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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {3,2}
   transitions:
    a1(11) -> 12*
    a1(13) -> 14*
    c1(10) -> 11*
    c1(12) -> 13*
    b1(7) -> 8*
    b1(8) -> 9*
    b2(27) -> 28*
    b2(24) -> 25*
    b2(26) -> 27*
    b2(23) -> 24*
    a0(1) -> 2*
    b0(1) -> 1*
    c0(1) -> 3*
    1 -> 10,7,2
    9 -> 2*
    10 -> 13,23,14,2
    11 -> 26,12
    13 -> 23,14
    14 -> 2*
    25 -> 14*
    28 -> 12*
  problem:
   
  Qed