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: 2
  enrichment: roof
  automaton:
   final states: {10,9,6}
   transitions:
    f0(9,6) -> 6*
    f0(9,10) -> 6*
    f0(10,9) -> 6*
    f0(6,6) -> 6*
    f0(6,10) -> 6*
    f0(9,9) -> 6*
    f0(10,6) -> 6*
    f0(10,10) -> 6*
    f0(6,9) -> 6*
    a0() -> 6*
    n__b0() -> 6*
    b0() -> 6*
    activate0(10) -> 6*
    activate0(9) -> 6*
    activate0(6) -> 6*
    b1() -> 6*
    n__b1() -> 9*,6,7
    a1() -> 10*,6,8
    f1(8,7) -> 6*
    f1(8,9) -> 6*
    f1(10,7) -> 6*
    f1(10,9) -> 6*
    n__b2() -> 7,9*,6
    a2() -> 8,10*,6
    9 -> 6*
    10 -> 6*
  problem:
   
  Qed