YES

NOTE: input TRS is reduced

original is
   3: g0(c0()) -> c1()
   4: g0(c0()) -> g0(c2())
   5: c0() -> c3()
   6: g0(c3()) -> c1()
   7: g0(c2()) -> c1()
   8: c3() -> c2()

reduced to
   5: c0() -> c3()
   7: g0(c2()) -> c1()
   8: c3() -> c2()

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