```* Step 1: ToInnermost WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
g(x,h(y,z)) -> h(g(x,y),z)
g(f(x,y),z) -> f(x,g(y,z))
g(h(x,y),z) -> g(x,f(y,z))
- Signature:
{g/2} / {f/2,h/2}
- Obligation:
runtime complexity wrt. defined symbols {g} and constructors {f,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:
g(x,h(y,z)) -> h(g(x,y),z)
g(f(x,y),z) -> f(x,g(y,z))
g(h(x,y),z) -> g(x,f(y,z))
- Signature:
{g/2} / {f/2,h/2}
- Obligation:
innermost runtime complexity wrt. defined symbols {g} and constructors {f,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) -> 2
f_1(2,2) -> 4
f_1(2,3) -> 1
f_1(2,3) -> 3
f_1(2,4) -> 4
g_0(2,2) -> 1
g_1(2,2) -> 3
g_1(2,4) -> 1
g_1(2,4) -> 3
h_0(2,2) -> 2
h_1(3,2) -> 1
h_1(3,2) -> 3
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
g(x,h(y,z)) -> h(g(x,y),z)
g(f(x,y),z) -> f(x,g(y,z))
g(h(x,y),z) -> g(x,f(y,z))
- Signature:
{g/2} / {f/2,h/2}
- Obligation:
innermost runtime complexity wrt. defined symbols {g} and constructors {f,h}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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