some issues about lightdm

I installed arch linux on my hp chromebook 11.
I run post-install.sh and it seems that I installed desktop environment and now when I boot from usb, arch start desktop but error occurred about lightdm and it stuck.
So I try to fix it.
First the system said "check out 'systemctl status lightdm.service'", so I typed in shell. It shows bunch of messages and it seems loaded successfully
Loaded: loaded (/usr/lib/systemd/system/lightdm.service; enabled)
but it failed to be activated
Active: failed (Result: start-limit) since Sat 2014-08-09 14:40:38 UTC; 14min ago
These are not very much helping. As long as I found there is something wrong about lightdm.
So I read a man page of lightdm a bit and I found something when typed $ lightdm -d. -d means debug mode and it dumped debug messages. (logged at /var/log/lightdm/lightdm.log)
In debug messages I found
"DEBUG: Could not run plymouth --ping: Failed to execute child process "plymouth" (No such file or directory)
"DEBUG: Using VT 1
"DEBUG: Seat: Starting local X display on VT1
"
This is useful. It seems I didn't install plymouth on my arch. I also found
I need to do some research about plymouth