```* Step 1: ToInnermost WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
f(x,a()) -> x
f(x,g(y)) -> f(g(x),y)
- Signature:
{f/2} / {a/0,g/1}
- Obligation:
runtime complexity wrt. defined symbols {f} and constructors {a,g}
+ 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(x,a()) -> x
f(x,g(y)) -> f(g(x),y)
- Signature:
{f/2} / {a/0,g/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f} and constructors {a,g}
+ Applied Processor:
Bounds {initialAutomaton = perSymbol, enrichment = match}
+ Details:
The problem is match-bounded by 1.
The enriched problem is compatible with follwoing automaton.
a_0() -> 1
a_0() -> 2
f_0(1,1) -> 2
f_0(1,3) -> 2
f_0(3,1) -> 2
f_0(3,3) -> 2
f_1(4,1) -> 2
f_1(4,3) -> 2
g_0(1) -> 2
g_0(1) -> 3
g_0(3) -> 2
g_0(3) -> 3
g_1(1) -> 2
g_1(1) -> 4
g_1(3) -> 2
g_1(3) -> 4
g_1(4) -> 2
g_1(4) -> 4
1 -> 2
3 -> 2
4 -> 2
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
f(x,a()) -> x
f(x,g(y)) -> f(g(x),y)
- Signature:
{f/2} / {a/0,g/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f} and constructors {a,g}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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