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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {6,5}
   transitions:
    f1(55) -> 56*
    f1(12) -> 13*
    f1(69) -> 70*
    f1(14) -> 15*
    f1(61) -> 62*
    f1(63) -> 64*
    g1(53) -> 54*
    g1(13) -> 14*
    mark1(25) -> 26*
    mark1(27) -> 28*
    mark1(17) -> 18*
    mark1(33) -> 34*
    c1(45) -> 46*
    c1(15) -> 16*
    c1(47) -> 48*
    c1(37) -> 38*
    c1(39) -> 40*
    a1() -> 12*
    a__f1(18) -> 19*
    f2(75) -> 76*
    f2(77) -> 78*
    f2(71) -> 72*
    a__f0(2) -> 5*
    a__f0(4) -> 5*
    a__f0(1) -> 5*
    a__f0(3) -> 5*
    c2(78) -> 79*
    f0(2) -> 1*
    f0(4) -> 1*
    f0(1) -> 1*
    f0(3) -> 1*
    g2(76) -> 77*
    a0() -> 2*
    a2() -> 75*
    c0(2) -> 3*
    c0(4) -> 3*
    c0(1) -> 3*
    c0(3) -> 3*
    g0(2) -> 4*
    g0(4) -> 4*
    g0(1) -> 4*
    g0(3) -> 4*
    mark0(2) -> 6*
    mark0(4) -> 6*
    mark0(1) -> 6*
    mark0(3) -> 6*
    1 -> 61,45,27
    2 -> 69,37,17
    3 -> 55,47,33
    4 -> 63,39,25
    12 -> 18,53,6
    16 -> 5*
    18 -> 71,53
    19 -> 28,18,53,6
    26 -> 18*
    28 -> 18*
    34 -> 18*
    38 -> 34,18,53,6
    40 -> 34,18,53,6
    46 -> 34,18,53,6
    48 -> 34,18,53,6
    54 -> 26,18,53,6
    56 -> 5*
    62 -> 5*
    64 -> 5*
    70 -> 5*
    72 -> 19,6
    79 -> 19,28,6,18,71
  problem:
   
  Qed