YES

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

Proof:
 DP Processor:
  DPs:
   f#(x,f(a(),a())) -> f#(a(),x)
   f#(x,f(a(),a())) -> f#(f(a(),a()),a())
   f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(a(),x))
  TRS:
   f(x,f(a(),a())) -> f(f(f(a(),a()),a()),f(a(),x))
  EDG Processor:
   DPs:
    f#(x,f(a(),a())) -> f#(a(),x)
    f#(x,f(a(),a())) -> f#(f(a(),a()),a())
    f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(a(),x))
   TRS:
    f(x,f(a(),a())) -> f(f(f(a(),a()),a()),f(a(),x))
   graph:
    f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(a(),x)) ->
    f#(x,f(a(),a())) -> f#(a(),x)
    f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(a(),x)) ->
    f#(x,f(a(),a())) -> f#(f(a(),a()),a())
    f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(a(),x)) ->
    f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(a(),x))
    f#(x,f(a(),a())) -> f#(a(),x) -> f#(x,f(a(),a())) -> f#(a(),x)
    f#(x,f(a(),a())) -> f#(a(),x) ->
    f#(x,f(a(),a())) -> f#(f(a(),a()),a())
    f#(x,f(a(),a())) -> f#(a(),x) -> f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(a(),x))
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 6/9
    DPs:
     f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(a(),x))
     f#(x,f(a(),a())) -> f#(a(),x)
    TRS:
     f(x,f(a(),a())) -> f(f(f(a(),a()),a()),f(a(),x))
    Bounds Processor:
     bound: 1
     enrichment: match-dp
     automaton:
      final states: {5}
      transitions:
       f{#,1}(17,15) -> 3*
       f{#,1}(17,19) -> 5*
       f{#,1}(14,17) -> 3*
       f1(17,16) -> 15*
       f1(14,2) -> 15*
       f1(14,8) -> 19*
       f1(14,14) -> 16*
       f1(16,14) -> 17*
       f1(17,15) -> 15*
       f1(14,1) -> 15*
       f1(14,3) -> 15*
       f1(14,17) -> 15*
       a1() -> 14*
       f{#,0}(3,1) -> 3*
       f{#,0}(3,3) -> 3*
       f{#,0}(1,2) -> 3*
       f{#,0}(1,8) -> 5*
       f{#,0}(2,1) -> 3*
       f{#,0}(2,3) -> 3*
       f{#,0}(3,2) -> 3*
       f{#,0}(8,6) -> 5*
       f{#,0}(1,1) -> 3*
       f{#,0}(1,3) -> 3*
       f{#,0}(2,2) -> 3*
       f0(3,1) -> 2*
       f0(3,3) -> 2*
       f0(1,2) -> 2*
       f0(1,4) -> 6*
       f0(7,1) -> 8*
       f0(2,1) -> 2*
       f0(2,3) -> 2*
       f0(3,2) -> 2*
       f0(1,1) -> 7,2
       f0(1,3) -> 2*
       f0(2,2) -> 6,2
       a0() -> 1*
       1 -> 4*
       2 -> 4*
       3 -> 4*
     problem:
      DPs:
       f#(x,f(a(),a())) -> f#(a(),x)
      TRS:
       f(x,f(a(),a())) -> f(f(f(a(),a()),a()),f(a(),x))
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [f#](x0, x1) = x0 + x1,
       
       [f](x0, x1) = 1,
       
       [a] = 0
      orientation:
       f#(x,f(a(),a())) = x + 1 >= x = f#(a(),x)
       
       f(x,f(a(),a())) = 1 >= 1 = f(f(f(a(),a()),a()),f(a(),x))
      problem:
       DPs:
        
       TRS:
        f(x,f(a(),a())) -> f(f(f(a(),a()),a()),f(a(),x))
      Qed