YES

NOTE: input TRS is reduced

original is
   1: c1() -> c0()
   2: c1() -> c2()
   3: c2() -> c2()
   4: c3() -> c2()
   5: c3() -> c4()
   6: f0(x1,c0()) -> c5()
   7: f0(x2,c4()) -> c5()
   8: f0(x3,c5()) -> c5()
   9: f0(c2(),x4) -> c5()

reduced to
   1: c1() -> c0()
   2: c1() -> c2()
   4: c3() -> c2()
   5: c3() -> c4()
   6: f0(x1,c0()) -> c5()
   7: f0(x2,c4()) -> c5()
   8: f0(x3,c5()) -> c5()
   9: f0(c2(),x4) -> c5()

0.01