YES

Problem:
 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)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [f''](x0) = x0,
   
   [triple](x0, x1, x2) = x0 + 4x1 + 2x2,
   
   [f'](x0, x1) = x0 + x1 + 1,
   
   [foldC](x0, x1) = x0 + 2x1,
   
   [f](x0, x1) = x0 + x1 + 1,
   
   [s](x0) = x0 + 2,
   
   [foldB](x0, x1) = x0 + 4x1 + 1,
   
   [0] = 0,
   
   [C] = 3,
   
   [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()) = 3 >= 2 = A()
   
   g(C()) = 3 >= 2 = B()
   
   g(C()) = 3 >= 3 = C()
   
   foldB(t,0()) = t + 1 >= t = t
   
   foldB(t,s(n)) = 4n + t + 9 >= 4n + t + 4 = f(foldB(t,n),B())
   
   foldC(t,0()) = t >= t = t
   
   foldC(t,s(n)) = 2n + t + 4 >= 2n + t + 4 = f(foldC(t,n),C())
   
   f(t,x) = t + x + 1 >= t + x + 1 = f'(t,g(x))
   
   f'(triple(a,b,c),C()) = a + 4b + 2c + 4 >= a + 4b + 2c + 4 = triple(a,b,s(c))
   
   f'(triple(a,b,c),B()) = a + 4b + 2c + 3 >= a + 4b + 2c + 3 = f(triple(a,b,c),A())
   
   f'(triple(a,b,c),A()) = a + 4b + 2c + 3 >= a + 4b + 2c + 3 = f''(foldB(triple(s(a),0(),c),b))
   
   f''(triple(a,b,c)) = a + 4b + 2c >= a + 4b + 2c = foldC(triple(a,b,0()),c)
  problem:
   g(A()) -> A()
   g(B()) -> A()
   g(B()) -> B()
   g(C()) -> C()
   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)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [f''](x0) = x0 + 3,
    
    [triple](x0, x1, x2) = x0 + x1 + 2x2 + 6,
    
    [f'](x0, x1) = x0 + x1 + 4,
    
    [foldC](x0, x1) = x0 + 2x1 + 1,
    
    [f](x0, x1) = x0 + x1 + 4,
    
    [s](x0) = x0 + 4,
    
    [foldB](x0, x1) = x0 + x1,
    
    [0] = 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 = C()
    
    foldC(t,0()) = t + 3 >= t = t
    
    foldC(t,s(n)) = 2n + t + 9 >= 2n + t + 9 = f(foldC(t,n),C())
    
    f(t,x) = t + x + 4 >= t + x + 4 = f'(t,g(x))
    
    f'(triple(a,b,c),C()) = a + b + 2c + 14 >= a + b + 2c + 14 = triple(a,b,s(c))
    
    f'(triple(a,b,c),B()) = a + b + 2c + 14 >= a + b + 2c + 14 = f(triple(a,b,c),A())
    
    f'(triple(a,b,c),A()) = a + b + 2c + 14 >= a + b + 2c + 14 = f''(foldB(triple(s(a),0(),c),b))
    
    f''(triple(a,b,c)) = a + b + 2c + 9 >= a + b + 2c + 9 = foldC(triple(a,b,0()),c)
   problem:
    g(A()) -> A()
    g(B()) -> A()
    g(B()) -> B()
    g(C()) -> C()
    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)
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [f''](x0) = x0 + 5,
     
     [triple](x0, x1, x2) = x0 + x1 + x2 + 2,
     
     [f'](x0, x1) = x0 + x1 + 5,
     
     [foldC](x0, x1) = x0 + x1 + 1,
     
     [f](x0, x1) = x0 + x1 + 5,
     
     [s](x0) = x0 + 5,
     
     [foldB](x0, x1) = x0 + x1,
     
     [0] = 1,
     
     [C] = 0,
     
     [B] = 6,
     
     [g](x0) = x0,
     
     [A] = 6
    orientation:
     g(A()) = 6 >= 6 = A()
     
     g(B()) = 6 >= 6 = A()
     
     g(B()) = 6 >= 6 = B()
     
     g(C()) = 0 >= 0 = C()
     
     foldC(t,s(n)) = n + t + 6 >= n + t + 6 = f(foldC(t,n),C())
     
