Attempt to root AVD running Android 4.4/5.1 is failing
I have tested and found that irrespective of the version of Android, if the ABI is arm, armeabi or maybe even mips (not sure), the process of rooting is going to work. They didn't worked for me, as of now, if the ABI is x86 or x86_x64 for Android 4 and 4+.

Below, anything after "#" is supposed to be a helpful comment.

Testing working on - Android 1.x, 2.x, 3.x, 4.0, 4.1, 4.2 (add additional space in subsequent boot):

adb shell mount
# Preferred command: adb shell mount -o rw,remount -t yaffs2 /dev/block/mtdblock0 /system
adb shell mount -o rw,remount /system
adb push su /system/xbin/su
# Appropriate su binary from Chainfire's SuperSu.zip package.
adb shell chmod 06755 /system
adb shell chmod 06755 /system/xbin/su
adb install "Super user.apk"
# Update the su binary for sure.
#adb install "Rootchecker app OR Terminal Emulator app to test."


Testing working on - Android 4.3-4.4 (add additional space in subsequent boot), 5.1, 6.0:

adb shell df
# See the available space in /system
adb shell mount -o remount,rw /system
adb push su /system/bin/su
adb shell chmod 0755 /system/bin/su
adb push su /system/xbin/su
adb shell chmod 0755 /system/xbin/su
adb shell su --install
adb shell "su --daemon&amp;"
adb shell setenforce 0
# optional and recommended; adb shell mount -o remount,ro /system
adb install "Super user app"
# Update the su binary.
#adb install "Rootchecker app OR Terminal Emulator app to test."