YES
Input TRS:
      1: g(A()) -> A()
      2: g(B()) -> A()
      3: g(B()) -> B()
      4: g(C()) -> A()
      5: g(C()) -> B()
      6: g(C()) -> C()
      7: foldB(t,0()) -> t
      8: foldB(t,s(n)) -> f(foldB(t,n),B())
      9: foldC(t,0()) -> t
      10: foldC(t,s(n)) -> f(foldC(t,n),C())
      11: f(t,x) -> f'(t,g(x))
      12: f'(triple(a,b,c),C()) -> triple(a,b,s(c))
      13: f'(triple(a,b,c),B()) -> f(triple(a,b,c),A())
      14: f'(triple(a,b,c),A()) -> f''(foldB(triple(s(a),0(),c),b))
      15: f''(triple(a,b,c)) -> foldC(triple(a,b,0()),c)
Number of strict rules: 15
Direct POLO(bPol) ... removes: 8
      s 	w: x1 + 11820
      triple	w: x1 + 2 * x2 + x3
      C 	w: 11685
      f 	w: x1 + x2 + 135
      B 	w: 11685
      foldB	w: x1 + 2 * x2
      0 	w: 0
      A 	w: 11685
      f'	w: x1 + x2 + 135
      foldC	w: x1 + x2
      g 	w: x1
      f''	w: x1
Number of strict rules: 14
Direct POLO(bPol) ... removes: 4 15 5 7 14 9 13 2
      s 	w: x1 + 17706
      triple	w: x1 + 2 * x2 + 2 * x3 + 10114
      C 	w: 17468
      f 	w: x1 + 2 * x2 + 476
      B 	w: 17467
      foldB	w: x1 + 2 * x2 + 15329
      0 	w: 1
      A 	w: 16283
      f'	w: x1 + 2 * x2 + 476
      foldC	w: x1 + 2 * x2 + 1
      g 	w: x1
      f''	w: x1 + 4
Number of strict rules: 6
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #f(t,x) -> #f'(t,g(x))
     #2: #f(t,x) -> #g(x)
     #3: #foldC(t,s(n)) -> #f(foldC(t,n),C())
     #4: #foldC(t,s(n)) -> #foldC(t,n)
Number of SCCs: 1, DPs: 1
  SCC { #4 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      #foldC	w: x2
      #f'	w: 0
      triple	w: 0
      C 	w: 0
      f 	w: 0
      B 	w: 0
      foldB	w: 0
      0 	w: 0
      A 	w: 0
      #f 	w: 0
      #g 	w: 0
      f'	w: 0
      foldC	w: 0
      g 	w: 0
      f''	w: 0
    USABLE RULES: { }
    Removed DPs: #4
Number of SCCs: 0, DPs: 0