```* Step 1: ToInnermost WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
f(0()) -> s(0())
f(s(0())) -> s(0())
f(s(s(x))) -> f(f(s(x)))
- Signature:
{f/1} / {0/0,s/1}
- Obligation:
runtime complexity wrt. defined symbols {f} and constructors {0,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()) -> s(0())
f(s(0())) -> s(0())
f(s(s(x))) -> f(f(s(x)))
- Signature:
{f/1} / {0/0,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f} and constructors {0,s}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 2.
The enriched problem is compatible with follwoing automaton.
0_0() -> 2
0_1() -> 3
0_2() -> 6
f_0(2) -> 1
f_1(4) -> 1
f_1(4) -> 4
f_1(5) -> 4
s_0(2) -> 2
s_1(2) -> 5
s_1(3) -> 1
s_1(3) -> 4
s_2(6) -> 1
s_2(6) -> 4
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
f(0()) -> s(0())
f(s(0())) -> s(0())
f(s(s(x))) -> f(f(s(x)))
- Signature:
{f/1} / {0/0,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f} and constructors {0,s}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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