YES

NOTE: input TRS is reduced

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

reduced to
   3: g0(g0(g0(x1))) -> c0()
   5: g0(c0()) -> c0()
   6: g0(g0(g1(g1(x2)))) -> g0(c0())
   8: g1(c0()) -> c0()

NOTE: input TRS is reduced

original is
   1: c0() -> c0()
   2: c1() -> f0(g0(g0(g0(c1()))),f0(c1(),g0(c0())))

reduced to
   2: c1() -> f0(g0(g0(g0(c1()))),f0(c1(),g0(c0())))

0.01