YES

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

Proof:
 DP Processor:
  DPs:
   f#(y,f(x,f(a(),x))) -> f#(a(),y)
   f#(y,f(x,f(a(),x))) -> f#(x,a())
   f#(y,f(x,f(a(),x))) -> f#(a(),f(x,a()))
   f#(y,f(x,f(a(),x))) -> f#(f(a(),f(x,a())),f(a(),y))
   f#(x,f(x,y)) -> f#(x,a())
   f#(x,f(x,y)) -> f#(f(x,a()),a())
   f#(x,f(x,y)) -> f#(f(f(x,a()),a()),a())
  TRS:
   f(y,f(x,f(a(),x))) -> f(f(a(),f(x,a())),f(a(),y))
   f(x,f(x,y)) -> f(f(f(x,a()),a()),a())
  EDG Processor:
   DPs:
    f#(y,f(x,f(a(),x))) -> f#(a(),y)
    f#(y,f(x,f(a(),x))) -> f#(x,a())
    f#(y,f(x,f(a(),x))) -> f#(a(),f(x,a()))
    f#(y,f(x,f(a(),x))) -> f#(f(a(),f(x,a())),f(a(),y))
    f#(x,f(x,y)) -> f#(x,a())
    f#(x,f(x,y)) -> f#(f(x,a()),a())
    f#(x,f(x,y)) -> f#(f(f(x,a()),a()),a())
   TRS:
    f(y,f(x,f(a(),x))) -> f(f(a(),f(x,a())),f(a(),y))
    f(x,f(x,y)) -> f(f(f(x,a()),a()),a())
   graph:
    f#(y,f(x,f(a(),x))) -> f#(f(a(),f(x,a())),f(a(),y)) ->
    f#(y,f(x,f(a(),x))) -> f#(a(),y)
    f#(y,f(x,f(a(),x))) -> f#(f(a(),f(x,a())),f(a(),y)) ->
    f#(y,f(x,f(a(),x))) -> f#(x,a())
    f#(y,f(x,f(a(),x))) -> f#(f(a(),f(x,a())),f(a(),y)) ->
    f#(y,f(x,f(a(),x))) -> f#(a(),f(x,a()))
    f#(y,f(x,f(a(),x))) -> f#(f(a(),f(x,a())),f(a(),y)) ->
    f#(y,f(x,f(a(),x))) -> f#(f(a(),f(x,a())),f(a(),y))
    f#(y,f(x,f(a(),x))) -> f#(f(a(),f(x,a())),f(a(),y)) ->
    f#(x,f(x,y)) -> f#(x,a())
    f#(y,f(x,f(a(),x))) -> f#(f(a(),f(x,a())),f(a(),y)) ->
    f#(x,f(x,y)) -> f#(f(x,a()),a())
    f#(y,f(x,f(a(),x))) -> f#(f(a(),f(x,a())),f(a(),y)) ->
    f#(x,f(x,y)) -> f#(f(f(x,a()),a()),a())
    f#(y,f(x,f(a(),x))) -> f#(a(),f(x,a())) ->
    f#(x,f(x,y)) -> f#(x,a())
    f#(y,f(x,f(a(),x))) -> f#(a(),f(x,a())) ->
    f#(x,f(x,y)) -> f#(f(x,a()),a())
    f#(y,f(x,f(a(),x))) -> f#(a(),f(x,a())) ->
    f#(x,f(x,y)) -> f#(f(f(x,a()),a()),a())
    f#(y,f(x,f(a(),x))) -> f#(a(),y) ->
    f#(y,f(x,f(a(),x))) -> f#(a(),y)
    f#(y,f(x,f(a(),x))) -> f#(a(),y) ->
    f#(y,f(x,f(a(),x))) -> f#(x,a())
    f#(y,f(x,f(a(),x))) -> f#(a(),y) ->
    f#(y,f(x,f(a(),x))) -> f#(a(),f(x,a()))
    f#(y,f(x,f(a(),x))) -> f#(a(),y) ->
    f#(y,f(x,f(a(),x))) -> f#(f(a(),f(x,a())),f(a(),y))
    f#(y,f(x,f(a(),x))) -> f#(a(),y) -> f#(x,f(x,y)) -> f#(x,a())
    f#(y,f(x,f(a(),x))) -> f#(a(),y) ->
    f#(x,f(x,y)) -> f#(f(x,a()),a())
    f#(y,f(x,f(a(),x))) -> f#(a(),y) -> f#(x,f(x,y)) -> f#(f(f(x,a()),a()),a())
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 17/49
    DPs:
     f#(y,f(x,f(a(),x))) -> f#(f(a(),f(x,a())),f(a(),y))
     f#(y,f(x,f(a(),x))) -> f#(a(),y)
    TRS:
     f(y,f(x,f(a(),x))) -> f(f(a(),f(x,a())),f(a(),y))
