YES

NOTE: input TRS is reduced

original is
   1: g0(g0(g0(x1))) -> c0()
   2: g0(g0(c0())) -> c0()
   3: g0(c0()) -> c0()
   4: g0(g0(g1(g1(x2)))) -> g0(c0())
   5: g1(g0(c0())) -> c0()
   6: g1(c0()) -> c0()

reduced to
   1: g0(g0(g0(x1))) -> c0()
   3: g0(c0()) -> c0()
   4: g0(g0(g1(g1(x2)))) -> g0(c0())
   6: g1(c0()) -> c0()

0.04