YES

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

Proof:
 DP Processor:
  DPs:
   c#(z,x,a()) -> f#(z)
   c#(z,x,a()) -> b#(f(z),z)
   c#(z,x,a()) -> b#(b(f(z),z),x)
   c#(z,x,a()) -> f#(b(b(f(z),z),x))
   b#(y,b(z,a())) -> f#(a())
   b#(y,b(z,a())) -> c#(f(a()),y,z)
   b#(y,b(z,a())) -> b#(c(f(a()),y,z),z)
   b#(y,b(z,a())) -> f#(b(c(f(a()),y,z),z))
  TRS:
   c(z,x,a()) -> f(b(b(f(z),z),x))
   b(y,b(z,a())) -> f(b(c(f(a()),y,z),z))
   f(c(c(z,a(),a()),x,a())) -> z
  TDG Processor:
   DPs:
    c#(z,x,a()) -> f#(z)
    c#(z,x,a()) -> b#(f(z),z)
    c#(z,x,a()) -> b#(b(f(z),z),x)
    c#(z,x,a()) -> f#(b(b(f(z),z),x))
    b#(y,b(z,a())) -> f#(a())
    b#(y,b(z,a())) -> c#(f(a()),y,z)
    b#(y,b(z,a())) -> b#(c(f(a()),y,z),z)
    b#(y,b(z,a())) -> f#(b(c(f(a()),y,z),z))
   TRS:
    c(z,x,a()) -> f(b(b(f(z),z),x))
    b(y,b(z,a())) -> f(b(c(f(a()),y,z),z))
    f(c(c(z,a(),a()),x,a())) -> z
   graph:
    b#(y,b(z,a())) -> b#(c(f(a()),y,z),z) ->
    b#(y,b(z,a())) -> f#(b(c(f(a()),y,z),z))
    b#(y,b(z,a())) -> b#(c(f(a()),y,z),z) ->
    b#(y,b(z,a())) -> b#(c(f(a()),y,z),z)
    b#(y,b(z,a())) -> b#(c(f(a()),y,z),z) ->
    b#(y,b(z,a())) -> c#(f(a()),y,z)
    b#(y,b(z,a())) -> b#(c(f(a()),y,z),z) ->
    b#(y,b(z,a())) -> f#(a())
    b#(y,b(z,a())) -> c#(f(a()),y,z) ->
    c#(z,x,a()) -> f#(b(b(f(z),z),x))
    b#(y,b(z,a())) -> c#(f(a()),y,z) ->
    c#(z,x,a()) -> b#(b(f(z),z),x)
    b#(y,b(z,a())) -> c#(f(a()),y,z) -> c#(z,x,a()) -> b#(f(z),z)
    b#(y,b(z,a())) -> c#(f(a()),y,z) -> c#(z,x,a()) -> f#(z)
    c#(z,x,a()) -> b#(b(f(z),z),x) ->
    b#(y,b(z,a())) -> f#(b(c(f(a()),y,z),z))
    c#(z,x,a()) -> b#(b(f(z),z),x) ->
    b#(y,b(z,a())) -> b#(c(f(a()),y,z),z)
    c#(z,x,a()) -> b#(b(f(z),z),x) ->
    b#(y,b(z,a())) -> c#(f(a()),y,z)
    c#(z,x,a()) -> b#(b(f(z),z),x) -> b#(y,b(z,a())) -> f#(a())
    c#(z,x,a()) -> b#(f(z),z) -> b#(y,b(z,a())) -> f#(b(c(f(a()),y,z),z))
    c#(z,x,a()) -> b#(f(z),z) -> b#(y,b(z,a())) -> b#(c(f(a()),y,z),z)
    c#(z,x,a()) -> b#(f(z),z) -> b#(y,b(z,a())) -> c#(f(a()),y,z)
    c#(z,x,a()) -> b#(f(z),z) -> b#(y,b(z,a())) -> f#(a())
   SCC Processor:
    #sccs: 1
    #rules: 4
    #arcs: 16/64
    DPs:
     b#(y,b(z,a())) -> b#(c(f(a()),y,z),z)
     b#(y,b(z,a())) -> c#(f(a()),y,z)
     c#(z,x,a()) -> b#(f(z),z)
     c#(z,x,a()) -> b#(b(f(z),z),x)
    TRS:
     c(z,x,a()) -> f(b(b(f(z),z),x))
     b(y,b(z,a())) -> f(b(c(f(a()),y,z),z))
     f(c(c(z,a(),a()),x,a())) -> z
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [b#](x0, x1) = x0 + x1 + 0,
      
