YES

NOTE: input TRS is reduced

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

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

0.03