YES

NOTE: input TRS is reduced

original is
   6: c2() -> g0(c2())
   7: c2() -> c2()
   8: g0(c0()) -> c1()
   9: c0() -> c2()

reduced to
   6: c2() -> g0(c2())
   8: g0(c0()) -> c1()
   9: c0() -> c2()

0.02