YES

NOTE: input TRS is reduced

original is
   3: g0(g0(g0(x2))) -> c0()
   4: g0(g0(c0())) -> c0()
   5: g0(c0()) -> c0()
   6: g0(g0(g1(g1(x3)))) -> g0(c0())
   7: g1(g0(c0())) -> c0()
   8: g1(c0()) -> c0()

reduced to
   3: g0(g0(g0(x2))) -> c0()
   5: g0(c0()) -> c0()
   6: g0(g0(g1(g1(x3)))) -> g0(c0())
   8: g1(c0()) -> c0()

0.02