```* Step 1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
0() -> n__0()
activate(X) -> X
activate(n__0()) -> 0()
activate(n__f(X)) -> f(activate(X))
activate(n__s(X)) -> s(activate(X))
f(X) -> n__f(X)
f(0()) -> cons(0(),n__f(n__s(n__0())))
f(s(0())) -> f(p(s(0())))
p(s(X)) -> X
s(X) -> n__s(X)
- Signature:
{0/0,activate/1,f/1,p/1,s/1} / {cons/2,n__0/0,n__f/1,n__s/1}
- Obligation:
runtime complexity wrt. defined symbols {0,activate,f,p,s} and constructors {cons,n__0,n__f,n__s}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 4.
The enriched problem is compatible with follwoing automaton.
0_0() -> 1
0_1() -> 1
0_1() -> 3
0_2() -> 4
0_2() -> 7
0_3() -> 9
activate_0(2) -> 1
activate_1(2) -> 3
cons_0(2,2) -> 1
cons_0(2,2) -> 2
cons_0(2,2) -> 3
cons_2(4,5) -> 1
cons_2(4,5) -> 3
cons_3(9,10) -> 1
cons_3(9,10) -> 3
f_0(2) -> 1
f_1(3) -> 1
f_1(3) -> 3
f_2(7) -> 1
f_2(7) -> 3
n__0_0() -> 1
n__0_0() -> 2
n__0_0() -> 3
n__0_1() -> 1
n__0_2() -> 1
n__0_2() -> 3
n__0_3() -> 4
n__0_3() -> 7
n__0_4() -> 9
n__f_0(2) -> 1
n__f_0(2) -> 2
n__f_0(2) -> 3
n__f_1(2) -> 1
n__f_2(3) -> 1
n__f_2(3) -> 3
n__f_2(6) -> 5
n__f_3(7) -> 1
n__f_3(7) -> 3
n__f_3(8) -> 10
n__s_0(2) -> 1
n__s_0(2) -> 2
n__s_0(2) -> 3
n__s_1(2) -> 1
n__s_2(1) -> 6
n__s_2(3) -> 1
n__s_2(3) -> 3
n__s_3(4) -> 8
p_0(2) -> 1
p_2(8) -> 7
s_0(2) -> 1
s_1(3) -> 1
s_1(3) -> 3
s_2(4) -> 8
2 -> 1
2 -> 3
4 -> 7
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
0() -> n__0()
activate(X) -> X
activate(n__0()) -> 0()
activate(n__f(X)) -> f(activate(X))
activate(n__s(X)) -> s(activate(X))
f(X) -> n__f(X)
f(0()) -> cons(0(),n__f(n__s(n__0())))
f(s(0())) -> f(p(s(0())))
p(s(X)) -> X
s(X) -> n__s(X)
- Signature:
{0/0,activate/1,f/1,p/1,s/1} / {cons/2,n__0/0,n__f/1,n__s/1}
- Obligation:
runtime complexity wrt. defined symbols {0,activate,f,p,s} and constructors {cons,n__0,n__f,n__s}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))
```