YES

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

Proof:
 DP Processor:
  DPs:
   f#(a(),f(f(a(),x),a())) -> f#(a(),f(a(),x))
   f#(a(),f(f(a(),x),a())) -> f#(f(a(),f(a(),x)),a())
  TRS:
   f(a(),f(f(a(),x),a())) -> f(f(a(),f(a(),x)),a())
  EDG Processor:
   DPs:
    f#(a(),f(f(a(),x),a())) -> f#(a(),f(a(),x))
    f#(a(),f(f(a(),x),a())) -> f#(f(a(),f(a(),x)),a())
   TRS:
    f(a(),f(f(a(),x),a())) -> f(f(a(),f(a(),x)),a())
   graph:
    f#(a(),f(f(a(),x),a())) -> f#(a(),f(a(),x)) ->
    f#(a(),f(f(a(),x),a())) -> f#(a(),f(a(),x))
    f#(a(),f(f(a(),x),a())) -> f#(a(),f(a(),x)) ->
    f#(a(),f(f(a(),x),a())) -> f#(f(a(),f(a(),x)),a())
   Restore Modifier:
    DPs:
     f#(a(),f(f(a(),x),a())) -> f#(a(),f(a(),x))
     f#(a(),f(f(a(),x),a())) -> f#(f(a(),f(a(),x)),a())
    TRS:
     f(a(),f(f(a(),x),a())) -> f(f(a(),f(a(),x)),a())
    SCC Processor:
     #sccs: 1
     #rules: 1
     #arcs: 2/4
     DPs:
      f#(a(),f(f(a(),x),a())) -> f#(a(),f(a(),x))
     TRS:
      f(a(),f(f(a(),x),a())) -> f(f(a(),f(a(),x)),a())
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [f#](x0, x1) = x1,
       
       [f](x0, x1) = x0 + x1 + 1,
       
       [a] = 0
      orientation:
       f#(a(),f(f(a(),x),a())) = x + 2 >= x + 1 = f#(a(),f(a(),x))
       
       f(a(),f(f(a(),x),a())) = x + 3 >= x + 3 = f(f(a(),f(a(),x)),a())
      problem:
       DPs:
        
       TRS:
        f(a(),f(f(a(),x),a())) -> f(f(a(),f(a(),x)),a())
      Qed