f(e, x) = x
f(g(x), x) = e
f(f(x, y), z) = f(x, f(y, z))
h(x, y) = f(x, f(y, f(g(x), g(y))))
f(x, f(x, x)) = e

h(h(c1,c2),c2) != e

!preorder h>g>f>e>c1>c2