YES

NOTE: input TRS is reduced

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

reduced to
   3: c2() -> c1()
   5: g0(g0(c0())) -> c2()

NOTE: input TRS is reduced

original is
   1: c1() -> c2()
   2: c0() -> c0()

reduced to
   1: c1() -> c2()

0.01