MAYBE

Problem:
 app(app(:(),app(app(:(),x),y)),z) -> app(app(:(),x),app(app(:(),y),z))
 app(app(:(),app(app(+(),x),y)),z) -> app(app(+(),app(app(:(),x),z)),app(app(:(),y),z))
 app(app(:(),z),app(app(+(),x),app(f,y))) -> app(app(:(),app(app(g(),z),y)),app(app(+(),x),a()))
 app(app(map(),f),nil()) -> nil()
 app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
 app(app(filter(),f),nil()) -> nil()
 app(app(filter(),f),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(f,x)),f),x),xs)
 app(app(app(app(filter2(),true()),f),x),xs) -> app(app(cons(),x),app(app(filter(),f),xs))
 app(app(app(app(filter2(),false()),f),x),xs) -> app(app(filter(),f),xs)

Proof:
 Open