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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {5,4}
   transitions:
    f1(24) -> 25*
    f1(26) -> 27*
    f1(18) -> 19*
    n__f1(10) -> 11*
    n__f1(16) -> 17*
    n__f1(8) -> 9*
    n__f2(30) -> 31*
    n__f2(36) -> 37*
    n__f2(38) -> 39*
    f0(2) -> 4*
    f0(1) -> 4*
    f0(3) -> 4*
    a0() -> 1*
    g0(2) -> 2*
    g0(1) -> 2*
    g0(3) -> 2*
    n__f0(2) -> 3*
    n__f0(1) -> 3*
    n__f0(3) -> 3*
    activate0(2) -> 5*
    activate0(1) -> 5*
    activate0(3) -> 5*
    1 -> 5,24,10
    2 -> 5,18,16
    3 -> 5,26,8
    9 -> 4*
    11 -> 4*
    17 -> 4*
    18 -> 36*
    19 -> 5*
    24 -> 38*
    25 -> 5*
    26 -> 30*
    27 -> 5*
    31 -> 27*
    37 -> 19,5
    39 -> 25,5
  problem:
   
  Qed