Problem:
 f(X) -> g(n__h(n__f(X)))
 h(X) -> n__h(X)
 f(X) -> n__f(X)
 activate(n__h(X)) -> h(activate(X))
 activate(n__f(X)) -> f(activate(X))
 activate(X) -> X

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {6,5,4}
   transitions:
    f1(51) -> 52*
    activate1(45) -> 46*
    activate1(35) -> 36*
    activate1(43) -> 44*
    h1(36) -> 37*
    n__f1(15) -> 16*
    n__f1(21) -> 22*
    n__f1(11) -> 12*
    n__h1(12) -> 13*
    n__h1(29) -> 30*
    n__h1(31) -> 32*
    n__h1(23) -> 24*
    g1(13) -> 14*
    n__f2(57) -> 58*
    f0(2) -> 4*
    f0(1) -> 4*
    f0(3) -> 4*
    n__h2(63) -> 64*
    n__h2(58) -> 59*
    g0(2) -> 1*
    g0(1) -> 1*
    g0(3) -> 1*
    g2(59) -> 60*
    n__h0(2) -> 2*
    n__h0(1) -> 2*
    n__h0(3) -> 2*
    n__f0(2) -> 3*
    n__f0(1) -> 3*
    n__f0(3) -> 3*
    h0(2) -> 5*
    h0(1) -> 5*
    h0(3) -> 5*
    activate0(2) -> 6*
    activate0(1) -> 6*
    activate0(3) -> 6*
    1 -> 6,43,29,15
    2 -> 6,35,31,21
    3 -> 6,45,23,11
    12 -> 4*
    14 -> 4*
    16 -> 12*
    22 -> 12*
    24 -> 5*
    30 -> 5*
    32 -> 5*
    35 -> 36*
    36 -> 63,51
    37 -> 36,51,6
    43 -> 44*
    44 -> 36*
    45 -> 46,36
    46 -> 36*
    51 -> 57*
    52 -> 46,36,51,6
    58 -> 52,6
    60 -> 52,6
    64 -> 37,6
  problem:
   
  Qed