Think about orientation...these equations have something in common,
but what? How about average term depth of subterms?

f(a, g(b,c))   =    g(f(a,b), f(a,c))
1+2+2+3+3           1+2+2+3+3+3+3

i(f(a,b))      =    f(i(a),i(b))
1+2+3+3             1+2+2+3+3

But this usually orients larger to smaller terms...undesirable!

f(f(a))        = a
1+2+3            1

Average term depth of terminal nodes / max term depth, larger ->
smaller if equal seems to work for these examples. Easier:

Average term depth of terminal nodes / maximum term depth + 1

Now I need an algorithm to generate an ordering for desired
orientations -> Check Joachims LPO algorithm.


Okayti Wonder