YES

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

Proof:
 Extended Uncurrying Processor:
  application symbol: f
  symbol table:
   a ==> a0/0 a1/1 a2/2
   
  uncurry-rules:
   f(a1(x1),x2) -> a2(x1,x2)
   f(a0(),x1) -> a1(x1)
  eta-rules:
   
  problem:
   a2(a0(),x) -> f(f(x,a0()),a1(a1(a0())))
   f(a1(x1),x2) -> a2(x1,x2)
   f(a0(),x1) -> a1(x1)
  DP Processor:
   DPs:
    a{2,#}(a0(),x) -> f#(x,a0())
    a{2,#}(a0(),x) -> f#(f(x,a0()),a1(a1(a0())))
    f#(a1(x1),x2) -> a{2,#}(x1,x2)
   TRS:
    a2(a0(),x) -> f(f(x,a0()),a1(a1(a0())))
    f(a1(x1),x2) -> a2(x1,x2)
    f(a0(),x1) -> a1(x1)
   TDG Processor:
    DPs:
     a{2,#}(a0(),x) -> f#(x,a0())
     a{2,#}(a0(),x) -> f#(f(x,a0()),a1(a1(a0())))
     f#(a1(x1),x2) -> a{2,#}(x1,x2)
    TRS:
     a2(a0(),x) -> f(f(x,a0()),a1(a1(a0())))
     f(a1(x1),x2) -> a2(x1,x2)
     f(a0(),x1) -> a1(x1)
    graph:
     f#(a1(x1),x2) -> a{2,#}(x1,x2) ->
     a{2,#}(a0(),x) -> f#(f(x,a0()),a1(a1(a0())))
     f#(a1(x1),x2) -> a{2,#}(x1,x2) ->
     a{2,#}(a0(),x) -> f#(x,a0())
     a{2,#}(a0(),x) -> f#(f(x,a0()),a1(a1(a0()))) ->
     f#(a1(x1),x2) -> a{2,#}(x1,x2)
     a{2,#}(a0(),x) -> f#(x,a0()) -> f#(a1(x1),x2) -> a{2,#}(x1,x2)
    Bounds Processor:
     bound: 1
     enrichment: match-dp
     automaton:
      final states: {4}
      transitions:
       a{0,0}() -> 5*
       f0(18,7) -> 9*
       f0(8,5) -> 9*
       f0(20,7) -> 9*
       f0(5,5) -> 20*
       a{1,0}(5) -> 20,6
       a{1,0}(6) -> 7*
       a{2,#,0}(5,7) -> 4*
       a{2,#,0}(6,5) -> 4*
       a{2,0}(8,5) -> 9*
       a{2,0}(5,7) -> 9*
       f{#,1}(18,17) -> 4*
       f1(7,15) -> 18*
       a{0,1}() -> 15*
       a{1,1}(15) -> 16*
       a{1,1}(16) -> 17*
       f70() -> 8*
       a{2,1}(6,15) -> 18*
       f{#,0}(7,5) -> 4*
       f{#,0}(9,7) -> 4*
       6 -> 9*
     problem:
      DPs:
       a{2,#}(a0(),x) -> f#(x,a0())
       f#(a1(x1),x2) -> a{2,#}(x1,x2)
      TRS:
       a2(a0(),x) -> f(f(x,a0()),a1(a1(a0())))
       f(a1(x1),x2) -> a2(x1,x2)
       f(a0(),x1) -> a1(x1)
     Bounds Processor:
      bound: 0
      enrichment: match-dp
      automaton:
       final states: {1}
       transitions:
        a{2,#,0}(3,2) -> 1*
        f{#,0}(3,2) -> 1*
        f{#,0}(2,2) -> 1*
        f210() -> 3*
        a{0,0}() -> 2*
      problem:
       DPs:
        f#(a1(x1),x2) -> a{2,#}(x1,x2)
       TRS:
        a2(a0(),x) -> f(f(x,a0()),a1(a1(a0())))
        f(a1(x1),x2) -> a2(x1,x2)
        f(a0(),x1) -> a1(x1)
      SCC Processor:
       #sccs: 0
       #rules: 0
       #arcs: 4/1