The trick to manipulating and comparing dates and times in PHP is to store date/time values in an integer variable and to use the mktime(), date() and strtotime() functions. The integer repesentation of a date/time is the number of seconds since midnight, 1970-Jan-1, which is referred to as the 'epoch'. Once your date/time is in integer form you'll be able to efficiently compare it to other dates that are also in integer form.
Of course since you'll most likely be receiving date/time values from page requests and database select queries you'll need to convert your date/time string into an integer before you can do any comparison or arithmetic.
Assuming you are sure that the $resttimefrom and $resttimeto variables contain properly formatted time you can use the strtotime() function to convert your string time into an integer. strtotime() takes a string that is formatted as a date and converts it to the number of seconds since epoch.
$time_from = strtotime($resttimefrom);
$time_to = strtotime($resttimeto);
Side note: strtotime() always returns a full date in integer form. If your string doesn't have a date, only a time, strtotime() return today's date along with the time you gave in the string. This is not important to you, though, because the two dates returned by strtotime() will have the same date and comparing the two variables will have the desired effect of comparing the two times as the dates cancel each other out.
When you compare the two integers keep in mind that the earlier the date/time is, the smaller its integer value will be. So if you want to see if $time_from is earlier than $time_to, you would have this:
if ($time_from < $time_to)
{
// $time_from is ealier than $time_to
}
Now to compare a date/time with the current system date/time, just use mktime() with no parameters to represent the current date/time:
if ($time_from < mktime())
{
// $time_from is in the past
}