YES

Problem:
 b(a(),f(b(b(z,y),a()))) -> z
 c(c(z,x,a()),a(),y) -> f(f(c(y,a(),f(c(z,y,x)))))
 f(f(c(a(),y,z))) -> b(y,b(z,z))

Proof:
 DP Processor:
  DPs:
   c#(c(z,x,a()),a(),y) -> c#(z,y,x)
   c#(c(z,x,a()),a(),y) -> f#(c(z,y,x))
   c#(c(z,x,a()),a(),y) -> c#(y,a(),f(c(z,y,x)))
   c#(c(z,x,a()),a(),y) -> f#(c(y,a(),f(c(z,y,x))))
   c#(c(z,x,a()),a(),y) -> f#(f(c(y,a(),f(c(z,y,x)))))
   f#(f(c(a(),y,z))) -> b#(z,z)
   f#(f(c(a(),y,z))) -> b#(y,b(z,z))
  TRS:
   b(a(),f(b(b(z,y),a()))) -> z
   c(c(z,x,a()),a(),y) -> f(f(c(y,a(),f(c(z,y,x)))))
   f(f(c(a(),y,z))) -> b(y,b(z,z))
  TDG Processor:
   DPs:
    c#(c(z,x,a()),a(),y) -> c#(z,y,x)
    c#(c(z,x,a()),a(),y) -> f#(c(z,y,x))
    c#(c(z,x,a()),a(),y) -> c#(y,a(),f(c(z,y,x)))
    c#(c(z,x,a()),a(),y) -> f#(c(y,a(),f(c(z,y,x))))
    c#(c(z,x,a()),a(),y) -> f#(f(c(y,a(),f(c(z,y,x)))))
    f#(f(c(a(),y,z))) -> b#(z,z)
    f#(f(c(a(),y,z))) -> b#(y,b(z,z))
   TRS:
    b(a(),f(b(b(z,y),a()))) -> z
    c(c(z,x,a()),a(),y) -> f(f(c(y,a(),f(c(z,y,x)))))
    f(f(c(a(),y,z))) -> b(y,b(z,z))
   graph:
    c#(c(z,x,a()),a(),y) -> f#(c(z,y,x)) ->
    f#(f(c(a(),y,z))) -> b#(y,b(z,z))
    c#(c(z,x,a()),a(),y) -> f#(c(z,y,x)) ->
    f#(f(c(a(),y,z))) -> b#(z,z)
    c#(c(z,x,a()),a(),y) -> f#(c(y,a(),f(c(z,y,x)))) ->
    f#(f(c(a(),y,z))) -> b#(y,b(z,z))
    c#(c(z,x,a()),a(),y) -> f#(c(y,a(),f(c(z,y,x)))) ->
    f#(f(c(a(),y,z))) -> b#(z,z)
    c#(c(z,x,a()),a(),y) -> f#(f(c(y,a(),f(c(z,y,x))))) ->
    f#(f(c(a(),y,z))) -> b#(y,b(z,z))
    c#(c(z,x,a()),a(),y) -> f#(f(c(y,a(),f(c(z,y,x))))) ->
    f#(f(c(a(),y,z))) -> b#(z,z)
    c#(c(z,x,a()),a(),y) -> c#(z,y,x) ->
    c#(c(z,x,a()),a(),y) -> f#(f(c(y,a(),f(c(z,y,x)))))
    c#(c(z,x,a()),a(),y) -> c#(z,y,x) ->
    c#(c(z,x,a()),a(),y) -> f#(c(y,a(),f(c(z,y,x))))
    c#(c(z,x,a()),a(),y) -> c#(z,y,x) ->
    c#(c(z,x,a()),a(),y) -> c#(y,a(),f(c(z,y,x)))
    c#(c(z,x,a()),a(),y) -> c#(z,y,x) ->
    c#(c(z,x,a()),a(),y) -> f#(c(z,y,x))
    c#(c(z,x,a()),a(),y) -> c#(z,y,x) ->
    c#(c(z,x,a()),a(),y) -> c#(z,y,x)
    c#(c(z,x,a()),a(),y) -> c#(y,a(),f(c(z,y,x))) ->
    c#(c(z,x,a()),a(),y) -> f#(f(c(y,a(),f(c(z,y,x)))))
    c#(c(z,x,a()),a(),y) -> c#(y,a(),f(c(z,y,x))) ->
    c#(c(z,x,a()),a(),y) -> f#(c(y,a(),f(c(z,y,x))))
    c#(c(z,x,a()),a(),y) -> c#(y,a(),f(c(z,y,x))) ->
    c#(c(z,x,a()),a(),y) -> c#(y,a(),f(c(z,y,x)))
    c#(c(z,x,a()),a(),y) -> c#(y,a(),f(c(z,y,x))) ->
    c#(c(z,x,a()),a(),y) -> f#(c(z,y,x))
    c#(c(z,x,a()),a(),y) -> c#(y,a(),f(c(z,y,x))) -> c#(c(z,x,a()),a(),y) -> c#(z,y,x)
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 16/49
    DPs:
     c#(c(z,x,a()),a(),y) -> c#(z,y,x)
     c#(c(z,x,a()),a(),y) -> c#(y,a(),f(c(z,y,x)))
    TRS:
     b(a(),f(b(b(z,y),a()))) -> z
     c(c(z,x,a()),a(),y) -> f(f(c(y,a(),f(c(z,y,x)))))
     f(f(c(a(),y,z))) -> b(y,b(z,z))
    Arctic Interpretation Processor:
     dimension: 2
     interpretation:
      [c#](x0, x1, x2) = [0 1]x0 + [0 0]x1 + [1 1]x2 + [0],
      
