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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {3,2}
   transitions:
    c1(17) -> 18*
    c1(16) -> 17*
    c1(18) -> 19*
    a1(15) -> 16*
    a1(14) -> 15*
    b1(4) -> 5*
    b2(20) -> 21*
    b2(26) -> 27*
    a0(1) -> 2*
    b0(1) -> 3*
    c0(1) -> 1*
    1 -> 4*
    4 -> 21,15,26
    5 -> 14,2
    14 -> 20*
    15 -> 26*
    19 -> 16,2
    20 -> 27*
    21 -> 15*
    27 -> 16*
  problem:
   
  Qed