YES

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

Proof:
 DP Processor:
  DPs:
   c#(c(z,y,a()),a(),a()) -> b#(z,y)
   f#(c(x,y,z)) -> b#(y,z)
   f#(c(x,y,z)) -> f#(b(y,z))
   f#(c(x,y,z)) -> c#(z,f(b(y,z)),a())
   b#(z,b(c(a(),y,a()),f(f(x)))) -> c#(y,a(),z)
   b#(z,b(c(a(),y,a()),f(f(x)))) -> c#(c(y,a(),z),z,x)
  TRS:
   c(c(z,y,a()),a(),a()) -> b(z,y)
   f(c(x,y,z)) -> c(z,f(b(y,z)),a())
   b(z,b(c(a(),y,a()),f(f(x)))) -> c(c(y,a(),z),z,x)
  TDG Processor:
   DPs:
    c#(c(z,y,a()),a(),a()) -> b#(z,y)
    f#(c(x,y,z)) -> b#(y,z)
    f#(c(x,y,z)) -> f#(b(y,z))
    f#(c(x,y,z)) -> c#(z,f(b(y,z)),a())
    b#(z,b(c(a(),y,a()),f(f(x)))) -> c#(y,a(),z)
    b#(z,b(c(a(),y,a()),f(f(x)))) -> c#(c(y,a(),z),z,x)
   TRS:
    c(c(z,y,a()),a(),a()) -> b(z,y)
    f(c(x,y,z)) -> c(z,f(b(y,z)),a())
    b(z,b(c(a(),y,a()),f(f(x)))) -> c(c(y,a(),z),z,x)
   graph:
    f#(c(x,y,z)) -> f#(b(y,z)) -> f#(c(x,y,z)) -> c#(z,f(b(y,z)),a())
    f#(c(x,y,z)) -> f#(b(y,z)) -> f#(c(x,y,z)) -> f#(b(y,z))
    f#(c(x,y,z)) -> f#(b(y,z)) -> f#(c(x,y,z)) -> b#(y,z)
    f#(c(x,y,z)) -> b#(y,z) ->
    b#(z,b(c(a(),y,a()),f(f(x)))) -> c#(c(y,a(),z),z,x)
    f#(c(x,y,z)) -> b#(y,z) ->
    b#(z,b(c(a(),y,a()),f(f(x)))) -> c#(y,a(),z)
    f#(c(x,y,z)) -> c#(z,f(b(y,z)),a()) ->
    c#(c(z,y,a()),a(),a()) -> b#(z,y)
    b#(z,b(c(a(),y,a()),f(f(x)))) -> c#(c(y,a(),z),z,x) ->
    c#(c(z,y,a()),a(),a()) -> b#(z,y)
    b#(z,b(c(a(),y,a()),f(f(x)))) -> c#(y,a(),z) ->
    c#(c(z,y,a()),a(),a()) -> b#(z,y)
    c#(c(z,y,a()),a(),a()) -> b#(z,y) ->
    b#(z,b(c(a(),y,a()),f(f(x)))) -> c#(c(y,a(),z),z,x)
    c#(c(z,y,a()),a(),a()) -> b#(z,y) -> b#(z,b(c(a(),y,a()),f(f(x)))) -> c#(y,a(),z)
   SCC Processor:
    #sccs: 2
    #rules: 4
    #arcs: 10/36
    DPs:
     f#(c(x,y,z)) -> f#(b(y,z))
    TRS:
     c(c(z,y,a()),a(),a()) -> b(z,y)
     f(c(x,y,z)) -> c(z,f(b(y,z)),a())
     b(z,b(c(a(),y,a()),f(f(x)))) -> c(c(y,a(),z),z,x)
    Matrix Interpretation Processor: dim=2
     
     interpretation:
      [f#](x0) = [1 0]x0 + [2],
      
                [1 2]     [1]
      [f](x0) = [2 0]x0 + [2],
      
                    [0 0]     [0 1]  
      [b](x0, x1) = [0 1]x0 + [0 1]x1,
      
                        [0 1]     [0 0]     [0 2]     [1]
      [c](x0, x1, x2) = [0 1]x0 + [0 1]x1 + [0 0]x2 + [0],
      
            [0]
      [a] = [0]
     orientation:
      f#(c(x,y,z)) = [0 1]x + [0 2]z + [3] >= [0 1]z + [2] = f#(b(y,z))
      
