YES

NOTE: input TRS is reduced

original is
   1: f0(c0(),c0()) -> g0(c2())
   2: c0() -> c0()
   2: c0() -> c0()
   3: c1() -> f0(c2(),c0())

reduced to
   1: f0(c0(),c0()) -> g0(c2())
   3: c1() -> f0(c2(),c0())

0.02