code: def test_FreeGroupElm_eliminate_word():
      w = x**5 * y * x**2 * y**-4 * x
      assert (
          w.eliminate_word(x, x**2)
          == x**10 * y * x**4 * y**-4 * x**2
      )
      w3 = x**2 * y**3 * x**-1 * y
      assert (
          w3.eliminate_word(x, x**2) == x**4 * y**3 * x**-2 * y
      )
      assert w3.eliminate_word(x, y) == y**5
      assert w3.eliminate_word(x, y**4) == y**8
      assert w3.eliminate_word(y, x**-1) == x**-3
      assert (
          w3.eliminate_word(x, y * z)
          == y * z * y * z * y**3 * z**-1
      )
      assert (y**-3).eliminate_word(
          y, x**-1 * z**-1
      ) == z * x * z * x * z * x
  
imports: from sympy.combinatorics.free_groups import free_group, FreeGroup
  from sympy.core import Symbol
  from sympy.testing.pytest import raises
  from sympy.core.numbers import oo
label_desc: Use image node_id 11 for calling a global function with example usage: test_FreeGroupElm_eliminate_word() without return types