```* Step 1: ToInnermost WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
activate(X) -> X
activate(n__f(X)) -> f(X)
f(X) -> n__f(X)
f(0()) -> cons(0(),n__f(s(0())))
f(s(0())) -> f(p(s(0())))
p(s(X)) -> X
- Signature:
{activate/1,f/1,p/1} / {0/0,cons/2,n__f/1,s/1}
- Obligation:
runtime complexity wrt. defined symbols {activate,f,p} and constructors {0,cons,n__f,s}
+ 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(X)
f(X) -> n__f(X)
f(0()) -> cons(0(),n__f(s(0())))
f(s(0())) -> f(p(s(0())))
p(s(X)) -> X
- Signature:
{activate/1,f/1,p/1} / {0/0,cons/2,n__f/1,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {activate,f,p} and constructors {0,cons,n__f,s}
+ Applied Processor:
Bounds {initialAutomaton = perSymbol, enrichment = match}
+ Details:
The problem is match-bounded by 2.
The enriched problem is compatible with follwoing automaton.
0_0() -> 1
0_0() -> 2
0_0() -> 6
0_1() -> 1
0_1() -> 2
0_1() -> 6
0_1() -> 8
0_1() -> 11
0_2() -> 12
0_2() -> 15
activate_0(1) -> 2
activate_0(3) -> 2
activate_0(5) -> 2
activate_0(7) -> 2
cons_0(1,1) -> 2
cons_0(1,1) -> 3
cons_0(1,1) -> 6
cons_0(1,3) -> 2
cons_0(1,3) -> 3
cons_0(1,3) -> 6
cons_0(1,5) -> 2
cons_0(1,5) -> 3
cons_0(1,5) -> 6
cons_0(1,7) -> 2
cons_0(1,7) -> 3
cons_0(1,7) -> 6
cons_0(3,1) -> 2
cons_0(3,1) -> 3
cons_0(3,1) -> 6
cons_0(3,3) -> 2
cons_0(3,3) -> 3
cons_0(3,3) -> 6
cons_0(3,5) -> 2
cons_0(3,5) -> 3
cons_0(3,5) -> 6
cons_0(3,7) -> 2
cons_0(3,7) -> 3
cons_0(3,7) -> 6
cons_0(5,1) -> 2
cons_0(5,1) -> 3
cons_0(5,1) -> 6
cons_0(5,3) -> 2
cons_0(5,3) -> 3
cons_0(5,3) -> 6
cons_0(5,5) -> 2
cons_0(5,5) -> 3
cons_0(5,5) -> 6
cons_0(5,7) -> 2
cons_0(5,7) -> 3
cons_0(5,7) -> 6
cons_0(7,1) -> 2
cons_0(7,1) -> 3
cons_0(7,1) -> 6
cons_0(7,3) -> 2
cons_0(7,3) -> 3
cons_0(7,3) -> 6
cons_0(7,5) -> 2
cons_0(7,5) -> 3
cons_0(7,5) -> 6
cons_0(7,7) -> 2
cons_0(7,7) -> 3
cons_0(7,7) -> 6
cons_1(8,9) -> 2
cons_1(11,9) -> 4
cons_2(12,13) -> 2
cons_2(15,13) -> 4
f_0(1) -> 4
f_0(3) -> 4
f_0(5) -> 4
f_0(7) -> 4
f_1(1) -> 2
f_1(1) -> 4
f_1(3) -> 2
f_1(5) -> 2
f_1(7) -> 2
n__f_0(1) -> 2
n__f_0(1) -> 5
n__f_0(1) -> 6
n__f_0(3) -> 2
n__f_0(3) -> 5
n__f_0(3) -> 6
n__f_0(5) -> 2
n__f_0(5) -> 5
n__f_0(5) -> 6
n__f_0(7) -> 2
n__f_0(7) -> 5
n__f_0(7) -> 6
n__f_1(1) -> 4
n__f_1(3) -> 4
n__f_1(5) -> 4
n__f_1(7) -> 4
n__f_1(10) -> 9
n__f_2(1) -> 2
n__f_2(1) -> 4
n__f_2(3) -> 2
n__f_2(5) -> 2
n__f_2(7) -> 2
n__f_2(14) -> 13
p_0(1) -> 6
p_0(3) -> 6
p_0(5) -> 6
p_0(7) -> 6
p_1(10) -> 1
p_1(10) -> 2
p_1(10) -> 6
s_0(1) -> 2
s_0(1) -> 6
s_0(1) -> 7
s_0(3) -> 2
s_0(3) -> 6
s_0(3) -> 7
s_0(5) -> 2
s_0(5) -> 6
s_0(5) -> 7
s_0(7) -> 2
s_0(7) -> 6
s_0(7) -> 7
s_1(11) -> 10
s_2(15) -> 14
1 -> 2
1 -> 6
3 -> 2
3 -> 6
5 -> 2
5 -> 6
7 -> 2
7 -> 6
11 -> 1
11 -> 2
11 -> 6
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
activate(X) -> X
activate(n__f(X)) -> f(X)
f(X) -> n__f(X)
f(0()) -> cons(0(),n__f(s(0())))
f(s(0())) -> f(p(s(0())))
p(s(X)) -> X
- Signature:
{activate/1,f/1,p/1} / {0/0,cons/2,n__f/1,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {activate,f,p} and constructors {0,cons,n__f,s}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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