YES

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

Proof:
 Uncurry Processor (mirror):
  a2(x,a()) -> f(f(f(x,a()),a1(a())),a())
  f(a1(x3),x4) -> a2(x3,x4)
  f(a(),x4) -> a1(x4)
  Bounds Processor:
   bound: 1
   enrichment: match
   automaton:
    final states: {8,7,1}
    transitions:
     a{2,1}(2,3) -> 6*
     f1(4,13) -> 15*
     f1(15,14) -> 16*
     f1(16,13) -> 5*
     a1() -> 13*
     a{1,1}(13) -> 14*
     f40() -> 4*
     f0(4,2) -> 5*
     f0(5,3) -> 6*
     f0(6,2) -> 5,1
     a0() -> 2*
     a{1,0}(2) -> 3*
     a{1,0}(4) -> 8*
     a{2,0}(4,2) -> 5*
     a{2,0}(4,4) -> 7*
     a{2,0}(2,3) -> 6*
     1 -> 7*
     3 -> 5*
   problem:
    
   Qed