YES(?,O(n^1))

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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {5,4,3,2}
   transitions:
    b1(7) -> 8*
    a1(6) -> 7*
    b0(1) -> 2*
    a0(1) -> 5*
    c0(1) -> 3*
    d0(1) -> 4*
    f80() -> 1*
    1 -> 6*
    8 -> 4*
  problem:
   
  Qed