YES

NOTE: input TRS is reduced

original is
   1: g0(c0()) -> c1()
   2: g0(c0()) -> g0(c2())
   3: c0() -> c3()
   4: g0(c3()) -> c1()
   5: g0(c2()) -> c1()
   6: c3() -> c2()

reduced to
   3: c0() -> c3()
   5: g0(c2()) -> c1()
   6: c3() -> c2()

0.02