      [c#](x0, x1, x2) = 1x0 + x1 + x2 + 1,
      
      [b](x0, x1) = x0 + x1 + 1,
      
      [f](x0) = x0 + 0,
      
      [c](x0, x1, x2) = 1x0 + x1 + x2 + 1,
      
      [a] = 0
     orientation:
      b#(y,b(z,a())) = y + z + 1 >= y + z + 1 = b#(c(f(a()),y,z),z)
      
      b#(y,b(z,a())) = y + z + 1 >= y + z + 1 = c#(f(a()),y,z)
      
      c#(z,x,a()) = x + 1z + 1 >= z + 0 = b#(f(z),z)
      
      c#(z,x,a()) = x + 1z + 1 >= x + z + 1 = b#(b(f(z),z),x)
      
      c(z,x,a()) = x + 1z + 1 >= x + z + 1 = f(b(b(f(z),z),x))
      
      b(y,b(z,a())) = y + z + 1 >= y + z + 1 = f(b(c(f(a()),y,z),z))
      
      f(c(c(z,a(),a()),x,a())) = x + 2z + 2 >= z = z
     problem:
      DPs:
       b#(y,b(z,a())) -> b#(c(f(a()),y,z),z)
       b#(y,b(z,a())) -> c#(f(a()),y,z)
       c#(z,x,a()) -> b#(b(f(z),z),x)
      TRS:
       c(z,x,a()) -> f(b(b(f(z),z),x))
       b(y,b(z,a())) -> f(b(c(f(a()),y,z),z))
       f(c(c(z,a(),a()),x,a())) -> z
     Arctic Interpretation Processor:
      dimension: 1
      interpretation:
       [b#](x0, x1) = 2x0 + x1 + 4,
       
       [c#](x0, x1, x2) = 4x0 + 2x1 + x2 + 5,
       
       [b](x0, x1) = x0 + 1x1 + 0,
       
       [f](x0) = -3x0 + 0,
       
       [c](x0, x1, x2) = 2x0 + x1 + -2x2 + -16,
       
       [a] = 4
      orientation:
       b#(y,b(z,a())) = 2y + z + 5 >= 2y + z + 5 = b#(c(f(a()),y,z),z)
       
       b#(y,b(z,a())) = 2y + z + 5 >= 2y + z + 5 = c#(f(a()),y,z)
       
       c#(z,x,a()) = 2x + 4z + 5 >= x + 3z + 4 = b#(b(f(z),z),x)
       
       c(z,x,a()) = x + 2z + 2 >= -2x + -2z + 0 = f(b(b(f(z),z),x))
       
       b(y,b(z,a())) = y + 1z + 6 >= -3y + -2z + 0 = f(b(c(f(a()),y,z),z))
       
       f(c(c(z,a(),a()),x,a())) = -3x + 1z + 3 >= z = z
      problem:
       DPs:
        b#(y,b(z,a())) -> b#(c(f(a()),y,z),z)
        b#(y,b(z,a())) -> c#(f(a()),y,z)
       TRS:
        c(z,x,a()) -> f(b(b(f(z),z),x))
        b(y,b(z,a())) -> f(b(c(f(a()),y,z),z))
        f(c(c(z,a(),a()),x,a())) -> z
      SCC Processor:
       #sccs: 1
       #rules: 1
       #arcs: 8/4
       DPs:
        b#(y,b(z,a())) -> b#(c(f(a()),y,z),z)
       TRS:
        c(z,x,a()) -> f(b(b(f(z),z),x))
        b(y,b(z,a())) -> f(b(c(f(a()),y,z),z))
        f(c(c(z,a(),a()),x,a())) -> z
       Subterm Criterion Processor:
        simple projection:
         pi(b#) = 1
        problem:
         DPs:
          
         TRS:
          c(z,x,a()) -> f(b(b(f(z),z),x))
          b(y,b(z,a())) -> f(b(c(f(a()),y,z),z))
          f(c(c(z,a(),a()),x,a())) -> z
        Qed