YES

NOTE: input TRS is reduced

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

reduced to
   5: c0() -> c3()
   7: g0(c2()) -> c1()
   8: c3() -> c2()

0.05