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 + -2x1 + -16,
      
      [c#](x0, x1, x2) = 2x0 + -1x1 + -2x2 + 0,
      
      [b](x0, x1) = 1x0 + 1x1 + 0,
      
      [f](x0) = -5x0 + 0,
      
      [c](x0, x1, x2) = 3x0 + -1x1 + -4x2 + -16,
      
      [a] = 5
     orientation:
      b#(y,b(z,a())) = y + -1z + 4 >= -1y + -2z + 3 = b#(c(f(a()),y,z),z)
      
      b#(y,b(z,a())) = y + -1z + 4 >= -1y + -2z + 2 = c#(f(a()),y,z)
      
      c#(z,x,a()) = -1x + 2z + 3 >= -2z + 0 = b#(f(z),z)
      
      c#(z,x,a()) = -1x + 2z + 3 >= -2x + 1z + 1 = b#(b(f(z),z),x)
      
      c(z,x,a()) = -1x + 3z + 1 >= -4x + -3z + 0 = f(b(b(f(z),z),x))
      
      b(y,b(z,a())) = 1y + 2z + 7 >= -5y + -4z + 0 = f(b(c(f(a()),y,z),z))
      
      f(c(c(z,a(),a()),x,a())) = -6x + 1z + 2 >= z = z
     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