```* Step 1: ToInnermost WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
f(x,g(x)) -> x
f(x,h(y)) -> f(h(x),y)
- Signature:
{f/2} / {g/1,h/1}
- Obligation:
runtime complexity wrt. defined symbols {f} and constructors {g,h}
+ 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,g(x)) -> x
f(x,h(y)) -> f(h(x),y)
- Signature:
{f/2} / {g/1,h/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f} and constructors {g,h}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 1.
The enriched problem is compatible with follwoing automaton.
f_0(2,2) -> 1
f_1(3,2) -> 1
g_0(2) -> 1
g_0(2) -> 2
h_0(2) -> 1
h_0(2) -> 2
h_1(2) -> 1
h_1(2) -> 3
h_1(3) -> 1
h_1(3) -> 3
2 -> 1
3 -> 1
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
f(x,g(x)) -> x
f(x,h(y)) -> f(h(x),y)
- Signature:
{f/2} / {g/1,h/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f} and constructors {g,h}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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