     f(t,x) = t + x + 5 >= t + x + 5 = f'(t,g(x))
     
     f'(triple(a,b,c),C()) = a + b + c + 7 >= a + b + c + 7 = triple(a,b,s(c))
     
     f'(triple(a,b,c),B()) = a + b + c + 13 >= a + b + c + 13 = f(triple(a,b,c),A())
     
     f'(triple(a,b,c),A()) = a + b + c + 13 >= a + b + c + 13 = f''(foldB(triple(s(a),0(),c),b))
     
     f''(triple(a,b,c)) = a + b + c + 7 >= a + b + c + 4 = foldC(triple(a,b,0()),c)
    problem:
     g(A()) -> A()
     g(B()) -> A()
     g(B()) -> B()
     g(C()) -> C()
     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))
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [f''](x0) = x0 + 2,
      
      [triple](x0, x1, x2) = x0 + 2x1 + 4x2 + 4,
      
      [f'](x0, x1) = x0 + x1 + 6,
      
      [foldC](x0, x1) = 4x0 + 7x1 + 2,
      
      [f](x0, x1) = x0 + 4x1 + 6,
      
      [s](x0) = x0 + 2,
      
      [foldB](x0, x1) = x0 + 2x1 + 2,
      
      [0] = 0,
      
      [C] = 2,
      
      [B] = 4,
      
      [g](x0) = 2x0,
      
      [A] = 0
     orientation:
      g(A()) = 0 >= 0 = A()
      
      g(B()) = 8 >= 0 = A()
      
      g(B()) = 8 >= 4 = B()
      
      g(C()) = 4 >= 2 = C()
      
      foldC(t,s(n)) = 7n + 4t + 16 >= 7n + 4t + 16 = f(foldC(t,n),C())
      
      f(t,x) = t + 4x + 6 >= t + 2x + 6 = f'(t,g(x))
      
      f'(triple(a,b,c),C()) = a + 2b + 4c + 12 >= a + 2b + 4c + 12 = triple(a,b,s(c))
      
      f'(triple(a,b,c),B()) = a + 2b + 4c + 14 >= a + 2b + 4c + 10 = f(triple(a,b,c),A())
      
      f'(triple(a,b,c),A()) = a + 2b + 4c + 10 >= a + 2b + 4c + 10 = f''(foldB(triple(s(a),0(),c),b))
     problem:
      g(A()) -> A()
      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),A()) -> f''(foldB(triple(s(a),0(),c),b))
     DP Processor:
      DPs:
       foldC#(t,s(n)) -> foldC#(t,n)
       foldC#(t,s(n)) -> f#(foldC(t,n),C())
       f#(t,x) -> g#(x)
       f#(t,x) -> f'#(t,g(x))
      TRS:
       g(A()) -> A()
       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),A()) -> f''(foldB(triple(s(a),0(),c),b))
      TDG Processor:
       DPs:
        foldC#(t,s(n)) -> foldC#(t,n)
        foldC#(t,s(n)) -> f#(foldC(t,n),C())
        f#(t,x) -> g#(x)
        f#(t,x) -> f'#(t,g(x))
       TRS:
        g(A()) -> A()
        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),A()) -> f''(foldB(triple(s(a),0(),c),b))
       graph:
        foldC#(t,s(n)) -> f#(foldC(t,n),C()) ->
        f#(t,x) -> f'#(t,g(x))
        foldC#(t,s(n)) -> f#(foldC(t,n),C()) -> f#(t,x) -> g#(x)
        foldC#(t,s(n)) -> foldC#(t,n) ->
        foldC#(t,s(n)) -> f#(foldC(t,n),C())
        foldC#(t,s(n)) -> foldC#(t,n) -> foldC#(t,s(n)) -> foldC#(t,n)
       SCC Processor:
        #sccs: 1
        #rules: 1
        #arcs: 4/16
        DPs:
         foldC#(t,s(n)) -> foldC#(t,n)
        TRS:
         g(A()) -> A()
         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),A()) -> f''(foldB(triple(s(a),0(),c),b))
        Subterm Criterion Processor:
         simple projection:
          pi(foldC#) = 1
         problem:
          DPs:
           
          TRS:
           g(A()) -> A()
           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),A()) -> f''(foldB(triple(s(a),0(),c),b))
         Qed