     f(x,f(x,y)) -> f(f(f(x,a()),a()),a())
    Bounds Processor:
     bound: 1
     enrichment: match-dp
     automaton:
      final states: {1}
      transitions:
       f0(19,10) -> 4*
       f0(3,5) -> 6*
       f0(3,24) -> 4*
       f0(21,3) -> 23*,2
       f0(4,10) -> 4*
       f0(23,3) -> 26*
       f0(3,23) -> 6,20*,4
       f0(26,10) -> 4*
       f0(24,10) -> 4*
       f0(6,10) -> 4*
       f0(24,3) -> 2,27*
       f0(19,3) -> 21*
       f0(3,25) -> 6,4,20*
       f0(3,6) -> 4*
       f0(3,22) -> 20*,6,4
       f0(27,10) -> 4*
       f0(25,10) -> 4*
       f0(27,3) -> 2,26*
       f0(25,3) -> 27*,2
       f0(5,3) -> 19*,4,11
       f0(3,2) -> 4*
       f0(3,20) -> 4*
       f0(4,3) -> 21*,6,2
       f0(23,10) -> 4*
       f0(3,21) -> 4*
       f0(20,3) -> 21*,2
       f0(3,11) -> 6*
       f0(22,3) -> 25*
       f0(3,27) -> 6,20*,4
       f0(3,26) -> 6,4,20*
       f0(22,10) -> 4*
       f0(26,3) -> 26*,2
       f0(6,3) -> 2*
       f0(2,3) -> 22*,4,5
       f0(3,19) -> 20*,6,4
       f0(3,4) -> 4*
       f0(21,10) -> 4*
       f0(20,10) -> 4*
       f{#,1}(20,10) -> 1*
       f{#,1}(24,10) -> 1*
       f{#,1}(25,10) -> 1*
       f{#,1}(21,10) -> 1*
       f{#,1}(6,10) -> 1*
       f{#,1}(26,10) -> 1*
       f{#,1}(27,10) -> 1*
       f30() -> 2*
       f{#,0}(3,3) -> 1*
       f{#,0}(25,10) -> 1*
       f{#,0}(6,27) -> 1*
       f{#,0}(20,24) -> 1*
       f{#,0}(24,23) -> 1*
       f{#,0}(26,23) -> 1*
       f{#,0}(27,27) -> 1*
       f{#,0}(23,27) -> 1*
       f{#,0}(4,19) -> 1*
       f{#,0}(19,4) -> 1*
       f{#,0}(4,10) -> 1*
       f{#,0}(3,23) -> 1*
       f{#,0}(6,25) -> 1*
       f{#,0}(4,22) -> 1*
       f{#,0}(27,19) -> 1*
       f{#,0}(19,25) -> 1*
       f{#,0}(21,24) -> 1*
       f{#,0}(19,22) -> 1*
       f{#,0}(20,20) -> 1*
       f{#,0}(19,27) -> 1*
       f{#,0}(26,22) -> 1*
       f{#,0}(27,10) -> 1*
       f{#,0}(4,4) -> 1*
       f{#,0}(6,26) -> 1*
       f{#,0}(26,4) -> 1*
       f{#,0}(3,24) -> 1*
       f{#,0}(24,27) -> 1*
       f{#,0}(3,21) -> 1*
       f{#,0}(4,27) -> 1*
       f{#,0}(25,26) -> 1*
       f{#,0}(22,10) -> 1*
       f{#,0}(6,23) -> 1*
       f{#,0}(3,4) -> 1*
       f{#,0}(27,25) -> 1*
       f{#,0}(21,26) -> 1*
       f{#,0}(6,22) -> 1*
       f{#,0}(20,19) -> 1*
       f{#,0}(19,20) -> 1*
       f{#,0}(21,20) -> 1*
       f{#,0}(3,19) -> 1*
       f{#,0}(25,24) -> 1*
       f{#,0}(20,10) -> 1*
       f{#,0}(27,20) -> 1*
       f{#,0}(22,26) -> 1*
       f{#,0}(22,20) -> 1*
       f{#,0}(25,19) -> 1*
       f{#,0}(22,23) -> 1*
       f{#,0}(20,22) -> 1*
       f{#,0}(21,22) -> 1*
       f{#,0}(6,19) -> 1*
