YES

NOTE: input TRS is reduced

original is
   3: f0(c0(),c1()) -> c2()
   4: c0() -> c3()
   5: c1() -> c4()
   6: c2() -> f0(c3(),c1())
   7: c2() -> f0(c0(),c4())
   8: c2() -> f0(c0(),c1())

reduced to
   3: f0(c0(),c1()) -> c2()
   4: c0() -> c3()
   5: c1() -> c4()
   8: c2() -> f0(c0(),c1())

0.02