YES

NOTE: input TRS is reduced

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

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

0.01