YES

TRS:

  g(A()) -> A()
  g(B()) -> A()
  g(B()) -> B()
  g(C()) -> A()
  g(C()) -> B()
  g(C()) -> C()
  foldf(x,nil()) -> x
  foldf(x,cons(y,z)) -> f(foldf(x,z),y)
  f(t,x) -> f'(t,g(x))
  f'(triple(a,b,c),C()) -> triple(a,b,cons(C(),c))
  f'(triple(a,b,c),B()) -> f(triple(a,b,c),A())
  f'(triple(a,b,c),A()) -> f''(foldf(triple(cons(A(),a),nil(),c),b))
  f''(triple(a,b,c)) -> foldf(triple(a,b,nil()),c)

linear polynomial interpretations on N:

  g_A(x1) = x1
  g#_A(x1) = 2
  A_A = 1
  A#_A = 1
  B_A = 3
  B#_A = 3
  C_A = 3
  C#_A = 4
  foldf_A(x1,x2) = x1 + x2 + 1
  foldf#_A(x1,x2) = x1 + x2 + 5
  nil_A = 1
  nil#_A = 0
  cons_A(x1,x2) = x1 + x2 + 7
  cons#_A(x1,x2) = 4
  f_A(x1,x2) = x1 + x2 + 7
  f#_A(x1,x2) = x1 + x2 + 10
  f'_A(x1,x2) = x1 + x2 + 7
  f'#_A(x1,x2) = x1 + x2 + 9
  triple_A(x1,x2,x3) = x2 + x3
  triple#_A(x1,x2,x3) = 5
  f''_A(x1) = x1 + 2
  f''#_A(x1) = x1 + 7

precedence:

  C > B > g > A = cons > f' > f'' > triple > foldf = nil > f