YES(?,O(n^1))

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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {4,3,2}
   transitions:
    d1(5) -> 6*
    d1(17) -> 18*
    d1(16) -> 17*
    c1(7) -> 8*
    c1(6) -> 7*
    d2(20) -> 21*
    d2(27) -> 28*
    d2(29) -> 30*
    d2(19) -> 20*
    d2(21) -> 22*
    d2(28) -> 29*
    a0(1) -> 2*
    b0(1) -> 3*
    c0(1) -> 4*
    d0(1) -> 1*
    1 -> 5*
    6 -> 27,16
    7 -> 19*
    8 -> 3*
    18 -> 4*
    22 -> 8*
    30 -> 7*
  problem:
   
  Qed