```* 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(X)
activate(n__g(X)) -> g(activate(X))
f(X) -> n__f(X)
f(n__f(n__a())) -> f(n__g(n__f(n__a())))
g(X) -> n__g(X)
- Signature:
{a/0,activate/1,f/1,g/1} / {n__a/0,n__f/1,n__g/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {a,activate,f,g} and constructors {n__a,n__f,n__g}
+ Applied Processor:
Bounds {initialAutomaton = perSymbol, enrichment = match}
+ Details:
The problem is match-bounded by 3.
The enriched problem is compatible with follwoing automaton.
a_0() -> 1
a_1() -> 2
a_1() -> 8
activate_0(5) -> 2
activate_0(6) -> 2
activate_0(7) -> 2
activate_1(5) -> 8
activate_1(6) -> 8
activate_1(7) -> 8
activate_1(9) -> 8
activate_2(9) -> 12
f_0(5) -> 3
f_0(6) -> 3
f_0(7) -> 3
f_1(5) -> 2
f_1(5) -> 3
f_1(5) -> 8
f_1(6) -> 2
f_1(6) -> 8
f_1(7) -> 2
f_1(7) -> 8
f_2(1) -> 8
f_2(1) -> 12
g_0(5) -> 4
g_0(6) -> 4
g_0(7) -> 4
g_1(8) -> 2
g_1(8) -> 8
g_2(12) -> 8
n__a_0() -> 2
n__a_0() -> 5
n__a_0() -> 8
n__a_1() -> 1
n__a_2() -> 2
n__a_2() -> 8
n__f_0(5) -> 2
n__f_0(5) -> 6
n__f_0(5) -> 8
n__f_0(6) -> 2
n__f_0(6) -> 6
n__f_0(6) -> 8
n__f_0(7) -> 2
n__f_0(7) -> 6
n__f_0(7) -> 8
n__f_1(1) -> 8
n__f_1(1) -> 9
n__f_1(1) -> 12
n__f_1(5) -> 3
n__f_1(6) -> 3
n__f_1(7) -> 3
n__f_2(5) -> 2
n__f_2(5) -> 3
n__f_2(5) -> 8
n__f_2(6) -> 2
n__f_2(6) -> 8
n__f_2(7) -> 2
n__f_2(7) -> 8
n__f_3(1) -> 8
n__f_3(1) -> 12
n__g_0(5) -> 2
n__g_0(5) -> 7
n__g_0(5) -> 8
n__g_0(6) -> 2
n__g_0(6) -> 7
n__g_0(6) -> 8
n__g_0(7) -> 2
n__g_0(7) -> 7
n__g_0(7) -> 8
n__g_1(5) -> 4
n__g_1(6) -> 4
n__g_1(7) -> 4
n__g_1(9) -> 2
n__g_1(9) -> 5
n__g_1(9) -> 8
n__g_2(8) -> 2
n__g_2(8) -> 8
n__g_3(12) -> 8
5 -> 2
5 -> 8
6 -> 2
6 -> 8
7 -> 2
7 -> 8
9 -> 8
9 -> 12
* 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(X)
activate(n__g(X)) -> g(activate(X))
f(X) -> n__f(X)
f(n__f(n__a())) -> f(n__g(n__f(n__a())))
g(X) -> n__g(X)
- Signature:
{a/0,activate/1,f/1,g/1} / {n__a/0,n__f/1,n__g/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {a,activate,f,g} and constructors {n__a,n__f,n__g}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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