YES

NOTE: input TRS is reduced

original is
   1: g0(c1()) -> c0()
   2: g0(c1()) -> g0(c2())
   3: g0(c2()) -> g0(c1())
   4: g0(c2()) -> c3()
   5: c1() -> c4()
   6: c2() -> c5()
   7: g0(c4()) -> c0()
   8: g0(c5()) -> c3()

reduced to
   2: g0(c1()) -> g0(c2())
   3: g0(c2()) -> g0(c1())
   5: c1() -> c4()
   6: c2() -> c5()
   7: g0(c4()) -> c0()
   8: g0(c5()) -> c3()

0.02