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:
   [nil] = 0,
   
   [f'](x0, x1) = x0 + 2x1,
   
   [g](x0) = x0,
   
   [C] = 1,
   
   [foldf](x0, x1) = x0 + 2x1,
   
   [f''](x0) = x0 + 1,
   
   [A] = 1,
   
   [f](x0, x1) = x0 + 2x1,
   
   [triple](x0, x1, x2) = x0 + 4x1 + 2x2,
   
   [cons](x0, x1) = x0 + x1,
   
   [B] = 1
  orientation:
   g(A()) = 1 >= 1 = A()
   
   g(B()) = 1 >= 1 = A()
   
   g(B()) = 1 >= 1 = B()
   
   g(C()) = 1 >= 1 = A()
   
   g(C()) = 1 >= 1 = B()
   
   g(C()) = 1 >= 1 = C()
   
   foldf(x,nil()) = x >= x = x
   
   foldf(x,cons(y,z)) = x + 2y + 2z >= x + 2y + 2z = f(foldf(x,z),y)
   
   f(t,x) = t + 2x >= t + 2x = f'(t,g(x))
   
   f'(triple(a,b,c),C()) = a + 4b + 2c + 2 >= a + 4b + 2c + 2 = triple(a,b,cons(C(),c))
   
   f'(triple(a,b,c),B()) = a + 4b + 2c + 2 >= a + 4b + 2c + 2 = f(triple(a,b,c),A())
   
   f'(triple(a,b,c),A()) = a + 4b + 2c + 2 >= a + 2b + 2c + 2 = f''(foldf(triple(cons(A(),a),nil(),c),b))
   
   f''(triple(a,b,c)) = a + 4b + 2c + 1 >= a + 4b + 2c = 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())
   f'(triple(a,b,c),A()) -> f''(foldf(triple(cons(A(),a),nil(),c),b))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [nil] = 4,
    
    [f'](x0, x1) = x0 + 5x1,
    
    [g](x0) = x0,
    
    [C] = 6,
    
    [foldf](x0, x1) = x0 + 5x1,
    
    [f''](x0) = x0,
    
    [A] = 5,
    
    [f](x0, x1) = x0 + 5x1,
    
    [triple](x0, x1, x2) = x0 + 5x1 + 2x2,
    
    [cons](x0, x1) = x0 + x1,
    
    [B] = 6
   orientation:
    g(A()) = 5 >= 5 = A()
    
    g(B()) = 6 >= 5 = A()
    
    g(B()) = 6 >= 6 = B()
    
    g(C()) = 6 >= 5 = A()
    
    g(C()) = 6 >= 6 = B()
    
    g(C()) = 6 >= 6 = C()
    
    foldf(x,nil()) = x + 20 >= x = x
    
    foldf(x,cons(y,z)) = x + 5y + 5z >= x + 5y + 5z = f(foldf(x,z),y)
    
    f(t,x) = t + 5x >= t + 5x = f'(t,g(x))
    
    f'(triple(a,b,c),C()) = a + 5b + 2c + 30 >= a + 5b + 2c + 12 = triple(a,b,cons(C(),c))
    
    f'(triple(a,b,c),B()) = a + 5b + 2c + 30 >= a + 5b + 2c + 25 = f(triple(a,b,c),A())
    
    f'(triple(a,b,c),A()) = a + 5b + 2c + 25 >= a + 5b + 2c + 25 = f''(foldf(triple(cons(A(),a),nil(),c),b))
   problem:
    g(A()) -> A()
    g(B()) -> B()
    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),A()) -> f''(foldf(triple(cons(A(),a),nil(),c),b))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [nil] = 1,
     
