```* Step 1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
activate(X) -> X
activate(n__f(X)) -> f(X)
f(X) -> if(X,c(),n__f(true()))
f(X) -> n__f(X)
if(false(),X,Y) -> activate(Y)
if(true(),X,Y) -> X
- Signature:
{activate/1,f/1,if/3} / {c/0,false/0,n__f/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {activate,f,if} and constructors {c,false,n__f,true}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 3.
The enriched problem is compatible with follwoing automaton.
activate_0(2) -> 1
activate_1(2) -> 1
activate_1(4) -> 1
activate_1(7) -> 1
c_0() -> 1
c_0() -> 2
c_1() -> 1
c_1() -> 3
c_2() -> 1
c_2() -> 6
c_3() -> 1
c_3() -> 9
f_0(2) -> 1
f_1(2) -> 1
f_2(5) -> 1
f_2(8) -> 1
false_0() -> 1
false_0() -> 2
if_0(2,2,2) -> 1
if_1(2,3,4) -> 1
if_2(2,6,7) -> 1
if_3(5,9,10) -> 1
if_3(8,9,10) -> 1
n__f_0(2) -> 1
n__f_0(2) -> 2
n__f_1(2) -> 1
n__f_1(5) -> 1
n__f_1(5) -> 4
n__f_2(2) -> 1
n__f_2(8) -> 1
n__f_2(8) -> 7
n__f_3(5) -> 1
n__f_3(8) -> 1
n__f_3(11) -> 10
true_0() -> 1
true_0() -> 2
true_1() -> 5
true_2() -> 8
true_3() -> 11
2 -> 1
3 -> 1
4 -> 1
6 -> 1
7 -> 1
9 -> 1
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
activate(X) -> X
activate(n__f(X)) -> f(X)
f(X) -> if(X,c(),n__f(true()))
f(X) -> n__f(X)
if(false(),X,Y) -> activate(Y)
if(true(),X,Y) -> X
- Signature:
{activate/1,f/1,if/3} / {c/0,false/0,n__f/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {activate,f,if} and constructors {c,false,n__f,true}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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