Problem:
 f(f(a())) -> f(g(n__f(n__a())))
 f(X) -> n__f(X)
 a() -> n__a()
 activate(n__f(X)) -> f(activate(X))
 activate(n__a()) -> a()
 activate(X) -> X

Proof:
 Bounds Processor:
  bound: 3
  enrichment: match
  automaton:
   final states: {6,5,4}
   transitions:
    a1() -> 35*
    f1(25) -> 26*
    activate1(27) -> 28*
    activate1(24) -> 25*
    activate1(33) -> 34*
    n__a1() -> 19*
    n__f1(17) -> 18*
    n__f1(9) -> 10*
    n__f1(11) -> 12*
    n__a2() -> 41*
    n__f2(37) -> 38*
    f0(2) -> 4*
    f0(1) -> 4*
    f0(3) -> 4*
    f2(47) -> 48*
    a0() -> 5*
    g2(46) -> 47*
    g0(2) -> 1*
    g0(1) -> 1*
    g0(3) -> 1*
    n__f3(51) -> 52*
    n__f0(2) -> 2*
    n__f0(1) -> 2*
    n__f0(3) -> 2*
    n__a0() -> 3*
    activate0(2) -> 6*
    activate0(1) -> 6*
    activate0(3) -> 6*
    1 -> 6,27,11
    2 -> 6,24,17
    3 -> 6,33,9
    10 -> 4*
    12 -> 4*
    18 -> 4*
    19 -> 5*
    24 -> 25*
    25 -> 37*
    26 -> 25,6
    27 -> 28,25
    28 -> 25*
    33 -> 34*
    34 -> 25*
    35 -> 34,25,6
    38 -> 46,26,6
    41 -> 35,6
    47 -> 51*
    48 -> 26,25,6,37
    52 -> 48,26
  problem:
   
  Qed