NO

---- Non-confluence check
R:
a(x) -> g(h(b(x)))
a(x) -> g(c(x))
b(x) -> g(b(x))
g(a(x)) -> g(h(a(x)))

Unjoinable conversion:
g(h(g(g(g(g(b(___y3()))))))) <->*
g(c(___y3()))