YES

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

Proof:
 DP Processor:
  DPs:
   f#(f(a(),x),a()) -> f#(a(),a())
   f#(f(a(),x),a()) -> f#(x,f(a(),a()))
   f#(f(a(),x),a()) -> f#(f(x,f(a(),a())),a())
   f#(f(a(),x),a()) -> f#(a(),f(f(x,f(a(),a())),a()))
  TRS:
   f(f(a(),x),a()) -> f(a(),f(f(x,f(a(),a())),a()))
  EDG Processor:
   DPs:
    f#(f(a(),x),a()) -> f#(a(),a())
    f#(f(a(),x),a()) -> f#(x,f(a(),a()))
    f#(f(a(),x),a()) -> f#(f(x,f(a(),a())),a())
    f#(f(a(),x),a()) -> f#(a(),f(f(x,f(a(),a())),a()))
   TRS:
    f(f(a(),x),a()) -> f(a(),f(f(x,f(a(),a())),a()))
   graph:
    f#(f(a(),x),a()) -> f#(f(x,f(a(),a())),a()) ->
    f#(f(a(),x),a()) -> f#(a(),a())
    f#(f(a(),x),a()) -> f#(f(x,f(a(),a())),a()) ->
    f#(f(a(),x),a()) -> f#(x,f(a(),a()))
    f#(f(a(),x),a()) -> f#(f(x,f(a(),a())),a()) ->
    f#(f(a(),x),a()) -> f#(f(x,f(a(),a())),a())
    f#(f(a(),x),a()) -> f#(f(x,f(a(),a())),a()) ->
    f#(f(a(),x),a()) -> f#(a(),f(f(x,f(a(),a())),a()))
   SCC Processor:
    #sccs: 1
    #rules: 1
    #arcs: 4/16
    DPs:
     f#(f(a(),x),a()) -> f#(f(x,f(a(),a())),a())
    TRS:
     f(f(a(),x),a()) -> f(a(),f(f(x,f(a(),a())),a()))
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [f#](x0, x1) = -3x0 + -7x1 + 0,
      
      [f](x0, x1) = -3x0 + -2x1 + 0,
      
      [a] = 7
     orientation:
      f#(f(a(),x),a()) = -5x + 1 >= -6x + 0 = f#(f(x,f(a(),a())),a())
      
      f(f(a(),x),a()) = -5x + 5 >= -8x + 4 = f(a(),f(f(x,f(a(),a())),a()))
     problem:
      DPs:
       
      TRS:
       f(f(a(),x),a()) -> f(a(),f(f(x,f(a(),a())),a()))
     Qed