```* Step 1: ToInnermost WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
activate(X) -> X
activate(n__f(X)) -> f(activate(X))
activate(n__h(X)) -> h(activate(X))
f(X) -> g(n__h(n__f(X)))
f(X) -> n__f(X)
h(X) -> n__h(X)
- Signature:
{activate/1,f/1,h/1} / {g/1,n__f/1,n__h/1}
- Obligation:
runtime complexity wrt. defined symbols {activate,f,h} and constructors {g,n__f,n__h}
+ Applied Processor:
ToInnermost
+ Details:
switch to innermost, as the system is overlay and right linear and does not contain weak rules
* Step 2: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
activate(X) -> X
activate(n__f(X)) -> f(activate(X))
activate(n__h(X)) -> h(activate(X))
f(X) -> g(n__h(n__f(X)))
f(X) -> n__f(X)
h(X) -> n__h(X)
- Signature:
{activate/1,f/1,h/1} / {g/1,n__f/1,n__h/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {activate,f,h} and constructors {g,n__f,n__h}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 2.
The enriched problem is compatible with follwoing automaton.
activate_0(2) -> 1
activate_1(2) -> 3
f_0(2) -> 1
f_1(3) -> 1
f_1(3) -> 3
g_0(2) -> 1
g_0(2) -> 2
g_0(2) -> 3
g_1(4) -> 1
g_2(6) -> 1
g_2(6) -> 3
h_0(2) -> 1
h_1(3) -> 1
h_1(3) -> 3
n__f_0(2) -> 1
n__f_0(2) -> 2
n__f_0(2) -> 3
n__f_1(2) -> 1
n__f_1(2) -> 5
n__f_2(3) -> 1
n__f_2(3) -> 3
n__f_2(3) -> 7
n__h_0(2) -> 1
n__h_0(2) -> 2
n__h_0(2) -> 3
n__h_1(2) -> 1
n__h_1(5) -> 4
n__h_2(3) -> 1
n__h_2(3) -> 3
n__h_2(7) -> 6
2 -> 1
2 -> 3
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
activate(X) -> X
activate(n__f(X)) -> f(activate(X))
activate(n__h(X)) -> h(activate(X))
f(X) -> g(n__h(n__f(X)))
f(X) -> n__f(X)
h(X) -> n__h(X)
- Signature:
{activate/1,f/1,h/1} / {g/1,n__f/1,n__h/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {activate,f,h} and constructors {g,n__f,n__h}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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