YES

NOTE: input TRS is reduced

original is
   1: c0() -> c0()
   3: c1() -> f0(g0(g0(g0(c1()))),f0(c1(),g0(c0())))

reduced to
   3: c1() -> f0(g0(g0(g0(c1()))),f0(c1(),g0(c0())))

NOTE: input TRS is reduced

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

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

0.01