YES

proof:
The input problem is infeasible because

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

	x = c ==> g(x) = c
	x = a ==> f(g(x)) = b
	x = a & x = c ==> 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(g(a)) = b
	g(c) = c
	t1(a) = true__
	t1(c) = 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:

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