YES

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

Proof:
 DP Processor:
  DPs:
   f#(x,f(a(),y)) -> f#(a(),a())
   f#(x,f(a(),y)) -> f#(f(a(),a()),a())
   f#(x,f(a(),y)) -> f#(y,f(f(a(),a()),a()))
   f#(x,f(a(),y)) -> f#(f(y,f(f(a(),a()),a())),x)
  TRS:
   f(x,f(a(),y)) -> f(f(y,f(f(a(),a()),a())),x)
  EDG Processor:
   DPs:
    f#(x,f(a(),y)) -> f#(a(),a())
    f#(x,f(a(),y)) -> f#(f(a(),a()),a())
    f#(x,f(a(),y)) -> f#(y,f(f(a(),a()),a()))
    f#(x,f(a(),y)) -> f#(f(y,f(f(a(),a()),a())),x)
   TRS:
    f(x,f(a(),y)) -> f(f(y,f(f(a(),a()),a())),x)
   graph:
    f#(x,f(a(),y)) -> f#(f(y,f(f(a(),a()),a())),x) ->
    f#(x,f(a(),y)) -> f#(a(),a())
    f#(x,f(a(),y)) -> f#(f(y,f(f(a(),a()),a())),x) ->
    f#(x,f(a(),y)) -> f#(f(a(),a()),a())
    f#(x,f(a(),y)) -> f#(f(y,f(f(a(),a()),a())),x) ->
    f#(x,f(a(),y)) -> f#(y,f(f(a(),a()),a()))
    f#(x,f(a(),y)) -> f#(f(y,f(f(a(),a()),a())),x) ->
    f#(x,f(a(),y)) -> f#(f(y,f(f(a(),a()),a())),x)
   SCC Processor:
    #sccs: 1
    #rules: 1
    #arcs: 4/16
    DPs:
     f#(x,f(a(),y)) -> f#(f(y,f(f(a(),a()),a())),x)
    TRS:
     f(x,f(a(),y)) -> f(f(y,f(f(a(),a()),a())),x)
    Bounds Processor:
     bound: 1
     enrichment: match-dp
     automaton:
      final states: {4}
      transitions:
       f{#,0}(7,3) -> 4*
       f0(5,1) -> 6*
       f0(1,2) -> 2*
       f0(2,1) -> 2*
       f0(3,6) -> 7*
       f0(1,1) -> 5,2
       f0(2,2) -> 2*
       a0() -> 1*
       f{#,1}(18,17) -> 4*
       f{#,1}(15,7) -> 4*
       f{#,1}(17,15) -> 4*
       f1(2,14) -> 15*
       f1(14,14) -> 18*
       f1(6,14) -> 17*
       f1(1,14) -> 15*
       f1(13,12) -> 14*
       f1(12,12) -> 13*
       a1() -> 12*
       1 -> 3*
       2 -> 3*
     problem:
      DPs:
       
      TRS:
       f(x,f(a(),y)) -> f(f(y,f(f(a(),a()),a())),x)
     Qed