YES

proof:
The input problem is infeasible because

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

	b = a
	a = b
	f(x, x) = c
	f(a, c) = 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
	b = a
	f(x, x) = c
	t1(a) = false__
	t1(f(a, c)) = 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:

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