YES

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

Proof:
 Uncurry Processor (mirror):
  a2(x,a()) -> a1(f(f(x,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}(2,18) -> 19*
     a{2,1}(2,3) -> 11*
     a{2,1}(3,2) -> 6*
     a{1,1}(20) -> 6*
     a{1,1}(17) -> 18*
     f1(3,18) -> 19*
     f1(19,17) -> 20*
     a1() -> 17*
     f40() -> 4*
     a{1,0}(12) -> 6*
     a{1,0}(2) -> 3*
     a{1,0}(4) -> 8*
     a{1,0}(6) -> 1*
     a{1,0}(3) -> 5*
     f0(3,3) -> 11*
     f0(11,2) -> 12*
     f0(4,3) -> 5*
     f0(5,2) -> 6*
     a0() -> 2*
     a{2,0}(4,4) -> 7*
     a{2,0}(2,3) -> 11*
     a{2,0}(3,2) -> 6*
     a{2,0}(4,3) -> 5*
     1 -> 7*
   problem:
    
   Qed