YES

NOTE: input TRS is reduced

original is
   4: g0(g0(g0(x1))) -> c0()
   5: g0(g0(c0())) -> c0()
   6: g0(c0()) -> c0()
   7: g0(g0(g1(g1(x2)))) -> g0(c0())
   8: g1(g0(c0())) -> c0()
   9: g1(c0()) -> c0()

reduced to
   4: g0(g0(g0(x1))) -> c0()
   6: g0(c0()) -> c0()
   7: g0(g0(g1(g1(x2)))) -> g0(c0())
   9: g1(c0()) -> c0()

0.02