YES

Problem:
 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)

Proof:
 DP Processor:
  DPs:
   foldf#(x,cons(y,z)) -> foldf#(x,z)
   foldf#(x,cons(y,z)) -> f#(foldf(x,z),y)
   f#(t,x) -> g#(x)
   f#(t,x) -> f'#(t,g(x))
   f'#(triple(a,b,c),B()) -> f#(triple(a,b,c),A())
   f'#(triple(a,b,c),A()) -> foldf#(triple(cons(A(),a),nil(),c),b)
   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)
  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)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [f''#](x0) = 2x0 + 2,
    
    [f'#](x0, x1) = 2x0 + x1 + 3,
    
    [f#](x0, x1) = 2x0 + 2x1 + 4,
    
    [foldf#](x0, x1) = 2x0 + 2x1 + 1,
    
    [g#](x0) = 2x0,
    
    [f''](x0) = x0 + 2,
    
    [triple](x0, x1, x2) = 2x1 + x2 + 2,
    
    [f'](x0, x1) = x0 + 4x1 + 2,
    
    [f](x0, x1) = x0 + 4x1 + 2,
    
    [cons](x0, x1) = 4x0 + x1 + 2,
    
    [foldf](x0, x1) = x0 + x1,
    
    [nil] = 0,
    
    [C] = 5,
    
    [B] = 4,
    
    [g](x0) = x0,
    
    [A] = 0
   orientation:
    foldf#(x,cons(y,z)) = 2x + 8y + 2z + 5 >= 2x + 2z + 1 = foldf#(x,z)
    
    foldf#(x,cons(y,z)) = 2x + 8y + 2z + 5 >= 2x + 2y + 2z + 4 = f#(foldf(x,z),y)
    
    f#(t,x) = 2t + 2x + 4 >= 2x = g#(x)
    
    f#(t,x) = 2t + 2x + 4 >= 2t + x + 3 = f'#(t,g(x))
    
    f'#(triple(a,b,c),B()) = 4b + 2c + 11 >= 4b + 2c + 8 = f#(triple(a,b,c),A())
    
    f'#(triple(a,b,c),A()) = 4b + 2c + 7 >= 2b + 2c + 5 = foldf#(triple(cons(A(),a),nil(),c),b)
    
    f'#(triple(a,b,c),A()) = 4b + 2c + 7 >= 2b + 2c + 6 = f''#(foldf(triple(cons(A(),a),nil(),c),b))
    
    f''#(triple(a,b,c)) = 4b + 2c + 6 >= 4b + 2c + 5 = foldf#(triple(a,b,nil()),c)
    
    g(A()) = 0 >= 0 = A()
    
    g(B()) = 4 >= 0 = A()
    
    g(B()) = 4 >= 4 = B()
    
    g(C()) = 5 >= 0 = A()
    
    g(C()) = 5 >= 4 = B()
    
    g(C()) = 5 >= 5 = C()
    
    foldf(x,nil()) = x >= x = x
    
    foldf(x,cons(y,z)) = x + 4y + z + 2 >= x + 4y + z + 2 = f(foldf(x,z),y)
    
    f(t,x) = t + 4x + 2 >= t + 4x + 2 = f'(t,g(x))
    
    f'(triple(a,b,c),C()) = 2b + c + 24 >= 2b + c + 24 = triple(a,b,cons(C(),c))
    
    f'(triple(a,b,c),B()) = 2b + c + 20 >= 2b + c + 4 = f(triple(a,b,c),A())
    
    f'(triple(a,b,c),A()) = 2b + c + 4 >= b + c + 4 = f''(foldf(triple(cons(A(),a),nil(),c),b))
    
    f''(triple(a,b,c)) = 2b + c + 4 >= 2b + c + 2 = foldf(triple(a,b,nil()),c)
   problem:
    DPs:
     
    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)
   Qed