When Wurmcoil Engine dies, it and Ashes of the Abhorrent trigger.
Resolve the Wurmcoil Engine trigger, creating two 3/3 Wurm artifact creature tokens.
Resolve the Ashes of the Abhorrent trigger, causing you to gain 1 life.
Activate Phyrexian Altar twice by sacrificing the Wurm tokens, adding ({B} magic symbol) ({B} magic symbol) .
When the Wurms die, Ashes of the Abhorrent trigger twice, causing you to gain 2 life.
Activate Chainer by paying ({B} magic symbol) ({B} magic symbol) ({B} magic symbol) and 3 life, putting Wurmcoil Engine from your graveyard onto the battlefield.