YES(?,O(n^1))

Problem:
 a(a(a(x1))) -> b(b(x1))
 b(b(b(x1))) -> c(x1)
 c(x1) -> d(d(x1))
 d(x1) -> a(a(x1))

Proof:
 Bounds Processor:
  bound: 3
  enrichment: match
  automaton:
   final states: {5,4,3,2}
   transitions:
    a1(12) -> 13*
    a1(13) -> 14*
    d1(10) -> 11*
    d1(9) -> 10*
    a2(25) -> 26*
    a2(22) -> 23*
    a2(24) -> 25*
    a2(21) -> 22*
    b3(40) -> 41*
    b3(30) -> 31*
    b3(39) -> 40*
    b3(31) -> 32*
    a0(1) -> 2*
    b0(1) -> 3*
    c0(1) -> 4*
    d0(1) -> 5*
    f80() -> 1*
    1 -> 12,9
    9 -> 24*
    10 -> 21*
    11 -> 4*
    14 -> 5*
    23 -> 11,4
    24 -> 39*
    25 -> 30*
    26 -> 10*
    32 -> 23,11
    41 -> 22*
  problem:
   
  Qed