YES

TRS:

  g(A()) -> A()
  g(B()) -> A()
  g(B()) -> B()
  g(C()) -> A()
  g(C()) -> B()
  g(C()) -> C()
  foldB(t,0()) -> t
  foldB(t,s(n)) -> f(foldB(t,n),B())
  foldC(t,0()) -> t
  foldC(t,s(n)) -> f(foldC(t,n),C())
  f(t,x) -> f'(t,g(x))
  f'(triple(a,b,c),C()) -> triple(a,b,s(c))
  f'(triple(a,b,c),B()) -> f(triple(a,b,c),A())
  f'(triple(a,b,c),A()) -> f''(foldB(triple(s(a),0(),c),b))
  f''(triple(a,b,c)) -> foldC(triple(a,b,0()),c)

linear polynomial interpretations on N:

  g_A(x1) = x1 + 1
  g#_A(x1) = 1
  A_A = 1
  A#_A = 0
  B_A = 4
  B#_A = 2
  C_A = 3
  C#_A = 3
  foldB_A(x1,x2) = x1 + x2
  foldB#_A(x1,x2) = x1 + x2 + 5
  0_A = 1
  0#_A = 4
  s_A(x1) = x1 + 10
  s#_A(x1) = 4
  f_A(x1,x2) = x1 + 10
  f#_A(x1,x2) = x1 + x2 + 9
  foldC_A(x1,x2) = x1 + x2 + 1
  foldC#_A(x1,x2) = x1 + x2 + 4
  f'_A(x1,x2) = x1 + 10
  f'#_A(x1,x2) = x1 + x2 + 7
  triple_A(x1,x2,x3) = x2 + x3
  triple#_A(x1,x2,x3) = 5
  f''_A(x1) = x1 + 2
  f''#_A(x1) = x1 + 6

precedence:

  f' > f'' > triple > foldB = s = foldC > C = f > A > g = 0 > B