YES

proof:
The input problem is infeasible because

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

	b = x ==> f(x) = b
	a = x ==> f(x) = a
	a = x & b = x ==> 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(a) = a
	f(b) = b
	t1(a) = false__
	t1(b) = 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:

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