Here's a python script for the simple machine and a 9 instruction solution program. It won't work if the addends are zero. The 0 case can be handled by checking for 0 and jumping ahead of the increment loop.

  class VM(object):
  	memory = []
  	ip = 0
  	while len(memory) < 1000:
  		memory.append(0)
  	memory[0] = 3
  	memory[1] = 4

  def z(idx):
  	VM.memory[idx] = 0
  	VM.ip += 1

  def i(idx):
  	VM.memory[idx] += 1
  	VM.ip += 1

  def j(idx, cmp, goto):
	if VM.memory[idx] == VM.memory[cmp]:
		VM.ip += 1

  else:
		VM.ip = goto

  program = (
	(z, (2,)),		#0 INITIALIZE USED MEMORY
	(z, (3,)),		#1
	(z, (4,)),		#2
	(i, (2,)),		#3 BEGIN LOOP, INCREMENT m[2]
	(i, (3,)),		#4 INCREMENT m[3]
	(j, (3, 0, 3)),	#5 LOOP UNTIL memory[3] == memory[0]
	(i, (2,)),		#6 SIM.
	(i, (4,)),		#7
	(j, (4, 1, 6))	#8

)

  def run():
	while VM.ip < len(program):
		func, args = program[VM.ip]
		func(*args)

  run()
  print VM.memory[2]