# monoid
# can be completed using LPO with preorder f > a > b, for instance

f(f(x,y),z) = f(x,f(y,z))
f(x,1) = x
f(1,x) = x
f(a,f(a,a)) = 1
f(b,f(b,b)) = 1
f(f(a,b),f(f(a,b),f(a,b))) = 1

!preorder f > a > b