YES

NOTE: input TRS is reduced

original is
   1: g0(c1()) -> c2()
   2: c2() -> c2()
   3: g0(c2()) -> c1()
   4: c0() -> c1()

reduced to
   1: g0(c1()) -> c2()
   3: g0(c2()) -> c1()
   4: c0() -> c1()

0.02