YES(?,O(n^1))

Problem:
 f(s(x)) -> s(s(f(p(s(x)))))
 f(0()) -> 0()
 p(s(x)) -> x

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {4,3}
   transitions:
    01() -> 21*
    s1(5) -> 6*
    s1(19) -> 20*
    s1(9) -> 10*
    s1(8) -> 9*
    f1(7) -> 8*
    p1(6) -> 7*
    f0(2) -> 3*
    f0(1) -> 3*
    s0(2) -> 1*
    s0(1) -> 1*
    p0(2) -> 4*
    p0(1) -> 4*
    00() -> 2*
    1 -> 4,19
    2 -> 4,5
    5 -> 7*
    10 -> 8,3
    19 -> 7*
    20 -> 6*
    21 -> 8,3
  problem:
   
  Qed