YES(?,O(n^1))

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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {4,3,2}
   transitions:
    a1(11) -> 12*
    d1(9) -> 10*
    d1(8) -> 9*
    a0(1) -> 2*
    b0(1) -> 3*
    c0(1) -> 4*
    d0(1) -> 1*
    1 -> 11,8
    10 -> 3*
    12 -> 4*
  problem:
   
  Qed