YES

NOTE: input TRS is reduced

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

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

0.05