Problem:
 active(f(f(a()))) -> mark(f(g(f(a()))))
 active(f(X)) -> f(active(X))
 f(mark(X)) -> mark(f(X))
 proper(f(X)) -> f(proper(X))
 proper(a()) -> ok(a())
 proper(g(X)) -> g(proper(X))
 f(ok(X)) -> ok(f(X))
 g(ok(X)) -> ok(g(X))
 top(mark(X)) -> top(proper(X))
 top(ok(X)) -> top(active(X))

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {8,7,6,5,4}
   transitions:
    top1(46) -> 47*
    active1(69) -> 70*
    active1(61) -> 62*
    active1(63) -> 64*
    proper1(55) -> 56*
    proper1(45) -> 46*
    proper1(53) -> 54*
    ok1(35) -> 36*
    ok1(25) -> 26*
    ok1(27) -> 28*
    g1(37) -> 38*
    g1(34) -> 35*
    g1(43) -> 44*
    f1(17) -> 18*
    f1(19) -> 20*
    f1(9) -> 10*
    a1() -> 25*
    mark1(10) -> 11*
    top2(75) -> 76*
    active0(2) -> 4*
    active0(1) -> 4*
    active0(3) -> 4*
    active2(74) -> 75*
    f0(2) -> 5*
    f0(1) -> 5*
    f0(3) -> 5*
    a0() -> 1*
    mark0(2) -> 2*
    mark0(1) -> 2*
    mark0(3) -> 2*
    g0(2) -> 7*
    g0(1) -> 7*
    g0(3) -> 7*
    proper0(2) -> 6*
    proper0(1) -> 6*
    proper0(3) -> 6*
    ok0(2) -> 3*
    ok0(1) -> 3*
    ok0(3) -> 3*
    top0(2) -> 8*
    top0(1) -> 8*
    top0(3) -> 8*
    1 -> 63,53,37,17
    2 -> 61,45,34,9
    3 -> 69,55,43,19
    10 -> 27*
    11 -> 10,27,5
    18 -> 10*
    20 -> 10*
    25 -> 74*
    26 -> 54,46,6
    28 -> 20,10,27,5
    36 -> 44,35,7
    38 -> 35*
    44 -> 35*
    47 -> 8*
    54 -> 46*
    56 -> 46*
    62 -> 46*
    64 -> 46*
    70 -> 46*
    76 -> 47,8
  problem:
   
  Qed