YES

NOTE: input TRS is reduced

original is
   1: c0() -> c1()
   2: c0() -> c2()
   3: c0() -> c4()
   4: c1() -> c3()
   5: c2() -> c0()
   6: c3() -> c0()
   7: c3() -> c4()
  10: g0(x3) -> g1(c0())
  11: g1(x4) -> c4()

reduced to
   1: c0() -> c1()
   2: c0() -> c2()
   4: c1() -> c3()
   5: c2() -> c0()
   6: c3() -> c0()
   7: c3() -> c4()
  10: g0(x3) -> g1(c0())
  11: g1(x4) -> c4()

NOTE: input TRS is reduced

original is
   1: c0() -> c1()
   2: c0() -> c2()
   3: c0() -> c4()
   4: c1() -> c3()
   5: c2() -> c0()
   6: c3() -> c0()
   7: c3() -> c4()
   8: g0(x1) -> g1(c0())
   9: g1(x2) -> c4()

reduced to
   1: c0() -> c1()
   2: c0() -> c2()
   4: c1() -> c3()
   5: c2() -> c0()
   6: c3() -> c0()
   7: c3() -> c4()
   8: g0(x1) -> g1(c0())
   9: g1(x2) -> c4()

0.23