     [f'](x0, x1) = x0 + 4x1,
     
     [g](x0) = x0,
     
     [C] = 1,
     
     [foldf](x0, x1) = x0 + 4x1,
     
     [f''](x0) = x0 + 2,
     
     [A] = 4,
     
     [f](x0, x1) = x0 + 4x1,
     
     [triple](x0, x1, x2) = x0 + 7x1 + x2 + 1,
     
     [cons](x0, x1) = x0 + x1,
     
     [B] = 0
    orientation:
     g(A()) = 4 >= 4 = A()
     
     g(B()) = 0 >= 0 = B()
     
     g(C()) = 1 >= 0 = B()
     
     g(C()) = 1 >= 1 = C()
     
     foldf(x,cons(y,z)) = x + 4y + 4z >= x + 4y + 4z = f(foldf(x,z),y)
     
     f(t,x) = t + 4x >= t + 4x = f'(t,g(x))
     
     f'(triple(a,b,c),A()) = a + 7b + c + 17 >= a + 4b + c + 14 = f''(foldf(triple(cons(A(),a),nil(),c),b))
    problem:
     g(A()) -> A()
     g(B()) -> B()
     g(C()) -> C()
     foldf(x,cons(y,z)) -> f(foldf(x,z),y)
     f(t,x) -> f'(t,g(x))
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [f'](x0, x1) = x0 + 2x1 + 2,
      
      [g](x0) = 2x0,
      
      [C] = 0,
      
      [foldf](x0, x1) = x0 + 2x1,
      
      [A] = 1,
      
      [f](x0, x1) = x0 + 4x1 + 2,
      
      [cons](x0, x1) = 2x0 + x1 + 1,
      
      [B] = 0
     orientation:
      g(A()) = 2 >= 1 = A()
      
      g(B()) = 0 >= 0 = B()
      
      g(C()) = 0 >= 0 = C()
      
      foldf(x,cons(y,z)) = x + 4y + 2z + 2 >= x + 4y + 2z + 2 = f(foldf(x,z),y)
      
      f(t,x) = t + 4x + 2 >= t + 4x + 2 = f'(t,g(x))
     problem:
      g(B()) -> B()
      g(C()) -> C()
      foldf(x,cons(y,z)) -> f(foldf(x,z),y)
      f(t,x) -> f'(t,g(x))
     Matrix Interpretation Processor: dim=1
      
      interpretation:
       [f'](x0, x1) = x0 + x1,
       
       [g](x0) = x0,
       
       [C] = 0,
       
       [foldf](x0, x1) = x0 + x1 + 6,
       
       [f](x0, x1) = x0 + x1 + 1,
       
       [cons](x0, x1) = x0 + x1 + 1,
       
       [B] = 0
      orientation:
       g(B()) = 0 >= 0 = B()
       
       g(C()) = 0 >= 0 = C()
       
       foldf(x,cons(y,z)) = x + y + z + 7 >= x + y + z + 7 = f(foldf(x,z),y)
       
       f(t,x) = t + x + 1 >= t + x = f'(t,g(x))
      problem:
       g(B()) -> B()
       g(C()) -> C()
       foldf(x,cons(y,z)) -> f(foldf(x,z),y)
      Matrix Interpretation Processor: dim=1
       
       interpretation:
        [g](x0) = x0,
        
        [C] = 2,
        
        [foldf](x0, x1) = x0 + x1 + 7,
        
        [f](x0, x1) = x0 + x1 + 1,
        
        [cons](x0, x1) = x0 + x1 + 2,
        
        [B] = 0
       orientation:
        g(B()) = 0 >= 0 = B()
        
        g(C()) = 2 >= 2 = C()
        
        foldf(x,cons(y,z)) = x + y + z + 9 >= x + y + z + 8 = f(foldf(x,z),y)
       problem:
        g(B()) -> B()
        g(C()) -> C()
       Matrix Interpretation Processor: dim=3
        
        interpretation:
                   [1 0 0]     [1]
         [g](x0) = [0 0 0]x0 + [0]
                   [0 0 0]     [0],
         
               [0]
         [C] = [0]
               [0],
         
               [0]
         [B] = [0]
               [0]
        orientation:
                  [1]    [0]      
         g(B()) = [0] >= [0] = B()
                  [0]    [0]      
         
                  [1]    [0]      
         g(C()) = [0] >= [0] = C()
                  [0]    [0]      
        problem:
         
        Qed