YES

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

Proof:
 DP Processor:
  DPs:
   b#(f(b(x,z)),y) -> b#(y,z)
   b#(f(b(x,z)),y) -> b#(z,b(y,z))
   c#(f(f(c(x,a(),z))),a(),y) -> b#(a(),z)
   c#(f(f(c(x,a(),z))),a(),y) -> b#(y,f(b(a(),z)))
  TRS:
   b(f(b(x,z)),y) -> f(f(f(b(z,b(y,z)))))
   c(f(f(c(x,a(),z))),a(),y) -> b(y,f(b(a(),z)))
   b(b(c(b(a(),a()),a(),z),f(a())),y) -> z
  TDG Processor:
   DPs:
    b#(f(b(x,z)),y) -> b#(y,z)
    b#(f(b(x,z)),y) -> b#(z,b(y,z))
    c#(f(f(c(x,a(),z))),a(),y) -> b#(a(),z)
    c#(f(f(c(x,a(),z))),a(),y) -> b#(y,f(b(a(),z)))
   TRS:
    b(f(b(x,z)),y) -> f(f(f(b(z,b(y,z)))))
    c(f(f(c(x,a(),z))),a(),y) -> b(y,f(b(a(),z)))
    b(b(c(b(a(),a()),a(),z),f(a())),y) -> z
   graph:
    c#(f(f(c(x,a(),z))),a(),y) -> b#(a(),z) ->
    b#(f(b(x,z)),y) -> b#(z,b(y,z))
    c#(f(f(c(x,a(),z))),a(),y) -> b#(a(),z) ->
    b#(f(b(x,z)),y) -> b#(y,z)
    c#(f(f(c(x,a(),z))),a(),y) -> b#(y,f(b(a(),z))) ->
    b#(f(b(x,z)),y) -> b#(z,b(y,z))
    c#(f(f(c(x,a(),z))),a(),y) -> b#(y,f(b(a(),z))) ->
    b#(f(b(x,z)),y) -> b#(y,z)
    b#(f(b(x,z)),y) -> b#(z,b(y,z)) ->
    b#(f(b(x,z)),y) -> b#(z,b(y,z))
    b#(f(b(x,z)),y) -> b#(z,b(y,z)) -> b#(f(b(x,z)),y) -> b#(y,z)
    b#(f(b(x,z)),y) -> b#(y,z) -> b#(f(b(x,z)),y) -> b#(z,b(y,z))
    b#(f(b(x,z)),y) -> b#(y,z) -> b#(f(b(x,z)),y) -> b#(y,z)
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 8/16
    DPs:
     b#(f(b(x,z)),y) -> b#(y,z)
     b#(f(b(x,z)),y) -> b#(z,b(y,z))
    TRS:
     b(f(b(x,z)),y) -> f(f(f(b(z,b(y,z)))))
     c(f(f(c(x,a(),z))),a(),y) -> b(y,f(b(a(),z)))
     b(b(c(b(a(),a()),a(),z),f(a())),y) -> z
    Usable Rule Processor:
     DPs:
      b#(f(b(x,z)),y) -> b#(y,z)
      b#(f(b(x,z)),y) -> b#(z,b(y,z))
     TRS:
      b(f(b(x,z)),y) -> f(f(f(b(z,b(y,z)))))
      b(b(c(b(a(),a()),a(),z),f(a())),y) -> z
     Arctic Interpretation Processor:
      dimension: 2
      usable rules:
       b(f(b(x,z)),y) -> f(f(f(b(z,b(y,z)))))
       b(b(c(b(a(),a()),a(),z),f(a())),y) -> z
      interpretation:
       [b#](x0, x1) = [-& 0 ]x0 + [1 1]x1,
       
                         [1  -&]     [0 0]     [1  1 ]     [0 ]
       [c](x0, x1, x2) = [-& -&]x0 + [1 0]x1 + [-& 0 ]x2 + [-&],
       
             [1 ]
       [a] = [-&],
       
                 [-& -&]     [0]
       [f](x0) = [2  -&]x0 + [0],
       
                     [-& 0 ]     [0  0 ]     [0]
       [b](x0, x1) = [0  0 ]x0 + [0  -&]x1 + [1]
      orientation:
       b#(f(b(x,z)),y) = [-& 2 ]x + [1 1]y + [2 2]z + [2] >= [-& 0 ]y + [1 1]z = b#(y,z)
       
       b#(f(b(x,z)),y) = [-& 2 ]x + [1 1]y + [2 2]z + [2] >= [1 1]y + [1 1]z + [2] = b#(z,b(y,z))
       
                        [-& 2 ]    [0  0 ]    [2 2]    [2]    [0]                       
       b(f(b(x,z)),y) = [-& 2 ]x + [0  -&]y + [2 2]z + [2] >= [2] = f(f(f(b(z,b(y,z)))))
       
                                            [0  0 ]    [1 1]    [2]         
       b(b(c(b(a(),a()),a(),z),f(a())),y) = [0  -&]y + [1 1]z + [3] >= z = z
      problem:
       DPs:
        b#(f(b(x,z)),y) -> b#(z,b(y,z))
       TRS:
        b(f(b(x,z)),y) -> f(f(f(b(z,b(y,z)))))
        b(b(c(b(a(),a()),a(),z),f(a())),y) -> z
      Restore Modifier:
       DPs:
        b#(f(b(x,z)),y) -> b#(z,b(y,z))
       TRS:
        b(f(b(x,z)),y) -> f(f(f(b(z,b(y,z)))))
        c(f(f(c(x,a(),z))),a(),y) -> b(y,f(b(a(),z)))
        b(b(c(b(a(),a()),a(),z),f(a())),y) -> z
       Subterm Criterion Processor:
        simple projection:
         pi(b#) = 0
        problem:
         DPs:
          
         TRS:
          b(f(b(x,z)),y) -> f(f(f(b(z,b(y,z)))))
          c(f(f(c(x,a(),z))),a(),y) -> b(y,f(b(a(),z)))
          b(b(c(b(a(),a()),a(),z),f(a())),y) -> z
        Qed