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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {3,2}
   transitions:
    c1(15) -> 16*
    c1(16) -> 17*
    a1(14) -> 15*
    a1(13) -> 14*
    b1(4) -> 5*
    b2(24) -> 25*
    b2(18) -> 19*
    a0(1) -> 2*
    b0(1) -> 3*
    c0(1) -> 1*
    1 -> 4,2
    4 -> 25,19
    5 -> 13,2
    13 -> 18,14
    14 -> 24,15
    17 -> 15,2
    18 -> 25,15
    19 -> 14*
    25 -> 15*
  problem:
   
  Qed