YES

NOTE: input TRS is reduced

original is
   5: c2() -> g0(f0(c1(),c1()))
   6: c2() -> c1()
   7: c1() -> c1()
   8: c2() -> c0()

reduced to
   5: c2() -> g0(f0(c1(),c1()))
   6: c2() -> c1()
   8: c2() -> c0()

NOTE: input TRS is reduced

original is
   1: c0() -> c0()
   2: c0() -> c1()
   3: f0(c1(),c1()) -> f0(c0(),c1())
   4: f0(x1,c0()) -> f0(c0(),c1())

reduced to
   2: c0() -> c1()
   3: f0(c1(),c1()) -> f0(c0(),c1())
   4: f0(x1,c0()) -> f0(c0(),c1())

0.01