It should be obvious that the basic identity or terminal for the goal "To Be Intelligent" is "An Intelligent Person". And that the basic Opterm would be "A Stupid Person". But the opposition really fans out to point back at the previous GPM ("Stupid Priests") and forward towards the next one ("Stupid Strong Men"). And the basic identity is really too general for living life. Although these basic ones underlie the entire line plot (pattern of identities), you will have more specific items that you have used to try and accomplish the goal.
For the terminals, you will use things (in this example) like "a free thinker" or "a sharp operator". Opterms will be things like "stubborn fools" or "dumb bigots". Near the beginning of the goal, the Opterm is frequently but not always related to the previous GPM (opterms like narrow minded evangelists). Near the end, it is often related to the next GPM that is coming (opterms like dumb bullies). In the middle (the bulk of the items), the Opposition just sort of hunts around (opterms like stupid bureaucrats) with only the common characteristic of some sort of relation to stupidity (in this example) always being present.
Early on, there are many things that you consider are on your side, such as teachers (in this example). So you use these kinds of things as terminals (being "a brilliant teacher" for example). But these gradually fail. So you abandon them and they become part of the opposition. I had already reached the point where "Dumb Teachers" was an opterm for me in living this goal to be intelligent. You should be able to see from this that eventually it would have reached the point where anything that I might use to live this goal would have been abandoned and turned into an opponent. This is how the goal decays.
I can look back at the goal to be holy and see a complete decay. It eventually reached the point were I had evil priests and hypocritical evangelists as opterms and there was no identity left with which the goal could successfully be lived.
Here on Earth, one of these items will usually last for an entire lifetime and the shock of dying and hitting the between lives area is what causes you to give up on it and postulate a new beingness with which to accomplish the goal. This is one of the reasons you forget your past lives and putting together a lineplot of the current actual GPM will give you some recollection of who you have been before.
There are a few exceptions to this. You don't usually abandon an item if either the lifetime is very very short (dying in childhood) or the lifetime went so extremely well that you felt that you were winning and hung on to the same item. There is also the possibility that if things were really horrible, you might change items more than once in a lifetime, perhaps experiencing amnesia or a massive personality shift as a result.
Before Earth, you will find that you generally gave an item a much more thorough workout and held it for many lifetimes before you abandoned it. The GPMs used to decay much more slowly. It is the impact of the between lives area that makes you give up so easily.