YES

NOTE: input TRS is reduced

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

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

NOTE: input TRS is reduced

original is
   1: c2() -> c1()
   2: c0() -> c0()
   3: c1() -> c1()
   4: g0(g0(c0())) -> c2()

reduced to
   1: c2() -> c1()
   4: g0(g0(c0())) -> c2()

0.01