How recursion works

Every time a procedure is called, it gets a fresh activation record on the call stack.

activation record

is a chunk of memory allocated to hold the local variables and parameters of that procedure

call stack

is a region of memory set aside to hold activation records. Activation records are placed onto the stack, and removed from the stack, in strict LIFO order (which is why it is a stack).

Here's a picture of the computation of add(3, 11)

1:		add(3, 11) return 1 + add(2, 11)
2:		add(3, 11) return 1 + add(2, 11)	add(2, 11) return 1 + add(1, 11)
3:		add(3, 11) return 1 + add(2, 11)	add(2, 11) return 1 + add(1, 11)	add(1, 11) return 1 + add(0, 11)
4:		add(3, 11) return 1 + add(2, 11)	add(2, 11) return 1 + add(1, 11)	add(1, 11) return 1 + add(0, 11)	add(0, 11) return 11
5:		add(3, 11) return 1 + add(2, 11)	add(2, 11) return 1 + add(1, 11)	add(1, 11) return 1 + 11
6:		add(3, 11) return 1 + add(2, 11)	add(2, 11) return 1 + 12
7:		add(3, 11) return 1 + 13
8:		14