YES

proof:
The input problem is infeasible because

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

	c = c
	h(x) = b ==> g(x) = a
	g(x) = x
	h(x) = a
	h(x) = b ==> true__ = false__
	true__ = false__ ==> \bottom

This holds because

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

E:
	g(x) = x
	h(x) = a
	t1(b, x) = a
	t1(h(x), x) = g(x)
	t2(b) = false__
	t2(h(x)) = true__
	t3(false__) = true__
	t3(true__) = false__
G:
	true__ = false__

This holds because

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

	g(x) -> x
	h(x) -> a
	t1(a, Y0) -> Y0
	t1(b, x) -> a
	t2(a) -> true__
	t2(b) -> false__
	t3(false__) -> true__
	t3(true__) -> false__
with the LPO induced by
	b > h > a > g > t1 > t3 > t2 > true__ > false__