YES(?,O(n^1))

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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {4,3,2}
   transitions:
    a1(15) -> 16*
    a1(17) -> 18*
    a1(16) -> 17*
    b1(6) -> 7*
    d1(5) -> 6*
    a2(25) -> 26*
    a2(24) -> 25*
    a2(23) -> 24*
    d0(1) -> 2*
    a0(1) -> 1*
    b0(1) -> 3*
    c0(1) -> 4*
    1 -> 15,5
    6 -> 23*
    7 -> 6,2
    18 -> 3*
    26 -> 7,2
  problem:
   
  Qed