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: 1
  enrichment: match
  automaton:
   final states: {7,6}
   transitions:
    g1(32) -> 33*
    g1(34) -> 35*
    g1(24) -> 25*
    g1(9) -> 10*
    g1(26) -> 27*
    g1(18) -> 19*
    d1(8) -> 9*
    h1(16) -> 17*
    01() -> 16*
    11() -> 8*
    f0(5) -> 6*
    f0(2) -> 6*
    f0(4) -> 6*
    f0(1) -> 6*
    f0(3) -> 6*
    c0(5) -> 1*
    c0(2) -> 1*
    c0(4) -> 1*
    c0(1) -> 1*
    c0(3) -> 1*
    d0(5) -> 2*
    d0(2) -> 2*
    d0(4) -> 2*
    d0(1) -> 2*
    d0(3) -> 2*
    g0(5) -> 7*
    g0(2) -> 7*
    g0(4) -> 7*
    g0(1) -> 7*
    g0(3) -> 7*
    h0(5) -> 3*
    h0(2) -> 3*
    h0(4) -> 3*
    h0(1) -> 3*
    h0(3) -> 3*
    00() -> 4*
    10() -> 5*
    1 -> 25,33,32,7
    2 -> 25,33,24,7
    3 -> 25,33,34,7
    4 -> 25,33,26,7
    5 -> 25,33,18,7
    8 -> 10*
    10 -> 33,7
    17 -> 8*
    19 -> 35,7
    25 -> 35,7
    27 -> 35,7
    33 -> 35,7
    35 -> 7*
  problem:
   
  Qed