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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {4,3}
   transitions:
    c1(22) -> 23*
    c1(7) -> 8*
    d1(21) -> 22*
    d1(8) -> 9*
    a1(20) -> 21*
    a1(5) -> 6*
    a1(17) -> 18*
    b1(19) -> 20*
    b1(31) -> 32*
    b1(6) -> 7*
    a0(2) -> 3*
    a0(1) -> 3*
    d0(2) -> 1*
    d0(1) -> 1*
    c0(2) -> 2*
    c0(1) -> 2*
    b0(2) -> 4*
    b0(1) -> 4*
    1 -> 7,21,32,20,6,4,3,31,17
    2 -> 7,21,32,20,6,4,3,19,5
    8 -> 7*
    9 -> 21,18,6,3
    18 -> 6*
    22 -> 21*
    23 -> 7,20,4
    32 -> 20*
  problem:
   
  Qed