YES

NOTE: input TRS is reduced

original is
   5: c1() -> c0()
   6: c1() -> c2()
   7: c2() -> c2()
   8: c3() -> c2()
   9: c3() -> c4()
  10: f0(x1,c0()) -> c5()
  11: f0(x2,c4()) -> c5()
  12: f0(x3,c5()) -> c5()
  13: f0(c2(),x4) -> c5()

reduced to
   5: c1() -> c0()
   6: c1() -> c2()
   8: c3() -> c2()
   9: c3() -> c4()
  10: f0(x1,c0()) -> c5()
  11: f0(x2,c4()) -> c5()
  12: f0(x3,c5()) -> c5()
  13: f0(c2(),x4) -> c5()

NOTE: input TRS is reduced

original is
   1: c2() -> c1()
   2: c0() -> c0()
   3: c1() -> c1()
   4: g0(g0(c0())) -> c2()

reduced to
   1: c2() -> c1()
   4: g0(g0(c0())) -> c2()

0.01