The example is the fib function given at the beginning of Lecture 15.
For reference, here is the function again:

        fib(x) = if x = 1 then 0 else
                   if x = 2 then 1 else
                      fib(x-1) + fib(x-2)


And here is the code for  cgen(fib(x) = if....)

fib_entry:
	move	$fp $sp     | start of code for fib(x) = if....then...else
	sw	$ra 0($sp)
	addiu	$sp $sp -4
                             | start of code for if...then...else
	lw 	$a0 4($fp)    | code for x
	sw	$a0 0($sp)
        addiu	$sp $sp -4    
        li	$a0 1	      | code for 1
        lw	$t1 4($sp)
	addiu 	$sp $sp 4
	beq	$a0 $t1 true_branch1
false_branch1:
                              | start of code for if x = 2 then 1 else ...
        lw      $a0 4($fp)     | code for x
        sw	$a0 0($sp)
        addiu	$sp $sp -4    
        li	$a0 2	       | code for 2
        lw	$t1 4($sp)
	addiu 	$sp $sp 4
	beq	$a0 $t1 true_branch2
false_branch2:
			       | start of code for fib(x-1) + fib(x-2)
        sw	$fp 0($sp)      | start of code for fib(x-1)
	addiu   $sp $sp -4
        	                 | start of code for x-1
	lw	$a0 4($fp)	  | code for x
        sw	$a0 0($sp)
        addiu	$sp $sp -4
	li	$a0 1		  | code for 1
        lw      $t1 4($sp)
        sub	$a0 $t1 $a0
        addiu   $sp $sp 4        | end of code for x-1
	sw	$a0 0($sp)
	addiu	$sp $sp -4
	jal	fib_entry	| end of code for fib(x-1)
	sw	$a0 0($sp)
	addiu	$sp $sp -4
        sw	$fp 0($sp)      | start of code for fib(x-1)
	addiu   $sp $sp -4
        	                 | start of code for x-2
	lw	$a0 4($fp)	  | code for x
        sw	$a0 0($sp)
        addiu	$sp $sp -4
	li	$a0 2		  | code for 2
        lw      $t1 4($sp)
        sub	$a0 $t1 $a0
        addiu   $sp $sp 4        | end of code for x-2
	sw	$a0 0($sp)
	addiu	$sp $sp -4
	jal	fib_entry	| end of code for fib(x-2)
	lw 	$t1 4($sp)
	add	$a0 $a0 $t1
	addiu	$sp $sp 4      | end of code for fib(x-1)+fib(x-2)
	b	end_if2
true_branch2:
	li	$a0 1	       | code for 1
end_if2:		      | end of code for if x = 2 then 1 else ...
	b	end_if1
true_branch1:
	li 	$a0 0	      | code for 0
end_if1: 		     | end of code for if x = 1 then 0 else ...      
        lw      $ra 4($sp)
        addiu 	$sp $sp 12
        lw    	$fp 0($sp)
        jr    	$ra         | end of code for def fib(x) = ...