       f{#,0}(25,20) -> 1*
       f{#,0}(23,24) -> 1*
       f{#,0}(22,4) -> 1*
       f{#,0}(20,23) -> 1*
       f{#,0}(24,25) -> 1*
       f{#,0}(26,26) -> 1*
       f{#,0}(20,25) -> 1*
       f{#,0}(21,19) -> 1*
       f{#,0}(21,23) -> 1*
       f{#,0}(20,4) -> 1*
       f{#,0}(25,23) -> 1*
       f{#,0}(24,19) -> 1*
       f{#,0}(6,24) -> 1*
       f{#,0}(23,20) -> 1*
       f{#,0}(22,27) -> 1*
       f{#,0}(23,10) -> 1*
       f{#,0}(25,22) -> 1*
       f{#,0}(19,24) -> 1*
       f{#,0}(26,24) -> 1*
       f{#,0}(4,26) -> 1*
       f{#,0}(6,4) -> 1*
       f{#,0}(23,26) -> 1*
       f{#,0}(27,22) -> 1*
       f{#,0}(24,26) -> 1*
       f{#,0}(6,20) -> 1*
       f{#,0}(24,24) -> 1*
       f{#,0}(24,20) -> 1*
       f{#,0}(26,10) -> 1*
       f{#,0}(23,22) -> 1*
       f{#,0}(27,24) -> 1*
       f{#,0}(21,27) -> 1*
       f{#,0}(24,22) -> 1*
       f{#,0}(27,23) -> 1*
       f{#,0}(19,23) -> 1*
       f{#,0}(20,26) -> 1*
       f{#,0}(19,19) -> 1*
       f{#,0}(22,24) -> 1*
       f{#,0}(26,27) -> 1*
       f{#,0}(3,25) -> 1*
       f{#,0}(3,26) -> 1*
       f{#,0}(3,27) -> 1*
       f{#,0}(26,19) -> 1*
       f{#,0}(20,27) -> 1*
       f{#,0}(27,4) -> 1*
       f{#,0}(26,20) -> 1*
       f{#,0}(22,25) -> 1*
       f{#,0}(4,24) -> 1*
       f{#,0}(3,20) -> 1*
       f{#,0}(22,22) -> 1*
       f{#,0}(21,25) -> 1*
       f{#,0}(27,26) -> 1*
       f{#,0}(3,22) -> 1*
       f{#,0}(25,27) -> 1*
       f{#,0}(25,4) -> 1*
       f{#,0}(24,4) -> 1*
       f{#,0}(24,10) -> 1*
       f{#,0}(4,20) -> 1*
       f{#,0}(23,4) -> 1*
       f{#,0}(22,19) -> 1*
       f{#,0}(21,4) -> 1*
       f{#,0}(23,23) -> 1*
       f{#,0}(3,6) -> 1*
       f{#,0}(4,23) -> 1*
       f{#,0}(25,25) -> 1*
       f{#,0}(19,26) -> 1*
       f{#,0}(23,25) -> 1*
       f{#,0}(26,25) -> 1*
       f{#,0}(19,10) -> 1*
       f{#,0}(23,19) -> 1*
       f{#,0}(4,25) -> 1*
       a1() -> 3*
       f1(25,3) -> 20,27*,2
       f1(26,3) -> 20,26*,2
       f1(3,3) -> 10*
       f1(3,10) -> 6*
       f1(11,3) -> 4,20*,6
       f1(19,3) -> 20,21,24*
       f1(10,3) -> 11*
     problem:
      DPs:
       f#(y,f(x,f(a(),x))) -> f#(a(),y)
      TRS:
       f(y,f(x,f(a(),x))) -> f(f(a(),f(x,a())),f(a(),y))
       f(x,f(x,y)) -> f(f(f(x,a()),a()),a())
     Bounds Processor:
      bound: 0
      enrichment: match-dp
      automaton:
       final states: {1}
       transitions:
        f130() -> 2*
        a0() -> 3*
        f{#,0}(3,3) -> 1*
        f{#,0}(3,2) -> 1*
      problem:
       DPs:
        
       TRS:
        f(y,f(x,f(a(),x))) -> f(f(a(),f(x,a())),f(a(),y))
        f(x,f(x,y)) -> f(f(f(x,a()),a()),a())
      Qed