YES

NOTE: input TRS is reduced

original is
   1: c0() -> c0()
   2: g0(g0(c0())) -> c1()
   3: g0(g0(x1)) -> g0(g0(g0(c1())))

reduced to
   2: g0(g0(c0())) -> c1()
   3: g0(g0(x1)) -> g0(g0(g0(c1())))

0.09