                        [-& 0 ]     [0 0]     [0 0]     [0]
      [c](x0, x1, x2) = [0  1 ]x0 + [2 1]x1 + [2 0]x2 + [0],
      
                [0  -&]     [1]
      [f](x0) = [0  -&]x0 + [2],
      
                    [0  0 ]     [0  0 ]     [0 ]
      [b](x0, x1) = [-& 0 ]x0 + [-& 0 ]x1 + [-&],
      
            [0]
      [a] = [2]
     orientation:
      c#(c(z,x,a()),a(),y) = [3 2]x + [1 1]y + [1 2]z + [3] >= [1 1]x + [0 0]y + [0 1]z + [0] = c#(z,y,x)
      
      c#(c(z,x,a()),a(),y) = [3 2]x + [1 1]y + [1 2]z + [3] >= [1 1]x + [1 1]y + [-& 1 ]z + [3] = c#(y,a(),f(c(z,y,x)))
      
                                [0 0]    [0 0]    [2]         
      b(a(),f(b(b(z,y),a()))) = [0 0]y + [0 0]z + [2] >= z = z
      
                            [2 1]    [0 0]    [0 1]    [2]    [0 0]    [0 0]    [-& 0 ]    [2]                             
      c(c(z,x,a()),a(),y) = [3 2]x + [2 0]y + [1 2]z + [3] >= [0 0]x + [0 0]y + [-& 0 ]z + [2] = f(f(c(y,a(),f(c(z,y,x)))))
      
                         [0 0]    [0 0]    [2]    [0  0 ]    [0  0 ]    [0 ]              
      f(f(c(a(),y,z))) = [0 0]y + [0 0]z + [2] >= [-& 0 ]y + [-& 0 ]z + [-&] = b(y,b(z,z))
     problem:
      DPs:
       c#(c(z,x,a()),a(),y) -> c#(y,a(),f(c(z,y,x)))
      TRS:
       b(a(),f(b(b(z,y),a()))) -> z
       c(c(z,x,a()),a(),y) -> f(f(c(y,a(),f(c(z,y,x)))))
       f(f(c(a(),y,z))) -> b(y,b(z,z))
     Matrix Interpretation Processor: dim=3
      
      interpretation:
       [c#](x0, x1, x2) = [1 0 0]x0 + [1 0 0]x2,
       
                         [0 0 0]     [0 0 1]     [1 0 0]  
       [c](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + [0 0 0]x2
                         [1 0 0]     [1 1 1]     [1 0 0]  ,
       
                 [0 1 0]  
       [f](x0) = [1 1 0]x0
                 [0 0 1]  ,
       
                     [0 0 0]     [1 0 0]     [0]
       [b](x0, x1) = [0 0 1]x0 + [1 0 0]x1 + [0]
                     [1 1 1]     [1 0 0]     [1],
       
             [1]
       [a] = [0]
             [0]
      orientation:
       c#(c(z,x,a()),a(),y) = [0 0 1]x + [1 0 0]y + [1] >= [1 0 0]y = c#(y,a(),f(c(z,y,x)))
       
                                 [1 0 0]    [1 1 1]    [2]         
       b(a(),f(b(b(z,y),a()))) = [1 0 0]y + [1 1 1]z + [2] >= z = z
                                 [1 0 0]    [1 1 1]    [4]         
       
                             [0 0 0]    [1 0 0]    [0]    [0 0 0]    [0]                             
       c(c(z,x,a()),a(),y) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]y + [0] = f(f(c(y,a(),f(c(z,y,x)))))
                             [0 0 1]    [1 0 0]    [2]    [1 0 0]    [1]                             
       
                          [0 0 1]    [1 0 0]    [0]    [0 0 0]    [1 0 0]    [0]              
       f(f(c(a(),y,z))) = [0 0 1]y + [1 0 0]z + [0] >= [0 0 1]y + [1 0 0]z + [0] = b(y,b(z,z))
                          [1 1 1]    [1 0 0]    [1]    [1 1 1]    [1 0 0]    [1]              
      problem:
       DPs:
        
       TRS:
        b(a(),f(b(b(z,y),a()))) -> z
        c(c(z,x,a()),a(),y) -> f(f(c(y,a(),f(c(z,y,x)))))
        f(f(c(a(),y,z))) -> b(y,b(z,z))
      Qed