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)
 a(d(x1)) -> d(a(x1))
 d(x1) -> b(a(x1))
 L(a(a(x1))) -> L(a(b(c(x1))))
 c(R(x1)) -> c(b(R(x1)))

Proof:
 Bounds Processor:
  bound: 3
  enrichment: match
  automaton:
   final states: {6,5,4,3,2}
   transitions:
    c1(15) -> 16*
    b1(14) -> 15*
    b1(11) -> 12*
    R1(13) -> 14*
    a1(10) -> 11*
    d2(23) -> 24*
    b3(29) -> 30*
    a3(28) -> 29*
    b0(1) -> 2*
    a0(1) -> 4*
    c0(1) -> 3*
    d0(1) -> 5*
    L0(1) -> 6*
    R0(1) -> 1*
    1 -> 13,10
    12 -> 5*
    14 -> 23*
    16 -> 3*
    23 -> 28*
    24 -> 16,3
    30 -> 24,16
  problem:
   
  Qed