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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {7,6,5,4}
   transitions:
    g1(55) -> 56*
    activate1(62) -> 63*
    activate1(64) -> 65*
    activate1(54) -> 55*
    a1() -> 53*
    f1(40) -> 41*
    f1(10) -> 11*
    f1(46) -> 47*
    f1(48) -> 49*
    n__g1(30) -> 31*
    n__g1(32) -> 33*
    n__g1(9) -> 10*
    n__g1(38) -> 39*
    n__a1() -> 8*
    n__f1(20) -> 21*
    n__f1(26) -> 27*
    n__f1(18) -> 19*
    n__f1(8) -> 9*
    n__g2(86) -> 87*
    f0(2) -> 4*
    f0(1) -> 4*
    f0(3) -> 4*
    n__a2() -> 84*
    n__f0(2) -> 1*
    n__f0(1) -> 1*
    n__f0(3) -> 1*
    n__f2(82) -> 83*
    n__f2(74) -> 75*
    n__f2(76) -> 77*
    n__f2(68) -> 69*
    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 -> 7,62,46,32,20
    2 -> 7,54,40,38,26
    3 -> 7,64,48,30,18
    8 -> 5*
    10 -> 68*
    11 -> 47,7,4
    19 -> 4*
    21 -> 4*
    27 -> 4*
    31 -> 6*
    33 -> 6*
    39 -> 6*
    40 -> 82*
    41 -> 63,55,7
    46 -> 74*
    47 -> 63,55,7
    48 -> 76*
    49 -> 63,55,7
    53 -> 55,7
    54 -> 55*
    55 -> 86*
    56 -> 65,55,7
    62 -> 63,55
    63 -> 55*
    64 -> 65*
    65 -> 55*
    69 -> 11*
    75 -> 47*
    77 -> 49,7
    83 -> 41,7
    84 -> 53,7
    87 -> 56,7
  problem:
   
  Qed