YES

proof:
The input problem is infeasible because

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

	a = c
	f(a, b, x) = f(x, x, x)
	F(x, x, x) = F(a, b, y) ==> 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 = c
	t1(F(a, b, y), y) = false__
	t1(F(x, x, x), y) = true__
	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 -> c
	t1(F(c, b, Y0), Y0) -> false__
	t1(F(x, x, x), y) -> true__
	t2(false__) -> true__
	t2(true__) -> false__
with the LPO induced by
	b > F > t1 > t2 > a > c > false__ > true__