YES(?,O(n^1))

Problem:
 f(s(x1)) -> s(s(f(p(s(x1)))))
 f(0(x1)) -> 0(x1)
 p(s(x1)) -> x1

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {4,3}
   transitions:
    01(27) -> 28*
    01(21) -> 22*
    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) -> 2*
    00(1) -> 2*
    1 -> 4,27,19
    2 -> 4,21,5
    5 -> 7*
    10 -> 8,3
    19 -> 7*
    20 -> 6*
    22 -> 8,3
    28 -> 8,3
  problem:
   
  Qed