YES

NOTE: input TRS is reduced

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

reduced to
   4: c1() -> c2()
   5: f0(c1(),c1()) -> c0()
   6: f0(c2(),c2()) -> c2()

NOTE: input TRS is reduced

original is
   1: c0() -> c0()
   2: c0() -> c1()
   3: f0(c0(),c0()) -> f0(c1(),f0(f0(c0(),c1()),c0()))

reduced to
   2: c0() -> c1()
   3: f0(c0(),c0()) -> f0(c1(),f0(f0(c0(),c1()),c0()))

0.02