YES

NOTE: input TRS is reduced

original is
   4: c0() -> c0()
   5: g0(f0(c0(),c0())) -> g0(c1())
   6: c2() -> c1()

reduced to
   5: g0(f0(c0(),c0())) -> g0(c1())
   6: c2() -> c1()

0.02