YES

Problem:
 f(f(a(),x),a()) -> f(f(f(x,a()),f(a(),a())),a())

Proof:
 DP Processor:
  DPs:
   f#(f(a(),x),a()) -> f#(a(),a())
   f#(f(a(),x),a()) -> f#(x,a())
   f#(f(a(),x),a()) -> f#(f(x,a()),f(a(),a()))
   f#(f(a(),x),a()) -> f#(f(f(x,a()),f(a(),a())),a())
  TRS:
   f(f(a(),x),a()) -> f(f(f(x,a()),f(a(),a())),a())
  EDG Processor:
   DPs:
    f#(f(a(),x),a()) -> f#(a(),a())
    f#(f(a(),x),a()) -> f#(x,a())
    f#(f(a(),x),a()) -> f#(f(x,a()),f(a(),a()))
    f#(f(a(),x),a()) -> f#(f(f(x,a()),f(a(),a())),a())
   TRS:
    f(f(a(),x),a()) -> f(f(f(x,a()),f(a(),a())),a())
   graph:
    f#(f(a(),x),a()) -> f#(x,a()) -> f#(f(a(),x),a()) -> f#(a(),a())
    f#(f(a(),x),a()) -> f#(x,a()) -> f#(f(a(),x),a()) -> f#(x,a())
    f#(f(a(),x),a()) -> f#(x,a()) ->
    f#(f(a(),x),a()) -> f#(f(x,a()),f(a(),a()))
    f#(f(a(),x),a()) -> f#(x,a()) -> f#(f(a(),x),a()) -> f#(f(f(x,a()),f(a(),a())),a())
   Restore Modifier:
    DPs:
     f#(f(a(),x),a()) -> f#(a(),a())
     f#(f(a(),x),a()) -> f#(x,a())
     f#(f(a(),x),a()) -> f#(f(x,a()),f(a(),a()))
     f#(f(a(),x),a()) -> f#(f(f(x,a()),f(a(),a())),a())
    TRS:
     f(f(a(),x),a()) -> f(f(f(x,a()),f(a(),a())),a())
    SCC Processor:
     #sccs: 1
     #rules: 1
     #arcs: 4/16
     DPs:
      f#(f(a(),x),a()) -> f#(x,a())
     TRS:
      f(f(a(),x),a()) -> f(f(f(x,a()),f(a(),a())),a())
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [f#](x0, x1) = x0 + 1,
       
       [f](x0, x1) = x1 + 1,
       
       [a] = 0
      orientation:
       f#(f(a(),x),a()) = x + 2 >= x + 1 = f#(x,a())
       
       f(f(a(),x),a()) = 1 >= 1 = f(f(f(x,a()),f(a(),a())),a())
      problem:
       DPs:
        
       TRS:
        f(f(a(),x),a()) -> f(f(f(x,a()),f(a(),a())),a())
      Qed