property querylist : {"backupd"}
property app_is_up : missing value --this line is superfluous

set app_is_up to false

do shell script
"/System/Library/CoreServices/backupd.bundle/Contents/Resources/backupd-helper > /dev/null 2>&1  &"

repeat
	delay 10
	repeat with i in querylist
		if IsProcRunning(i) then set app_is_up to true
	end repeat
	if app_is_up then
		set app_is_up to false
	else
		ignoring application responses
			tell application "loginwindow" to «event aevtshut»
		end ignoring
		exit repeat
	end if
end repeat

on IsProcRunning(theProc)
	try
		do shell script "ps auxc | grep \"" & theProc & "\""
		return true
	on error
		return false
	end try
end IsProcRunning

do shell script
"/System/Library/CoreServices/backupd.bundle/Contents/Resources/backupd-helper > /dev/null 2>&1  &"

repeat
	delay 10
	if not IsProcRunning("backupd") then
		ignoring application responses
			tell application "loginwindow" to «event aevtshut»
		end ignoring
		exit repeat
	end if
end repeat

on IsProcRunning(theProc)
	try
		do shell script "ps auxc | grep \"" & theProc & "\""
		return true
	on error
		return false
	end try
end IsProcRunning