A source code comment:
The order of *opers-list matters. For example, if f is threadable and
an involution, then f(f([1,2])) would simplify to f([f(1),f(2)]) if
the threadable rule was used first, or it would simplify to [1,2] if
the the involution rule was used first. A user doesn't have any control
over the order the rules are applied. There is a user-level list
$opproperties,
but re-ordering $opproperties doesn't change the order the rules are
applied.
Barton