YES

NOTE: input TRS is reduced

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

reduced to
   1: g0(f0(c1(),c2())) -> c2()
   2: c0() -> f0(f0(f0(g0(c0()),c1()),f0(c2(),c2())),g0(c1()))
   3: f0(g0(c0()),c0()) -> f0(c2(),c0())
   5: f0(f0(c1(),g0(c1())),f0(c0(),c2())) -> c1()

0.15