In Java, which gets executed first, "+" or "++"?

You are nearly correct but you are subtly misunderstanding how the precedence rules work.

Compare these two cases:

int t1 = 5;
int t2 = t1 + (++t1);
System.out.println (t2);

t1 = 5;
t2 = (++t1) + t1;
System.out.println (t2);

The result is:

11
12

The precedence does indeed say to evaluate the ++ before the +, but that doesn't apply until it reaches that part of the expression.

Your expression is of the form X + Y Where X is t1 and Y is (++t1)

The left branch, i.e. X, is evaluated first. Afterwards the right branch, i.e. Y, is evaluated. Only when it comes to evaluate Y the ++ operation is performed.

The precedence rules only say that the ++ is "inside" the Y expression, they don't say anything about the order of operations.

Your logic is close, but not quite right. The order of evaluation is Left to Right for the + operator. t1 comes before the binary op, LHS and then the increment is on the RHS of that binary op. The LHS is executed first.

t2 = t1 + (++t1);
t2 = 5 + 6;      // t1 becomes 6 here as a side effect before being read on the RHS
t2 = 11;

Visualised as a tree you have,

    +
  /   \
 t1   ++t1

Precedence Order

When two operators share an operand the operator with the higher precedence goes first. For example, 1 + 2 * 3 is treated as 1 + (2 * 3), whereas 1 * 2 + 3 is treated as (1 * 2) + 3 since multiplication has a higher precedence than addition.

Associativity

When two operators with the same precedence the expression is evaluated according to its associativity. For example x = y = z = 17 is treated as x = (y = (z = 17)), leaving all three variables with the value 17, since the = operator has right-to-left associativity (and an assignment statement evaluates to the value on the right hand side). On the other hand, 72 / 2 / 3 is treated as (72 / 2) / 3 since the / operator has left-to-right associativity.

Another way of thinking of it is to expand the ++ expression:

++t1 is the same as putting t1 = t1 + 1.

1) t1 = 5;
2) t2 = t1 + (++t1); 
3) t2 = t1 + (t1 = t1 + 1), 
4) t2 = 5 + (t1 = t1 + 1)
5) t2 = 5 + (t1 = 6)
6) t2 = 5 + 6 = 11

If you were to reverse the order to t2 = (++t1) + t1; Then the expression would expand to:

1) t2 = (t1 = t1 + 1) + t1     
2) t2 = (t1 = 5 + 1) + t1
3) t2 = (t1 = 6) + t1
4) t2 = 6 + 6 = 12

To add a point to Chris K,

The associativity is from left to right

So,

t2 = t1 + (++t1);
t2 = 5 + 6;      // first t1 is replaced with 5 and then the next 6 
t2 = 11;