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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {4,3,2}
   transitions:
    d1(19) -> 20*
    c1(18) -> 19*
    b1(5) -> 6*
    b1(17) -> 18*
    a1(16) -> 17*
    a1(6) -> 7*
    a2(22) -> 23*
    a0(1) -> 2*
    b2(21) -> 22*
    b0(1) -> 3*
    c0(1) -> 4*
    d0(1) -> 1*
    1 -> 16,5
    7 -> 4*
    18 -> 21*
    20 -> 4*
    23 -> 19*
  problem:
   
  Qed