YES

NOTE: input TRS is reduced

original is
   4: g0(c1()) -> c0()
   5: g0(c1()) -> g0(c2())
   6: g0(c2()) -> g0(c1())
   7: g0(c2()) -> c3()
   8: c1() -> c4()
   9: c2() -> c5()
  10: g0(c4()) -> c0()
  11: g0(c5()) -> c3()

reduced to
   5: g0(c1()) -> g0(c2())
   6: g0(c2()) -> g0(c1())
   8: c1() -> c4()
   9: c2() -> c5()
  10: g0(c4()) -> c0()
  11: g0(c5()) -> c3()

NOTE: input TRS is reduced

original is
   1: c0() -> c1()
   2: c0() -> g0(c1())
   3: c1() -> c1()

reduced to
   1: c0() -> c1()
   2: c0() -> g0(c1())

0.01