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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {7,6,5,4}
   transitions:
    g1(64) -> 65*
    g1(56) -> 57*
    g1(58) -> 59*
    a1() -> 52*
    f1(50) -> 51*
    f1(42) -> 43*
    f1(12) -> 13*
    f1(44) -> 45*
    f1(14) -> 15*
    n__g1(34) -> 35*
    n__g1(36) -> 37*
    n__g1(28) -> 29*
    n__g1(13) -> 14*
    n__a1() -> 12*
    n__f1(22) -> 23*
    n__f1(24) -> 25*
    n__f1(16) -> 17*
    n__g2(96) -> 97*
    n__g2(88) -> 89*
    n__g2(90) -> 91*
    n__a2() -> 86*
    f0(2) -> 4*
    f0(1) -> 4*
    f0(3) -> 4*
    n__f2(70) -> 71*
    n__f2(84) -> 85*
    n__f2(76) -> 77*
    n__f2(78) -> 79*
    n__f2(68) -> 69*
    n__f0(2) -> 1*
    n__f0(1) -> 1*
    n__f0(3) -> 1*
    n__a0() -> 2*
    n__g0(2) -> 3*
    n__g0(1) -> 3*
    n__g0(3) -> 3*
    a0() -> 5*
    g0(2) -> 6*
    g0(1) -> 6*
    g0(3) -> 6*
    activate0(2) -> 7*
    activate0(1) -> 7*
    activate0(3) -> 7*
    1 -> 7,58,44,34,22
    2 -> 7,56,42,36,24
    3 -> 7,64,50,28,16
    12 -> 84,5
    14 -> 76*
    15 -> 45,7,4
    17 -> 4*
    23 -> 4*
    25 -> 4*
    29 -> 6*
    35 -> 6*
    37 -> 6*
    42 -> 68*
    43 -> 7*
    44 -> 70*
    45 -> 7*
    50 -> 78*
    51 -> 7*
    52 -> 7*
    56 -> 88*
    57 -> 7*
    58 -> 90*
    59 -> 7*
    64 -> 96*
    65 -> 7*
    69 -> 43*
    71 -> 45*
    77 -> 15*
    79 -> 51,7
    85 -> 13*
    86 -> 52,7
    89 -> 57*
    91 -> 59,7
    97 -> 65,7
  problem:
   
  Qed