Problem:
 a(b(b(x1))) -> P(a(b(x1)))
 a(P(x1)) -> P(a(x(x1)))
 a(x(x1)) -> x(a(x1))
 b(P(x1)) -> b(Q(x1))
 Q(x(x1)) -> a(Q(x1))
 Q(a(x1)) -> b(b(a(x1)))

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {5,4,3}
   transitions:
    a1(7) -> 8*
    a1(26) -> 27*
    a1(38) -> 39*
    a1(18) -> 19*
    Q1(36) -> 37*
    Q1(28) -> 29*
    b1(29) -> 30*
    x1(19) -> 20*
    x1(16) -> 17*
    x1(6) -> 7*
    P1(8) -> 9*
    x2(46) -> 47*
    a0(2) -> 3*
    a0(1) -> 3*
    a2(50) -> 51*
    a2(45) -> 46*
    b0(2) -> 4*
    b0(1) -> 4*
    P0(2) -> 1*
    P0(1) -> 1*
    x0(2) -> 2*
    x0(1) -> 2*
    Q0(2) -> 5*
    Q0(1) -> 5*
    1 -> 36,26,16
    2 -> 28,18,6
    6 -> 50*
    9 -> 46,27,19,3
    16 -> 45*
    17 -> 7*
    20 -> 51,46,19,3
    27 -> 19*
    29 -> 38*
    30 -> 4*
    37 -> 29*
    39 -> 29,38,5
    47 -> 8*
    51 -> 46*
  problem:
   
  Qed