Problem:
 c(c(b(c(x)))) -> b(a(0(),c(x)))
 c(c(x)) -> b(c(b(c(x))))
 a(0(),x) -> c(c(x))

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {4,3}
   transitions:
    c1(2) -> 6*
    c1(6) -> 4*
    c1(1) -> 6*
    b2(10) -> 11*
    b2(12) -> 4*
    c2(2) -> 10*
    c2(11) -> 12*
    c2(1) -> 10*
    c0(2) -> 3*
    c0(1) -> 3*
    b0(2) -> 1*
    b0(1) -> 1*
    a0(1,2) -> 4*
    a0(2,1) -> 4*
    a0(1,1) -> 4*
    a0(2,2) -> 4*
    00() -> 2*
  problem:
   
  Qed