```* Step 1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
a() -> n__a()
activate(X) -> X
activate(n__a()) -> a()
activate(n__f(X)) -> f(activate(X))
f(X) -> n__f(X)
f(f(a())) -> f(g(n__f(n__a())))
- Signature:
{a/0,activate/1,f/1} / {g/1,n__a/0,n__f/1}
- Obligation:
runtime complexity wrt. defined symbols {a,activate,f} and constructors {g,n__a,n__f}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 3.
The enriched problem is compatible with follwoing automaton.
a_0() -> 1
a_1() -> 1
a_1() -> 3
activate_0(2) -> 1
activate_1(2) -> 3
f_0(2) -> 1
f_1(3) -> 1
f_1(3) -> 3
f_2(4) -> 1
f_2(4) -> 3
g_0(2) -> 1
g_0(2) -> 2
g_0(2) -> 3
g_2(5) -> 4
n__a_0() -> 1
n__a_0() -> 2
n__a_0() -> 3
n__a_1() -> 1
n__a_2() -> 1
n__a_2() -> 3
n__f_0(2) -> 1
n__f_0(2) -> 2
n__f_0(2) -> 3
n__f_1(2) -> 1
n__f_2(1) -> 5
n__f_2(3) -> 1
n__f_2(3) -> 3
n__f_3(4) -> 1
n__f_3(4) -> 3
2 -> 1
2 -> 3
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
a() -> n__a()
activate(X) -> X
activate(n__a()) -> a()
activate(n__f(X)) -> f(activate(X))
f(X) -> n__f(X)
f(f(a())) -> f(g(n__f(n__a())))
- Signature:
{a/0,activate/1,f/1} / {g/1,n__a/0,n__f/1}
- Obligation:
runtime complexity wrt. defined symbols {a,activate,f} and constructors {g,n__a,n__f}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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