YES
Input TRS:
      1: f(h(x)) -> f(i(x))
      2: g(i(x)) -> g(h(x))
      3: h(a()) -> b()
      4: i(a()) -> b()
Number of strict rules: 4
Direct POLO(bPol) ... removes: 4 3
      h 	w: 2 * x1 + 1
      a 	w: 2438
      b 	w: 4876
      f 	w: 2 * x1 + 21238
      i 	w: 2 * x1 + 1
      g 	w: x1 + 8855
Number of strict rules: 2
Direct POLO(bPol) ... failed.
Uncurrying f g
      1: f^1_h(x) -> f^1_i(x)
      2: g^1_i(x) -> g^1_h(x)
      5: g(h(_1)) ->= g^1_h(_1)
      6: g(i(_1)) ->= g^1_i(_1)
      7: f(h(_1)) ->= f^1_h(_1)
      8: f(i(_1)) ->= f^1_i(_1)
Number of strict rules: 2
Direct POLO(bPol) ... removes: 8 1 5 7 6 2
      h 	w: 2 * x1 + 1
      a 	w: 0
      b 	w: 0
      g^1_i	w: x1 + 1
      f^1_i	w: 2 * x1
      f 	w: 2 * x1 + 2437
      f^1_h	w: 2 * x1 + 1
      i 	w: 2 * x1 + 1
      g^1_h	w: x1
      g 	w: 2 * x1
Number of strict rules: 0