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)
    Usable Rule Processor:
     DPs:
      f#(c(x,y,z)) -> f#(b(y,z))
     TRS:
      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)
     Matrix Interpretation Processor: dim=3
      
      usable rules:
       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)
      interpretation:
                         [1 0 1]     [1 0 1]     [0 0 0]     [1]
       [c](x0, x1, x2) = [1 0 0]x0 + [1 0 0]x1 + [1 0 0]x2 + [1]
                         [0 0 0]     [0 0 0]     [0 0 0]     [0],
       
                 [1 1 1]     [1]
       [f](x0) = [0 0 0]x0 + [1]
                 [0 0 0]     [1],
       
             [1]
       [a] = [0]
             [1],
       
       [f#](x0) = [0 1 0]x0 + [1],
       
                     [1 0 1]     [1 0 0]  
       [b](x0, x1) = [1 0 0]x0 + [1 0 0]x1
                     [0 0 0]     [0 0 0]  
      orientation:
       f#(c(x,y,z)) = [1 0 0]x + [1 0 0]y + [1 0 0]z + [2] >= [1 0 0]y + [1 0 0]z + [1] = f#(b(y,z))
       
                                      [1 1 1]    [1 0 1]    [1 0 1]    [7]    [0 0 0]    [1 0 1]    [1 0 1]    [4]                    
       b(z,b(c(a(),y,a()),f(f(x)))) = [1 1 1]x + [1 0 1]y + [1 0 0]z + [7] >= [1 0 0]x + [1 0 1]y + [1 0 0]z + [4] = c(c(y,a(),z),z,x)
                                      [0 0 0]    [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]    [0 0 0]    [0]                    
       
                               [1 0 1]    [1 0 1]    [4]    [1 0 0]    [1 0 1]          
       c(c(z,y,a()),a(),a()) = [1 0 1]y + [1 0 1]z + [4] >= [1 0 0]y + [1 0 0]z = b(z,y)
                               [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]          
      problem:
       DPs:
        
       TRS:
        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)
      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)
    Subterm Criterion Processor:
     simple projection:
      pi(c) = [0,0,0,1,1]
      pi(b) = [0,0,0,1,1]
      pi(c#) = [0,2]
      pi(b#) = [0,0,1,1]
     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