YES

NOTE: input TRS is reduced

original is
   5: c0() -> c1()
   6: c0() -> c2()
   7: c0() -> c4()
   8: c1() -> c3()
   9: c2() -> c0()
  10: c3() -> c0()
  11: c3() -> c4()
  12: g0(x1) -> g1(c0())
  13: g1(x2) -> c4()

reduced to
   5: c0() -> c1()
   6: c0() -> c2()
   8: c1() -> c3()
   9: c2() -> c0()
  10: c3() -> c0()
  11: c3() -> c4()
  12: g0(x1) -> g1(c0())
  13: g1(x2) -> c4()

0.01