YES(?,O(n^1))

Problem:
 f(a()) -> f(c(a()))
 f(c(X)) -> X
 f(c(a())) -> f(d(b()))
 f(a()) -> f(d(a()))
 f(d(X)) -> X
 f(c(b())) -> f(d(a()))
 e(g(X)) -> e(X)

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {7,6}
   transitions:
    e1(30) -> 31*
    e1(22) -> 23*
    e1(36) -> 37*
    e1(38) -> 39*
    e1(28) -> 29*
    f1(9) -> 10*
    d1(20) -> 21*
    d1(14) -> 15*
    a1() -> 8*
    b1() -> 14*
    c1(8) -> 9*
    f2(46) -> 47*
    d2(45) -> 46*
    f0(5) -> 6*
    f0(2) -> 6*
    f0(4) -> 6*
    f0(1) -> 6*
    f0(3) -> 6*
    b2() -> 45*
    a0() -> 1*
    c0(5) -> 2*
    c0(2) -> 2*
    c0(4) -> 2*
    c0(1) -> 2*
    c0(3) -> 2*
    d0(5) -> 3*
    d0(2) -> 3*
    d0(4) -> 3*
    d0(1) -> 3*
    d0(3) -> 3*
    b0() -> 4*
    e0(5) -> 7*
    e0(2) -> 7*
    e0(4) -> 7*
    e0(1) -> 7*
    e0(3) -> 7*
    g0(5) -> 5*
    g0(2) -> 5*
    g0(4) -> 5*
    g0(1) -> 5*
    g0(3) -> 5*
    1 -> 36,6
    2 -> 28,6
    3 -> 38,6
    4 -> 30,6
    5 -> 22,6
    8 -> 10,6,20
    10 -> 6*
    14 -> 10,6
    15 -> 9*
    20 -> 10,6
    21 -> 9*
    23 -> 7*
    29 -> 23,7
    31 -> 23,7
    37 -> 23,7
    39 -> 23,7
    45 -> 47,10
    47 -> 10,6
  problem:
   
  Qed