YES

proof:
The input problem is infeasible because

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

	y' = y & y'' = y ==> f(y', h(y'')) = g(y)
	x' = x & x'' = x ==> f(x', x'') = g(x)
	x1 = x & h(x2) = x & x1 = x3 & x2 = x3 ==> true__ = false__
	true__ = false__ ==> \bottom

This holds because

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

E:
	f(x, x) = g(x)
	f(y, h(y)) = g(y)
	t1(h(x3), x3) = true__
	t1(x3, x3) = 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:

	f(y, h(y)) -> f(y, y)
	g(x) -> f(x, x)
	t1(h(x3), x3) -> true__
	t1(x3, x3) -> false__
	t2(false__) -> true__
	t2(true__) -> false__
with the LPO induced by
	t2 > t1 > h > g > f > false__ > true__