YES

NOTE: input TRS is reduced

original is
   4: c1() -> c0()
   5: c1() -> c2()
   6: c2() -> c2()
   7: c3() -> c2()
   8: c3() -> c4()
   9: f0(x2,c0()) -> c5()
  10: f0(x3,c4()) -> c5()
  11: f0(x4,c5()) -> c5()
  12: f0(c2(),x5) -> c5()

reduced to
   4: c1() -> c0()
   5: c1() -> c2()
   7: c3() -> c2()
   8: c3() -> c4()
   9: f0(x2,c0()) -> c5()
  10: f0(x3,c4()) -> c5()
  11: f0(x4,c5()) -> c5()
  12: f0(c2(),x5) -> c5()

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