = 2$;
• Thread $t$ enters the loop and reads $i = 2$;
• Thread $u$ executes $9$ loops in total; counter = 29
• Thread $t$ writes $i = 3$;
• …
• Thread $t$ writes $i = 9$;
• Thread $u$ enters the loop and reads $i = 9$;
• Thread $t$ executes $2$ loops in total; counter = 64
• Thread $u$ writes $i = 10$;
• Thread $u$ finishes the loop; counter = 65
• Both tests $i < 10$ are false and both threads exit.

The value $65$ is $10 +10 + 9 + 8 + … + 2 +1$.