YES

proof:
The input problem is infeasible because

[1] the following set of Horn clauses is satisfiable:

	f(g(a)) = f(a)
	a = b
	F(a) = F(g(a)) ==> true__ = false__
	true__ = false__ ==> \bottom

This holds because

[2] the following E does not entail the following G (Claessen-Smallbone's transformation (2018)):

E:
	a = b
	t1(F(a)) = true__
	t1(F(g(a))) = false__
	t2(false__) = true__
	t2(true__) = false__
G:
	true__ = false__

This holds because

[3] the following ground-complete ordered TRS entails E but does not entail G:

	a -> b
	t1(F(b)) -> true__
	t1(F(g(b))) -> false__
	t2(false__) -> true__
	t2(true__) -> false__
with the LPO induced by
	g > F > t1 > t2 > a > b > false__ > true__