YES

NOTE: input TRS is reduced

original is
   1: c0() -> c0()
   4: f0(c1(),c0()) -> f0(c0(),c1())
   5: f0(x2,c0()) -> c1()

reduced to
   4: f0(c1(),c0()) -> f0(c0(),c1())
   5: f0(x2,c0()) -> c1()

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())))

0.02