YES(?,O(n^1))

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

Proof:
 Bounds Processor:
  bound: 3
  enrichment: match
  automaton:
   final states: {4,3,2}
   transitions:
    b1(12) -> 13*
    c1(11) -> 12*
    a1(9) -> 10*
    a1(8) -> 9*
    a2(22) -> 23*
    a2(29) -> 30*
    a2(28) -> 29*
    b2(23) -> 24*
    c0(1) -> 2*
    c2(21) -> 22*
    a0(1) -> 1*
    a3(32) -> 33*
    a3(31) -> 32*
    d0(1) -> 3*
    b0(1) -> 4*
    1 -> 11,8
    10 -> 2*
    11 -> 28,21
    13 -> 3*
    21 -> 31*
    24 -> 13,3
    30 -> 12*
    33 -> 22*
  problem:
   
  Qed