YES(?,O(n^1))

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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {5,4,3}
   transitions:
    a1(30) -> 31*
    a1(9) -> 10*
    a1(36) -> 37*
    f1(10) -> 11*
    b1(22) -> 23*
    b1(7) -> 8*
    b1(28) -> 29*
    b1(8) -> 9*
    c1(20) -> 21*
    c1(6) -> 7*
    d2(44) -> 45*
    d2(46) -> 47*
    d2(38) -> 39*
    a0(2) -> 3*
    a0(1) -> 3*
    b0(2) -> 4*
    b0(1) -> 4*
    d0(2) -> 5*
    d0(1) -> 5*
    c0(2) -> 1*
    c0(1) -> 1*
    f0(2) -> 2*
    f0(1) -> 2*
    1 -> 36,28,20
    2 -> 30,22,6
    8 -> 46*
    11 -> 39,45,10,5
    21 -> 7*
    22 -> 38*
    23 -> 9*
    28 -> 44*
    29 -> 9*
    31 -> 3*
    37 -> 31,3
    39 -> 10*
    45 -> 10*
    47 -> 10*
  problem:
   
  Qed