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

Proof:
 Bounds Processor:
  bound: 3
  enrichment: match
  automaton:
   final states: {4,3}
   transitions:
    d3(70) -> 71*
    b1(17) -> 18*
    b1(23) -> 24*
    c3(85) -> 86*
    c3(77) -> 78*
    c3(69) -> 70*
    c3(91) -> 92*
    c3(68) -> 69*
    c1(15) -> 16*
    c1(5) -> 6*
    c1(26) -> 27*
    c1(6) -> 7*
    b3(92) -> 93*
    b3(86) -> 87*
    d1(27) -> 28*
    d1(7) -> 8*
    a1(35) -> 36*
    a1(25) -> 26*
    d2(57) -> 58*
    d2(39) -> 40*
    a0(2) -> 3*
    a0(1) -> 3*
    c2(65) -> 66*
    c2(47) -> 48*
    c2(37) -> 38*
    c2(49) -> 50*
    c2(56) -> 57*
    c2(38) -> 39*
    b0(2) -> 1*
    b0(1) -> 1*
    b2(50) -> 51*
    b2(66) -> 67*
    c0(2) -> 4*
    c0(1) -> 4*
    a2(55) -> 56*
    a2(59) -> 60*
    d0(2) -> 2*
    d0(1) -> 2*
    1 -> 35,5
    2 -> 25,15
    6 -> 23*
    8 -> 3*
    16 -> 17,6
    17 -> 55*
    18 -> 38,16,17,6,23,4
    23 -> 59*
    24 -> 38,16,17,6,23,4
    25 -> 37*
    27 -> 65*
    28 -> 69,39,7
    35 -> 47*
    36 -> 26*
    39 -> 49*
    40 -> 36,26
    48 -> 38*
    51 -> 27*
    55 -> 77*
    57 -> 91*
    58 -> 70,50
    59 -> 68*
    60 -> 56*
    67 -> 70,50
    70 -> 85*
    71 -> 60,56
    78 -> 69*
    87 -> 57*
    93 -> 86*
  problem:
   
  Qed