YES

NOTE: input TRS is reduced

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

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

0.02