YES(?,O(n^1))

Problem:
 not(true()) -> false()
 not(false()) -> true()
 evenodd(x,0()) -> not(evenodd(x,s(0())))
 evenodd(0(),s(0())) -> false()
 evenodd(s(x),s(0())) -> evenodd(x,0())

Proof:
 Bounds Processor:
  bound: 3
  enrichment: match
  automaton:
   final states: {6,5}
   transitions:
    false3() -> 6,18,9
    evenodd1(3,7) -> 18,9,6
    evenodd1(4,8) -> 9*
    evenodd1(1,8) -> 9*
    evenodd1(2,7) -> 18,9,6
    evenodd1(3,8) -> 9*
    evenodd1(4,7) -> 18,9,6
    evenodd1(1,7) -> 18,9,6
    evenodd1(2,8) -> 9*
    true3() -> 9,6,18
    01() -> 7*
    false1() -> 18,9,6,5
    not1(9) -> 6*
    s1(7) -> 8*
    true1() -> 5*
    not2(18) -> 18,9,6
    not0(2) -> 5*
    not0(4) -> 5*
    not0(1) -> 5*
    not0(3) -> 5*
    evenodd2(3,17) -> 18*
    evenodd2(2,17) -> 18*
    evenodd2(4,17) -> 18*
    evenodd2(1,17) -> 18*
    true0() -> 1*
    s2(16) -> 17*
    false0() -> 2*
    02() -> 16*
    evenodd0(3,1) -> 6*
    evenodd0(3,3) -> 6*
    evenodd0(4,2) -> 6*
    evenodd0(4,4) -> 6*
    evenodd0(1,2) -> 6*
    evenodd0(1,4) -> 6*
    evenodd0(2,1) -> 6*
    evenodd0(2,3) -> 6*
    evenodd0(3,2) -> 6*
    evenodd0(3,4) -> 6*
    evenodd0(4,1) -> 6*
    evenodd0(4,3) -> 6*
    evenodd0(1,1) -> 6*
    evenodd0(1,3) -> 6*
    evenodd0(2,2) -> 6*
    evenodd0(2,4) -> 6*
    true2() -> 18,9,6
    00() -> 3*
    false2() -> 6*
    s0(2) -> 4*
    s0(4) -> 4*
    s0(1) -> 4*
    s0(3) -> 4*
  problem:
   
  Qed