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))
    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))
      f'#(triple(a,b,c),B()) -> f#(triple(a,b,c),A())
     TRS:
      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))
     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))
       f'#(triple(a,b,c),B()) -> f#(triple(a,b,c),A())
      TRS:
       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))
      graph:
       f'#(triple(a,b,c),B()) -> f#(triple(a,b,c),A()) ->
       f#(t,x) -> f'#(t,g(x))
       f'#(triple(a,b,c),B()) -> f#(triple(a,b,c),A()) -> f#(t,x) -> g#(x)
       f#(t,x) -> f'#(t,g(x)) ->
       f'#(triple(a,b,c),B()) -> f#(triple(a,b,c),A())
       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: 2
       #rules: 3
       #arcs: 7/25
       DPs:
        foldC#(t,s(n)) -> foldC#(t,n)
       TRS:
        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))
       Subterm Criterion Processor:
        simple projection:
         pi(foldC#) = 1
        problem:
         DPs:
          
         TRS:
          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))
        Qed
       
       DPs:
        f'#(triple(a,b,c),B()) -> f#(triple(a,b,c),A())
        f#(t,x) -> f'#(t,g(x))
       TRS:
        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))
       Arctic Interpretation Processor:
        dimension: 1
        interpretation:
         [f'#](x0, x1) = x0 + x1 + 0,
         
         [f#](x0, x1) = x0 + 3x1 + 5,
         
         [f''](x0) = 0,
         
         [triple](x0, x1, x2) = 2,
         
         [f'](x0, x1) = x0,
         
         [foldC](x0, x1) = 2x0 + x1 + 6,
         
         [f](x0, x1) = x0 + 1x1 + 0,
         
         [s](x0) = 5x0 + 0,
         
         [foldB](x0, x1) = 4x0 + x1 + 0,
         
         [0] = 1,
         
         [C] = 5,
         
         [B] = 6,
         
         [g](x0) = x0 + 0,
         
         [A] = 1
        orientation:
         f'#(triple(a,b,c),B()) = 6 >= 5 = f#(triple(a,b,c),A())
         
         f#(t,x) = t + 3x + 5 >= t + x + 0 = f'#(t,g(x))
         
         g(A()) = 1 >= 1 = A()
         
         g(B()) = 6 >= 1 = A()
         
         g(B()) = 6 >= 6 = B()
         
         g(C()) = 5 >= 5 = C()
         
         foldC(t,s(n)) = 5n + 2t + 6 >= n + 2t + 6 = f(foldC(t,n),C())
         
         f(t,x) = t + 1x + 0 >= t = f'(t,g(x))
         
         f'(triple(a,b,c),C()) = 2 >= 2 = triple(a,b,s(c))
         
         f'(triple(a,b,c),B()) = 2 >= 2 = f(triple(a,b,c),A())
         
         f'(triple(a,b,c),A()) = 2 >= 0 = f''(foldB(triple(s(a),0(),c),b))
        problem:
         DPs:
          f#(t,x) -> f'#(t,g(x))
         TRS:
          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))
        SCC Processor:
         #sccs: 0
         #rules: 0
         #arcs: 2/1