YES

NOTE: input TRS is reduced

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

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

NOTE: input TRS is reduced

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

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

1.52