Problem:
 f(X) -> if(X,c(),n__f(true()))
 if(true(),X,Y) -> X
 if(false(),X,Y) -> activate(Y)
 f(X) -> n__f(X)
 activate(n__f(X)) -> f(X)
 activate(X) -> X

Proof:
 Bounds Processor:
  bound: 3
  enrichment: match
  automaton:
   final states: {7,6,5}
   transitions:
    true3() -> 20*
    f1(2) -> 6,7
    f1(4) -> 6,7
    f1(1) -> 6,7
    f1(3) -> 6,7
    n__f1(2) -> 5*
    n__f1(4) -> 5*
    n__f1(1) -> 5*
    n__f1(8) -> 9*
    n__f1(3) -> 5*
    activate1(15) -> 6,7
    activate1(2) -> 6*
    activate1(9) -> 5*
    activate1(4) -> 6*
    activate1(1) -> 6*
    activate1(3) -> 6*
    if1(1,10,9) -> 5*
    if1(3,10,9) -> 5*
    if1(2,10,9) -> 5*
    if1(4,10,9) -> 5*
    c1() -> 10*
    true1() -> 8*
    n__f2(2) -> 6,7
    n__f2(14) -> 15*
    n__f2(4) -> 6,7
    n__f2(1) -> 6,7
    n__f2(3) -> 6,7
    if2(4,16,15) -> 6,7
    if2(1,16,15) -> 6,7
    if2(3,16,15) -> 6,7
    if2(2,16,15) -> 6,7
    f0(2) -> 5*
    f0(4) -> 5*
    f0(1) -> 5*
    f0(3) -> 5*
    c2() -> 16*
    if0(3,4,2) -> 6*
    if0(1,1,4) -> 6*
    if0(1,3,4) -> 6*
    if0(4,1,2) -> 6*
    if0(1,1,1) -> 6*
    if0(4,3,2) -> 6*
    if0(1,3,1) -> 6*
    if0(2,2,4) -> 6*
    if0(2,4,4) -> 6*
    if0(1,2,3) -> 6*
    if0(1,4,3) -> 6*
    if0(2,2,1) -> 6*
    if0(2,4,1) -> 6*
    if0(3,1,4) -> 6*
    if0(3,3,4) -> 6*
    if0(2,1,3) -> 6*
    if0(2,3,3) -> 6*
    if0(3,1,1) -> 6*
    if0(1,1,2) -> 6*
    if0(3,3,1) -> 6*
    if0(1,3,2) -> 6*
    if0(4,2,4) -> 6*
    if0(4,4,4) -> 6*
    if0(3,2,3) -> 6*
    if0(3,4,3) -> 6*
    if0(4,2,1) -> 6*
    if0(2,2,2) -> 6*
    if0(4,4,1) -> 6*
    if0(2,4,2) -> 6*
    if0(4,1,3) -> 6*
    if0(4,3,3) -> 6*
    if0(3,1,2) -> 6*
    if0(3,3,2) -> 6*
    if0(1,2,4) -> 6*
    if0(1,4,4) -> 6*
    if0(4,2,2) -> 6*
    if0(1,2,1) -> 6*
    if0(4,4,2) -> 6*
    if0(1,4,1) -> 6*
    if0(2,1,4) -> 6*
    if0(2,3,4) -> 6*
    if0(1,1,3) -> 6*
    if0(1,3,3) -> 6*
    if0(2,1,1) -> 6*
    if0(2,3,1) -> 6*
    if0(3,2,4) -> 6*
    if0(3,4,4) -> 6*
    if0(2,2,3) -> 6*
    if0(2,4,3) -> 6*
    if0(3,2,1) -> 6*
    if0(1,2,2) -> 6*
    if0(3,4,1) -> 6*
    if0(1,4,2) -> 6*
    if0(4,1,4) -> 6*
    if0(4,3,4) -> 6*
    if0(3,1,3) -> 6*
    if0(3,3,3) -> 6*
    if0(4,1,1) -> 6*
    if0(2,1,2) -> 6*
    if0(4,3,1) -> 6*
    if0(2,3,2) -> 6*
    if0(4,2,3) -> 6*
    if0(4,4,3) -> 6*
    if0(3,2,2) -> 6*
    true2() -> 14*
    c0() -> 1*
    f2(14) -> 6,7
    f2(8) -> 5*
    n__f0(2) -> 2*
    n__f0(4) -> 2*
    n__f0(1) -> 2*
    n__f0(3) -> 2*
    n__f3(20) -> 21*
    n__f3(14) -> 6,7
    n__f3(8) -> 5*
    true0() -> 3*
    if3(8,22,21) -> 5*
    if3(14,22,21) -> 6,7
    false0() -> 4*
    c3() -> 22*
    activate0(2) -> 7*
    activate0(4) -> 7*
    activate0(1) -> 7*
    activate0(3) -> 7*
    1 -> 7,6
    2 -> 7,6
    3 -> 7,6
    4 -> 7,6
    9 -> 5*
    10 -> 5*
    15 -> 6,7
    16 -> 6,7
    22 -> 6,7,5
  problem:
   
  Qed