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:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [f''](x0) = x0 + 2,
   
   [triple](x0, x1, x2) = x0 + 5x1 + 4x2 + 1,
   
   [f'](x0, x1) = x0 + 2x1 + 4,
   
   [f](x0, x1) = x0 + 2x1 + 4,
   
   [cons](x0, x1) = x0 + x1 + 1,
   
   [foldf](x0, x1) = x0 + 4x1,
   
   [nil] = 0,
   
   [C] = 0,
   
   [B] = 0,
   
   [g](x0) = x0,
   
   [A] = 0
  orientation:
   g(A()) = 0 >= 0 = A()
   
   g(B()) = 0 >= 0 = A()
   
   g(B()) = 0 >= 0 = B()
   
   g(C()) = 0 >= 0 = A()
   
   g(C()) = 0 >= 0 = B()
   
   g(C()) = 0 >= 0 = C()
   
   foldf(x,nil()) = x >= x = x
   
   foldf(x,cons(y,z)) = x + 4y + 4z + 4 >= x + 2y + 4z + 4 = f(foldf(x,z),y)
   
   f(t,x) = t + 2x + 4 >= t + 2x + 4 = f'(t,g(x))
   
   f'(triple(a,b,c),C()) = a + 5b + 4c + 5 >= a + 5b + 4c + 5 = triple(a,b,cons(C(),c))
   
   f'(triple(a,b,c),B()) = a + 5b + 4c + 5 >= a + 5b + 4c + 5 = f(triple(a,b,c),A())
   
   f'(triple(a,b,c),A()) = a + 5b + 4c + 5 >= a + 4b + 4c + 4 = f''(foldf(triple(cons(A(),a),nil(),c),b))
   
   f''(triple(a,b,c)) = a + 5b + 4c + 3 >= a + 5b + 4c + 1 = foldf(triple(a,b,nil()),c)
  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())
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [triple](x0, x1, x2) = x0 + x1 + x2,
    
    [f'](x0, x1) = x0 + x1 + 3,
    
    [f](x0, x1) = x0 + x1 + 3,
    
    [cons](x0, x1) = x0 + x1 + 3,
    
    [foldf](x0, x1) = x0 + x1 + 2,
    
    [nil] = 1,
    
    [C] = 4,
    
    [B] = 4,
    
    [g](x0) = x0,
    
    [A] = 4
   orientation:
    g(A()) = 4 >= 4 = A()
    
    g(B()) = 4 >= 4 = A()
    
    g(B()) = 4 >= 4 = B()
    
    g(C()) = 4 >= 4 = A()
    
    g(C()) = 4 >= 4 = B()
    
    g(C()) = 4 >= 4 = C()
    
    foldf(x,nil()) = x + 3 >= x = x
    
    foldf(x,cons(y,z)) = x + y + z + 5 >= x + y + z + 5 = f(foldf(x,z),y)
    
    f(t,x) = t + x + 3 >= t + x + 3 = f'(t,g(x))
    
    f'(triple(a,b,c),C()) = a + b + c + 7 >= a + b + c + 7 = triple(a,b,cons(C(),c))
    
    f'(triple(a,b,c),B()) = a + b + c + 7 >= a + b + c + 7 = f(triple(a,b,c),A())
   problem:
    g(A()) -> A()
    g(B()) -> A()
    g(B()) -> B()
    g(C()) -> A()
    g(C()) -> B()
    g(C()) -> C()
    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())
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [triple](x0, x1, x2) = x0 + x1 + x2,
     
     [f'](x0, x1) = x0 + 3x1,
     
     [f](x0, x1) = x0 + 3x1,
     
     [cons](x0, x1) = 2x0 + x1 + 4,
     
     [foldf](x0, x1) = x0 + 5x1 + 6,
     
     [C] = 7,
     
     [B] = 2,
     
     [g](x0) = x0,
     
     [A] = 2
    orientation:
     g(A()) = 2 >= 2 = A()
     
     g(B()) = 2 >= 2 = A()
     
     g(B()) = 2 >= 2 = B()
     
     g(C()) = 7 >= 2 = A()
     
     g(C()) = 7 >= 2 = B()
     
     g(C()) = 7 >= 7 = C()
     
     foldf(x,cons(y,z)) = x + 10y + 5z + 26 >= x + 3y + 5z + 6 = f(foldf(x,z),y)
     
     f(t,x) = t + 3x >= t + 3x = f'(t,g(x))
     
     f'(triple(a,b,c),C()) = a + b + c + 21 >= a + b + c + 18 = triple(a,b,cons(C(),c))
     
     f'(triple(a,b,c),B()) = a + b + c + 6 >= a + b + c + 6 = f(triple(a,b,c),A())
    problem:
     g(A()) -> A()
     g(B()) -> A()
     g(B()) -> B()
     g(C()) -> C()
     f(t,x) -> f'(t,g(x))
     f'(triple(a,b,c),B()) -> f(triple(a,b,c),A())
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [triple](x0, x1, x2) = 2x0 + 4x1 + x2,
      
      [f'](x0, x1) = 2x0 + 4x1 + 6,
      
      [f](x0, x1) = 2x0 + 4x1 + 7,
      
      [C] = 1,
      
      [B] = 4,
      
      [g](x0) = x0,
      
      [A] = 0
     orientation:
      g(A()) = 0 >= 0 = A()
      
      g(B()) = 4 >= 0 = A()
      
      g(B()) = 4 >= 4 = B()
      
      g(C()) = 1 >= 1 = C()
      
      f(t,x) = 2t + 4x + 7 >= 2t + 4x + 6 = f'(t,g(x))
      
      f'(triple(a,b,c),B()) = 4a + 8b + 2c + 22 >= 4a + 8b + 2c + 7 = f(triple(a,b,c),A())
     problem:
      g(A()) -> A()
      g(B()) -> B()
      g(C()) -> C()
     Matrix Interpretation Processor: dim=3
      
      interpretation:
             [0]
       [C] = [0]
             [0],
       
             [0]
       [B] = [0]
             [0],
       
                 [1 0 0]     [1]
       [g](x0) = [0 0 0]x0 + [0]
                 [0 0 0]     [0],
       
             [0]
       [A] = [0]
             [0]
      orientation:
                [1]    [0]      
       g(A()) = [0] >= [0] = A()
                [0]    [0]      
       
                [1]    [0]      
       g(B()) = [0] >= [0] = B()
                [0]    [0]      
       
                [1]    [0]      
       g(C()) = [0] >= [0] = C()
                [0]    [0]      
      problem:
       
      Qed