YES

NOTE: input TRS is reduced

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

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

NOTE: input TRS is reduced

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

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

2.63