YES

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

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