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

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