YES

NOTE: input TRS is reduced

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

reduced to
   1: f0(c0(),c1()) -> c2()
   2: c0() -> c3()
   3: c1() -> c4()
   6: c2() -> f0(c0(),c1())

NOTE: input TRS is reduced

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

reduced to
   1: f0(c0(),c1()) -> c2()
   2: c0() -> c3()
   3: c1() -> c4()
   6: c2() -> f0(c0(),c1())

0.02