YES

---- CR(R)
---- Hot decreasingness.
R:
h(f(),a(),a()) -> h(g(),a(),a())
h(g(),a(),a()) -> h(f(),a(),a())
a() -> a'()
h(x,a'(),y) -> h(x,y,y)
g() -> f()
f() -> g()

C:


Label:
[h(f(),a(),a()) -> h(g(),a(),a())] = 2
[h(g(),a(),a()) -> h(f(),a(),a())] = 1
[a() -> a'()] = 0
[h(x,a'(),y) -> h(x,y,y)] = 0
[g() -> f()] = 0
[f() -> g()] = 0