input: Write a function to identify and resolve any bugs in the given Python code snippet for summing up elements in a list. If the given function has bugs, fix them; otherwise, return the correct function. If the input list is empty, return 0.
  
  def sum_list(list):
      sum_list = 0
      for num in list:
          sum_list += num
      return sum_list
  
  assert sum_list([1, 2, 3, 4])==10
  assert sum_list([-1, 0, 1])==0
  assert sum_list([5, 5, 5, 5, 5])==25
  assert sum_list([-1, -2, -3, -4])==-10
  assert sum_list([])==0
output: def sum_list(input_list):
      total_sum = 0
      for num in input_list:
          total_sum += num
      return total_sum