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

Proof:
 Bounds Processor:
  bound: 4
  enrichment: match
  automaton:
   final states: {5,4,3,2}
   transitions:
    a1(16) -> 17*
    a1(28) -> 29*
    d1(9) -> 10*
    d1(26) -> 27*
    d1(13) -> 14*
    b1(15) -> 16*
    c1(10) -> 11*
    c1(14) -> 15*
    e1(12) -> 13*
    d2(45) -> 46*
    d2(35) -> 36*
    d2(44) -> 45*
    d2(38) -> 39*
    a0(1) -> 2*
    c2(39) -> 40*
    c2(36) -> 37*
    b0(1) -> 3*
    a3(57) -> 58*
    a3(52) -> 53*
    c0(1) -> 4*
    c4(55) -> 56*
    d0(1) -> 1*
    d4(62) -> 63*
    d4(54) -> 55*
    e0(1) -> 5*
    1 -> 28,12,9
    10 -> 26*
    11 -> 2*
    15 -> 44*
    16 -> 35*
    17 -> 13,5
    27 -> 3*
    28 -> 38*
    29 -> 40,11,2,4
    37 -> 17,5
    40 -> 29,4
    44 -> 57*
    45 -> 52*
    46 -> 16*
    52 -> 54*
    53 -> 37*
    56 -> 58,53,37,17
    57 -> 62*
    58 -> 56,53
    63 -> 55*
  problem:
   
  Qed