Problem:
 f(f(a())) -> c(n__f(g(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: {6,5}
   transitions:
    f1(35) -> 36*
    f1(25) -> 26*
    f1(27) -> 28*
    f1(33) -> 34*
    n__f1(17) -> 18*
    n__f1(19) -> 20*
    n__f1(9) -> 10*
    n__f1(11) -> 12*
    n__f2(49) -> 50*
    n__f2(51) -> 52*
    n__f2(41) -> 42*
    n__f2(43) -> 44*
    f0(2) -> 5*
    f0(4) -> 5*
    f0(1) -> 5*
    f0(3) -> 5*
    a0() -> 1*
    c0(2) -> 2*
    c0(4) -> 2*
    c0(1) -> 2*
    c0(3) -> 2*
    n__f0(2) -> 3*
    n__f0(4) -> 3*
    n__f0(1) -> 3*
    n__f0(3) -> 3*
    g0(2) -> 4*
    g0(4) -> 4*
    g0(1) -> 4*
    g0(3) -> 4*
    activate0(2) -> 6*
    activate0(4) -> 6*
    activate0(1) -> 6*
    activate0(3) -> 6*
    1 -> 6,33,11
    2 -> 6,25,19
    3 -> 6,35,9
    4 -> 6,27,17
    10 -> 5*
    12 -> 5*
    18 -> 5*
    20 -> 5*
    25 -> 41*
    26 -> 6*
    27 -> 49*
    28 -> 6*
    33 -> 43*
    34 -> 6*
    35 -> 51*
    36 -> 6*
    42 -> 26*
    44 -> 34*
    50 -> 28,6
    52 -> 36,6
  problem:
   
  Qed