YES(?,O(n^1))

Problem:
 f(f(x)) -> f(c(f(x)))
 f(f(x)) -> f(d(f(x)))
 g(c(x)) -> x
 g(d(x)) -> x
 g(c(h(0()))) -> g(d(1()))
 g(c(1())) -> g(d(h(0())))
 g(h(x)) -> g(x)

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {8}
   transitions:
    g1(32) -> 33*
    g1(24) -> 25*
    g1(48) -> 49*
    d1(17) -> 18*
    d1(23) -> 24*
    h1(26) -> 27*
    01() -> 26*
    11() -> 23*
    f1(15) -> 16*
    f1(13) -> 14*
    c1(42) -> 43*
    c1(14) -> 15*
    f2(34) -> 35*
    f2(36) -> 37*
    f0(8) -> 8*
    d2(46) -> 47*
    c0(8) -> 8*
    c2(35) -> 36*
    d0(8) -> 8*
    g2(53) -> 54*
    g0(8) -> 8*
    h0(8) -> 8*
    00() -> 8*
    10() -> 8*
    8 -> 33,32,13
    14 -> 17*
    15 -> 34*
    16 -> 14,42,17,8
    18 -> 15*
    23 -> 25*
    25 -> 8*
    26 -> 53,48
    27 -> 23*
    33 -> 8*
    35 -> 46*
    37 -> 14,17
    43 -> 15*
    47 -> 36*
    49 -> 33*
    54 -> 33*
  problem:
   
  Qed