YES
Input TRS:
      1: f(a(),b()) -> f(a(),c())
      2: f(c(),d()) -> f(b(),d())
Number of strict rules: 2
Direct POLO(bPol) ... failed.
Uncurrying f
      1: f^1_a(b()) -> f^1_a(c())
      2: f^1_c(d()) -> f^1_b(d())
      3: f(a(),_1) ->= f^1_a(_1)
      4: f(c(),_1) ->= f^1_c(_1)
      5: f(b(),_1) ->= f^1_b(_1)
Number of strict rules: 2
Direct POLO(bPol) ... removes: 4 1 3 5 2
      a 	w: 11798
      d 	w: 1
      b 	w: 8857
      f^1_b	w: 2 * x1 + 8365
      c 	w: 1
      f 	w: 2 * x1 + 2 * x2 + 8365
      f^1_a	w: x1
      f^1_c	w: 2 * x1 + 8366
Number of strict rules: 0