Problem:
 f(0()) -> cons(0(),n__f(n__s(n__0())))
 f(s(0())) -> f(p(s(0())))
 p(s(0())) -> 0()
 f(X) -> n__f(X)
 s(X) -> n__s(X)
 0() -> n__0()
 activate(n__f(X)) -> f(activate(X))
 activate(n__s(X)) -> s(activate(X))
 activate(n__0()) -> 0()
 activate(X) -> X

Proof:
 Bounds Processor:
  bound: 4
  enrichment: match
  automaton:
   final states: {9,8,7,6,5}
   transitions:
    03() -> 19*
    01() -> 10,9
    n__04() -> 19*
    s1(10) -> 10,9
    cons3(19,22) -> 10,9
    activate1(2) -> 10*
    activate1(4) -> 10*
    activate1(1) -> 10*
    activate1(3) -> 10*
    f1(10) -> 10,9
    n__01() -> 8*
    n__s1(2) -> 7*
    n__s1(4) -> 7*
    n__s1(1) -> 7*
    n__s1(3) -> 7*
    n__f1(2) -> 5*
    n__f1(4) -> 5*
    n__f1(1) -> 5*
    n__f1(3) -> 5*
    n__02() -> 10,9
    n__s2(10) -> 10,9
    n__s2(9) -> 12*
    n__f2(10) -> 10,9
    n__f2(12) -> 13*
    f0(2) -> 5*
    f0(4) -> 5*
    f0(1) -> 5*
    f0(3) -> 5*
    f2(19) -> 9,10
    00() -> 8*
    p2(18) -> 19*
    cons0(3,1) -> 1*
    cons0(3,3) -> 1*
    cons0(4,2) -> 1*
    cons0(4,4) -> 1*
    cons0(1,2) -> 1*
    cons0(1,4) -> 1*
    cons0(2,1) -> 1*
    cons0(2,3) -> 1*
    cons0(3,2) -> 1*
    cons0(3,4) -> 1*
    cons0(4,1) -> 1*
    cons0(4,3) -> 1*
    cons0(1,1) -> 1*
    cons0(1,3) -> 1*
    cons0(2,2) -> 1*
    cons0(2,4) -> 1*
    s2(14) -> 18*
    n__f0(2) -> 2*
    n__f0(4) -> 2*
    n__f0(1) -> 2*
    n__f0(3) -> 2*
    02() -> 14*
    n__s0(2) -> 3*
    n__s0(4) -> 3*
    n__s0(1) -> 3*
    n__s0(3) -> 3*
    cons2(14,13) -> 9,10
    n__00() -> 4*
    n__03() -> 14*
    s0(2) -> 7*
    s0(4) -> 7*
    s0(1) -> 7*
    s0(3) -> 7*
    n__s3(14) -> 18*
    p0(2) -> 6*
    p0(4) -> 6*
    p0(1) -> 6*
    p0(3) -> 6*
    n__f3(19) -> 10,9
    n__f3(18) -> 22*
    activate0(2) -> 9*
    activate0(4) -> 9*
    activate0(1) -> 9*
    activate0(3) -> 9*
    1 -> 10,9
    2 -> 10,9
    3 -> 10,9
    4 -> 10,9
  problem:
   
  Qed