Problem:
 a(a(x)) -> c()
 b(u(x)) -> b(d(x))
 d(a(x)) -> a(d(x))
 d(b(x)) -> u(a(b(x)))
 a(u(x)) -> u(a(x))

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {5,4,3}
   transitions:
    u1(17) -> 18*
    a1(24) -> 25*
    a1(16) -> 17*
    b1(7) -> 8*
    d1(14) -> 15*
    d1(6) -> 7*
    a0(2) -> 3*
    a0(1) -> 3*
    c0() -> 1*
    b0(2) -> 4*
    b0(1) -> 4*
    u0(2) -> 2*
    u0(1) -> 2*
    d0(2) -> 5*
    d0(1) -> 5*
    1 -> 24,14
    2 -> 16,6
    8 -> 4*
    15 -> 7*
    18 -> 17,3
    25 -> 17*
  problem:
   
  Qed