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)
     Arctic Interpretation Processor:
      dimension: 2
      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:
       [f#](x0) = [0  -&]x0,
       
                 [0  -&]     [-&]
       [f](x0) = [1  1 ]x0 + [1 ],
       
                     [-& -&]     [0 0]  
       [b](x0, x1) = [1  1 ]x0 + [1 0]x1,
       
                         [-& 1 ]     [-& -&]     [1  1 ]     [0 ]
       [c](x0, x1, x2) = [0  1 ]x0 + [0  1 ]x1 + [-& -&]x2 + [-&],
       
             [0]
       [a] = [1]
      orientation:
       f#(c(x,y,z)) = [-& 1 ]x + [1 1]z + [0] >= [0 0]z = f#(b(y,z))
       
                                      [2 2]    [1 2]    [-& -&]    [3]    [1  1 ]    [1 2]    [-& -&]    [3]                    
       b(z,b(c(a(),y,a()),f(f(x)))) = [3 3]x + [1 2]y + [1  1 ]z + [3] >= [-& -&]x + [1 2]y + [1  1 ]z + [3] = c(c(y,a(),z),z,x)
       
                               [1 2]    [1 2]    [2]    [0 0]    [-& -&]          
       c(c(z,y,a()),a(),a()) = [1 2]y + [1 2]z + [2] >= [1 0]y + [1  1 ]z = b(z,y)
      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) = [0,0,1]
      pi(b) = [0,0,0,1,1]
      pi(c#) = [0,0,0,1,1]
      pi(b#) = [0,0,0,1,1]
     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