YES

NOTE: input TRS is reduced

original is
   3: 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()

0.01