Problem:
 active(f(f(a()))) -> mark(c(f(g(f(a())))))
 active(f(X)) -> f(active(X))
 active(g(X)) -> g(active(X))
 f(mark(X)) -> mark(f(X))
 g(mark(X)) -> mark(g(X))
 proper(f(X)) -> f(proper(X))
 proper(a()) -> ok(a())
 proper(c(X)) -> c(proper(X))
 proper(g(X)) -> g(proper(X))
 f(ok(X)) -> ok(f(X))
 c(ok(X)) -> ok(c(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: {9,8,7,6,5,4}
   transitions:
    top1(68) -> 69*
    active1(84) -> 85*
    active1(86) -> 87*
    active1(78) -> 79*
    proper1(70) -> 71*
    proper1(67) -> 68*
    proper1(76) -> 77*
    ok1(60) -> 61*
    ok1(50) -> 51*
    ok1(40) -> 41*
    ok1(42) -> 43*
    g1(32) -> 33*
    g1(34) -> 35*
    g1(24) -> 25*
    c1(52) -> 53*
    c1(49) -> 50*
    c1(58) -> 59*
    f1(22) -> 23*
    f1(16) -> 17*
    f1(13) -> 14*
    a1() -> 40*
    mark1(25) -> 26*
    mark1(14) -> 15*
    top2(94) -> 95*
    active0(2) -> 4*
    active0(1) -> 4*
    active0(3) -> 4*
    active2(93) -> 94*
    f0(2) -> 5*
    f0(1) -> 5*
    f0(3) -> 5*
    a0() -> 1*
    mark0(2) -> 2*
    mark0(1) -> 2*
    mark0(3) -> 2*
    c0(2) -> 8*
    c0(1) -> 8*
    c0(3) -> 8*
    g0(2) -> 6*
    g0(1) -> 6*
    g0(3) -> 6*
    proper0(2) -> 7*
    proper0(1) -> 7*
    proper0(3) -> 7*
    ok0(2) -> 3*
    ok0(1) -> 3*
    ok0(3) -> 3*
    top0(2) -> 9*
    top0(1) -> 9*
    top0(3) -> 9*
    1 -> 84,70,52,32,16
    2 -> 78,67,49,24,13
    3 -> 86,76,58,34,22
    14 -> 42*
    15 -> 14,42,5
    17 -> 14*
    23 -> 14*
    25 -> 60*
    26 -> 25,60,6
    33 -> 25*
    35 -> 25*
    40 -> 93*
    41 -> 71,68,7
    43 -> 23,14,42,5
    51 -> 59,50,8
    53 -> 50*
    59 -> 50*
    61 -> 35,25,60,6
    69 -> 9*
    71 -> 68*
    77 -> 68*
    79 -> 68*
    85 -> 68*
    87 -> 68*
    95 -> 69,9
  problem:
   
  Qed