```* Step 1: ToInnermost WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
f(0()) -> cons(0())
f(s(0())) -> f(p(s(0())))
p(s(X)) -> X
- Signature:
{f/1,p/1} / {0/0,cons/1,s/1}
- Obligation:
runtime complexity wrt. defined symbols {f,p} and constructors {0,cons,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:
f(0()) -> cons(0())
f(s(0())) -> f(p(s(0())))
p(s(X)) -> X
- Signature:
{f/1,p/1} / {0/0,cons/1,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f,p} and constructors {0,cons,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() -> 4
0_1() -> 6
0_1() -> 7
0_2() -> 9
cons_0(1) -> 2
cons_0(1) -> 4
cons_0(2) -> 2
cons_0(2) -> 4
cons_0(5) -> 2
cons_0(5) -> 4
cons_1(6) -> 3
cons_2(9) -> 3
f_0(1) -> 3
f_0(2) -> 3
f_0(5) -> 3
f_1(7) -> 3
p_0(1) -> 4
p_0(2) -> 4
p_0(5) -> 4
p_1(8) -> 7
s_0(1) -> 4
s_0(1) -> 5
s_0(2) -> 4
s_0(2) -> 5
s_0(5) -> 4
s_0(5) -> 5
s_1(6) -> 8
1 -> 4
2 -> 4
5 -> 4
6 -> 7
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
f(0()) -> cons(0())
f(s(0())) -> f(p(s(0())))
p(s(X)) -> X
- Signature:
{f/1,p/1} / {0/0,cons/1,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f,p} and constructors {0,cons,s}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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