                              [0 1]    [0 1]    [1]    [0 1]    [0 0]          
      c(c(z,y,a()),a(),a()) = [0 1]y + [0 1]z + [0] >= [0 1]y + [0 1]z = b(z,y)
      
                    [0 3]    [0 2]    [0 2]    [2]    [0 1]    [1]                     
      f(c(x,y,z)) = [0 2]x + [0 0]y + [0 4]z + [4] >= [0 3]z + [2] = c(z,f(b(y,z)),a())
      
                                     [2 4]    [0 1]    [0 0]    [4]    [0 2]    [0 1]    [0 0]    [1]                    
      b(z,b(c(a(),y,a()),f(f(x)))) = [2 4]x + [0 1]y + [0 1]z + [4] >= [0 0]x + [0 1]y + [0 1]z + [0] = c(c(y,a(),z),z,x)
     problem:
      DPs:
       
      TRS:
       c(c(z,y,a()),a(),a()) -> b(z,y)
       f(c(x,y,z)) -> c(z,f(b(y,z)),a())
       b(z,b(c(a(),y,a()),f(f(x)))) -> c(c(y,a(),z),z,x)
     Qed
    
    DPs:
     b#(z,b(c(a(),y,a()),f(f(x)))) -> c#(y,a(),z)
     c#(c(z,y,a()),a(),a()) -> b#(z,y)
     b#(z,b(c(a(),y,a()),f(f(x)))) -> c#(c(y,a(),z),z,x)
    TRS:
     c(c(z,y,a()),a(),a()) -> b(z,y)
     f(c(x,y,z)) -> c(z,f(b(y,z)),a())
     b(z,b(c(a(),y,a()),f(f(x)))) -> c(c(y,a(),z),z,x)
    Matrix Interpretation Processor: dim=2
     
     interpretation:
      [b#](x0, x1) = [0 1]x0 + [0 1]x1 + [1],
      
      [c#](x0, x1, x2) = [0 1]x0 + [0 1]x1 + [1],
      
                [1 2]     [0]
      [f](x0) = [2 1]x0 + [1],
      
                    [0 0]     [0 1]     [1]
      [b](x0, x1) = [0 1]x0 + [0 1]x1 + [0],
      
                        [0 1]     [0 0]     [0 2]     [1]
      [c](x0, x1, x2) = [0 1]x0 + [0 1]x1 + [0 0]x2 + [0],
      
            [0]
      [a] = [0]
     orientation:
      b#(z,b(c(a(),y,a()),f(f(x)))) = [4 5]x + [0 1]y + [0 1]z + [3] >= [0 1]y + [1] = c#(y,a(),z)
      
      c#(c(z,y,a()),a(),a()) = [0 1]y + [0 1]z + [1] >= [0 1]y + [0 1]z + [1] = b#(z,y)
      
      b#(z,b(c(a(),y,a()),f(f(x)))) = [4 5]x + [0 1]y + [0 1]z + [3] >= [0 1]y + [0 1]z + [1] = c#(c(y,a(),z),z,x)
      
                              [0 1]    [0 1]    [1]    [0 1]    [0 0]    [1]         
      c(c(z,y,a()),a(),a()) = [0 1]y + [0 1]z + [0] >= [0 1]y + [0 1]z + [0] = b(z,y)
      
                    [0 3]    [0 2]    [0 2]    [1]    [0 0]    [0 1]    [1]                     
      f(c(x,y,z)) = [0 3]x + [0 1]y + [0 4]z + [3] >= [0 1]y + [0 4]z + [3] = c(z,f(b(y,z)),a())
      
                                     [4 5]    [0 1]    [0 0]    [3]    [0 2]    [0 1]    [0 0]    [1]                    
      b(z,b(c(a(),y,a()),f(f(x)))) = [4 5]x + [0 1]y + [0 1]z + [2] >= [0 0]x + [0 1]y + [0 1]z + [0] = c(c(y,a(),z),z,x)
     problem:
      DPs:
       c#(c(z,y,a()),a(),a()) -> b#(z,y)
      TRS:
       c(c(z,y,a()),a(),a()) -> b(z,y)
       f(c(x,y,z)) -> c(z,f(b(y,z)),a())
       b(z,b(c(a(),y,a()),f(f(x)))) -> c(c(y,a(),z),z,x)
     SCC Processor:
      #sccs: 0
      #rules: 0
      #arcs: 4/1