YES

---- CR(R)
---- [Hirokawa and Middeldorp, 2013]
R:
f(a()) -> f(g(b(),b()))
a() -> g(c(),c())
c() -> d()
d() -> b()
b() -> d()
non-closed-CPS(R):
f(a()) -> f(g(c(),c()))
f(a()) -> f(g(b(),b()))