YES

NOTE: input TRS is reduced

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

reduced to
   4: c2() -> g0(c2())
   6: g0(c0()) -> c1()
   7: c0() -> c2()

0.02