Problem:
 f(0()) -> cons(0(),n__f(s(0())))
 f(s(0())) -> f(p(s(0())))
 p(s(X)) -> X
 f(X) -> n__f(X)
 activate(n__f(X)) -> f(X)
 activate(X) -> X

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {7,6,5}
   transitions:
    f1(15) -> 7,5
    f1(2) -> 7*
    f1(4) -> 7*
    f1(1) -> 7*
    f1(3) -> 7*
    n__f1(2) -> 5*
    n__f1(9) -> 10*
    n__f1(4) -> 5*
    n__f1(1) -> 5*
    n__f1(3) -> 5*
    p1(9) -> 15*
    s1(8) -> 9*
    01() -> 8*
    cons1(8,10) -> 7,5
    n__f2(15) -> 7,5
    n__f2(17) -> 18*
    n__f2(2) -> 7*
    n__f2(4) -> 7*
    n__f2(1) -> 7*
    n__f2(3) -> 7*
    cons2(16,18) -> 5,7
    f0(2) -> 5*
    f0(4) -> 5*
    f0(1) -> 5*
    f0(3) -> 5*
    02() -> 16*
    00() -> 1*
    s2(16) -> 17*
    cons0(3,1) -> 2*
    cons0(3,3) -> 2*
    cons0(4,2) -> 2*
    cons0(4,4) -> 2*
    cons0(1,2) -> 2*
    cons0(1,4) -> 2*
    cons0(2,1) -> 2*
    cons0(2,3) -> 2*
    cons0(3,2) -> 2*
    cons0(3,4) -> 2*
    cons0(4,1) -> 2*
    cons0(4,3) -> 2*
    cons0(1,1) -> 2*
    cons0(1,3) -> 2*
    cons0(2,2) -> 2*
    cons0(2,4) -> 2*
    n__f0(2) -> 3*
    n__f0(4) -> 3*
    n__f0(1) -> 3*
    n__f0(3) -> 3*
    s0(2) -> 4*
    s0(4) -> 4*
    s0(1) -> 4*
    s0(3) -> 4*
    p0(2) -> 6*
    p0(4) -> 6*
    p0(1) -> 6*
    p0(3) -> 6*
    activate0(2) -> 7*
    activate0(4) -> 7*
    activate0(1) -> 7*
    activate0(3) -> 7*
    1 -> 7,6
    2 -> 7,6
    3 -> 7,6
    4 -> 7,6
    8 -> 15*
  problem:
   
  Qed