```* Step 1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
activate(X) -> X
activate(n__f(X)) -> f(activate(X))
activate(n__true()) -> true()
f(X) -> if(X,c(),n__f(n__true()))
f(X) -> n__f(X)
if(false(),X,Y) -> activate(Y)
if(true(),X,Y) -> X
true() -> n__true()
- Signature:
{activate/1,f/1,if/3,true/0} / {c/0,false/0,n__f/1,n__true/0}
- Obligation:
runtime complexity wrt. defined symbols {activate,f,if,true} and constructors {c,false,n__f,n__true}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 4.
The enriched problem is compatible with follwoing automaton.
activate_0(2) -> 1
activate_1(2) -> 1
activate_1(2) -> 3
activate_1(5) -> 1
activate_1(8) -> 1
activate_1(8) -> 3
activate_2(6) -> 10
activate_2(9) -> 10
c_0() -> 1
c_0() -> 2
c_0() -> 3
c_1() -> 4
c_2() -> 1
c_2() -> 3
c_2() -> 7
c_3() -> 1
c_3() -> 3
c_3() -> 11
f_0(2) -> 1
f_1(3) -> 1
f_1(3) -> 3
f_2(10) -> 1
f_2(10) -> 3
false_0() -> 1
false_0() -> 2
false_0() -> 3
if_0(2,2,2) -> 1
if_1(2,4,5) -> 1
if_2(3,7,8) -> 1
if_2(3,7,8) -> 3
if_3(10,11,12) -> 1
if_3(10,11,12) -> 3
n__f_0(2) -> 1
n__f_0(2) -> 2
n__f_0(2) -> 3
n__f_1(2) -> 1
n__f_1(6) -> 1
n__f_1(6) -> 5
n__f_2(3) -> 1
n__f_2(3) -> 3
n__f_2(9) -> 1
n__f_2(9) -> 3
n__f_2(9) -> 8
n__f_3(10) -> 1
n__f_3(10) -> 3
n__f_3(13) -> 12
n__true_0() -> 1
n__true_0() -> 2
n__true_0() -> 3
n__true_1() -> 1
n__true_1() -> 6
n__true_1() -> 10
n__true_2() -> 1
n__true_2() -> 3
n__true_2() -> 9
n__true_2() -> 10
n__true_3() -> 10
n__true_3() -> 13
n__true_4() -> 10
true_0() -> 1
true_1() -> 1
true_1() -> 3
true_2() -> 10
true_3() -> 10
2 -> 1
2 -> 3
5 -> 1
6 -> 10
7 -> 1
7 -> 3
8 -> 1
8 -> 3
9 -> 10
11 -> 1
11 -> 3
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
activate(X) -> X
activate(n__f(X)) -> f(activate(X))
activate(n__true()) -> true()
f(X) -> if(X,c(),n__f(n__true()))
f(X) -> n__f(X)
if(false(),X,Y) -> activate(Y)
if(true(),X,Y) -> X
true() -> n__true()
- Signature:
{activate/1,f/1,if/3,true/0} / {c/0,false/0,n__f/1,n__true/0}
- Obligation:
runtime complexity wrt. defined symbols {activate,f,if,true} and constructors {c,false,n__f,n__true}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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