YES

Problem:
 f(X,X) -> f(a(),n__b())
 b() -> a()
 b() -> n__b()
 activate(n__b()) -> b()
 activate(X) -> X

Proof:
 Bounds Processor:
  bound: 1
  enrichment: top
  automaton:
   final states: {9,8,5,4,2,3,1}
   transitions:
    f50() -> 5*
    f0(8,9) -> 1*
    f0(3,9) -> 1*
    f0(8,2) -> 1*
    f0(3,2) -> 1*
    a0() -> 8*,4,3
    n__b0() -> 9*,4,2
    b0() -> 4*
    n__b1() -> 2,9*,4
    a1() -> 3,8*,4
  problem:
   
  Qed