Problem:
 a__f(f(a())) -> a__f(g(f(a())))
 mark(f(X)) -> a__f(X)
 mark(a()) -> a()
 mark(g(X)) -> g(mark(X))
 a__f(X) -> f(X)

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {5,4}
   transitions:
    f1(40) -> 41*
    f1(46) -> 47*
    f1(6) -> 7*
    f1(48) -> 49*
    g1(30) -> 31*
    g1(7) -> 8*
    mark1(32) -> 33*
    mark1(29) -> 30*
    mark1(38) -> 39*
    a1() -> 6*
    a__f1(24) -> 25*
    a__f1(16) -> 17*
    a__f1(18) -> 19*
    a__f1(8) -> 9*
    f2(60) -> 61*
    f2(52) -> 53*
    f2(66) -> 67*
    f2(58) -> 59*
    a__f0(2) -> 4*
    a__f0(1) -> 4*
    a__f0(3) -> 4*
    f0(2) -> 1*
    f0(1) -> 1*
    f0(3) -> 1*
    a0() -> 2*
    g0(2) -> 3*
    g0(1) -> 3*
    g0(3) -> 3*
    mark0(2) -> 5*
    mark0(1) -> 5*
    mark0(3) -> 5*
    1 -> 46,32,18
    2 -> 48,29,16
    3 -> 40,38,24
    6 -> 30,5
    8 -> 66*
    9 -> 19,5,4
    16 -> 52*
    17 -> 33,30,5
    18 -> 58*
    19 -> 33,30,5
    24 -> 60*
    25 -> 33,30,5
    31 -> 39,30,5
    33 -> 30*
    39 -> 30*
    41 -> 4*
    47 -> 4*
    49 -> 4*
    53 -> 17*
    59 -> 19,5
    61 -> 25,5
    67 -> 9,4
  problem:
   
  Qed