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
    Matrix Interpretation Processor: dim=4
     
     interpretation:
      [b#](x0, x1) = [0 0 0 1]x0 + [0 0 0 1]x1 + [1],
      
                        [0 0 0 1]     [0 0 0 0]     [0 1 1 0]  
                        [0 1 1 1]     [0 1 0 0]     [1 0 1 0]  
      [c](x0, x1, x2) = [0 1 0 1]x0 + [0 0 0 0]x1 + [1 1 1 1]x2
                        [0 1 0 0]     [0 0 0 0]     [0 0 0 1]  ,
      
            [0]
            [1]
      [a] = [0]
            [0],
      
                [0 0 1 0]     [0]
                [1 0 0 0]     [0]
      [f](x0) = [0 0 0 0]x0 + [0]
                [1 0 0 0]     [1],
      
                    [0 0 1 0]     [0 0 0 1]  
                    [0 0 1 0]     [0 0 0 0]  
      [b](x0, x1) = [1 0 1 0]x0 + [1 1 1 0]x1
                    [0 0 0 1]     [0 0 0 0]  
     orientation:
      b#(f(b(x,z)),y) = [0 0 1 0]x + [0 0 0 1]y + [0 0 0 1]z + [2] >= [0 0 0 1]y + [0 0 0 1]z + [1] = b#(y,z)
      
      b#(f(b(x,z)),y) = [0 0 1 0]x + [0 0 0 1]y + [0 0 0 1]z + [2] >= [0 0 0 1]y + [0 0 0 1]z + [1] = b#(z,b(y,z))
      
                       [0 0 0 0]    [0 0 0 1]    [0 0 0 0]    [0]    [0]                       
                       [0 0 0 0]    [0 0 0 0]    [0 0 0 0]    [0]    [0]                       
      b(f(b(x,z)),y) = [1 0 1 0]x + [1 1 1 0]y + [1 1 1 0]z + [0] >= [0] = f(f(f(b(z,b(y,z)))))
                       [0 0 1 0]    [0 0 0 0]    [0 0 0 1]    [1]    [1]                       
      
                                  [0 1 0 1]    [0 1 1 0]    [1 1 1 1]    [1]    [0 0 1 0]    [0 0 0 1]    [1]                   
                                  [0 2 0 2]    [1 0 1 0]    [2 2 2 2]    [2]    [0 0 1 0]    [0 0 0 0]    [0]                   
      c(f(f(c(x,a(),z))),a(),y) = [0 2 0 2]x + [1 1 1 1]y + [2 2 2 2]z + [1] >= [1 0 1 0]y + [1 1 1 1]z + [0] = b(y,f(b(a(),z)))
                                  [0 1 0 1]    [0 0 0 1]    [1 1 1 1]    [0]    [0 0 0 1]    [0 0 0 0]    [0]                   
      
                                           [0 0 0 1]    [1 2 2 1]    [0]         
                                           [0 0 0 0]    [1 2 2 1]    [0]         
      b(b(c(b(a(),a()),a(),z),f(a())),y) = [1 1 1 0]y + [2 3 3 2]z + [1] >= z = z
                                           [0 0 0 0]    [0 0 0 1]    [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