MAYBE

Problem:
 h(x,x) -> h(a(),b())
 g(g(x,a()),y) -> g(g(a(),y),g(a(),x))
 f(g(x,y)) -> g(g(f(f(y)),h(a(),a())),x)
 h(h(f(f(x)),y),h(z,v)) -> h(h(f(z),f(f(f(y)))),h(v,x))

Proof:
 Open