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(0())) -> g(d(1()))
 g(c(1())) -> g(d(0()))

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {6,5}
   transitions:
    g1(11) -> 12*
    d1(10) -> 11*
    01() -> 13*
    11() -> 10*
    f0(2) -> 5*
    f0(4) -> 5*
    f0(1) -> 5*
    f0(3) -> 5*
    c0(2) -> 1*
    c0(4) -> 1*
    c0(1) -> 1*
    c0(3) -> 1*
    d0(2) -> 2*
    d0(4) -> 2*
    d0(1) -> 2*
    d0(3) -> 2*
    g0(2) -> 6*
    g0(4) -> 6*
    g0(1) -> 6*
    g0(3) -> 6*
    00() -> 3*
    10() -> 4*
    1 -> 6*
    2 -> 6*
    3 -> 6*
    4 -> 6*
    10 -> 12,6
    12 -> 6*
    13 -> 10*
  problem:
   
  Qed