```* Step 1: ToInnermost WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
f(x,y) -> g(x,y)
g(h(x),y) -> h(f(x,y))
g(h(x),y) -> h(g(x,y))
- Signature:
{f/2,g/2} / {h/1}
- Obligation:
runtime complexity wrt. defined symbols {f,g} and constructors {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,y) -> g(x,y)
g(h(x),y) -> h(f(x,y))
g(h(x),y) -> h(g(x,y))
- Signature:
{f/2,g/2} / {h/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f,g} and constructors {h}
+ Applied Processor:
Bounds {initialAutomaton = perSymbol, enrichment = match}
+ Details:
The problem is match-bounded by 2.
The enriched problem is compatible with follwoing automaton.
f_0(3,3) -> 1
f_1(3,3) -> 4
g_0(3,3) -> 2
g_1(3,3) -> 1
g_2(3,3) -> 4
h_0(3) -> 3
h_1(1) -> 1
h_1(1) -> 2
h_1(1) -> 4
h_1(4) -> 1
h_1(4) -> 2
h_1(4) -> 4
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
f(x,y) -> g(x,y)
g(h(x),y) -> h(f(x,y))
g(h(x),y) -> h(g(x,y))
- Signature:
{f/2,g/2} / {h/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f,g} and constructors {h}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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