```* Step 1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
g(x,s(y)) -> g(f(x,y),0())
g(0(),f(x,x)) -> x
g(f(x,y),0()) -> f(g(x,0()),g(y,0()))
g(s(x),y) -> g(f(x,y),0())
- Signature:
{g/2} / {0/0,f/2,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {g} and constructors {0,f,s}
+ Applied Processor:
Bounds {initialAutomaton = perSymbol, enrichment = match}
+ Details:
The problem is match-bounded by 2.
The enriched problem is compatible with follwoing automaton.
0_0() -> 1
0_0() -> 3
0_1() -> 6
0_2() -> 11
0_2() -> 12
f_0(1,1) -> 2
f_0(1,1) -> 3
f_0(1,2) -> 2
f_0(1,2) -> 3
f_0(1,4) -> 2
f_0(1,4) -> 3
f_0(2,1) -> 2
f_0(2,1) -> 3
f_0(2,2) -> 2
f_0(2,2) -> 3
f_0(2,4) -> 2
f_0(2,4) -> 3
f_0(4,1) -> 2
f_0(4,1) -> 3
f_0(4,2) -> 2
f_0(4,2) -> 3
f_0(4,4) -> 2
f_0(4,4) -> 3
f_1(1,1) -> 5
f_1(1,2) -> 5
f_1(1,4) -> 5
f_1(1,6) -> 1
f_1(1,6) -> 3
f_1(1,12) -> 13
f_1(2,1) -> 5
f_1(2,2) -> 5
f_1(2,4) -> 5
f_1(2,6) -> 1
f_1(2,6) -> 3
f_1(2,12) -> 13
f_1(4,1) -> 5
f_1(4,2) -> 5
f_1(4,4) -> 5
f_1(4,6) -> 1
f_1(4,6) -> 3
f_1(4,12) -> 13
f_1(7,8) -> 3
f_1(8,8) -> 3
f_1(8,8) -> 8
f_1(8,8) -> 10
f_2(9,10) -> 3
f_2(10,10) -> 3
f_2(10,14) -> 7
f_2(10,14) -> 8
f_2(10,14) -> 9
f_2(10,14) -> 10
g_0(1,1) -> 3
g_0(1,2) -> 3
g_0(1,4) -> 3
g_0(2,1) -> 3
g_0(2,2) -> 3
g_0(2,4) -> 3
g_0(4,1) -> 3
g_0(4,2) -> 3
g_0(4,4) -> 3
g_1(1,6) -> 7
g_1(1,6) -> 8
g_1(2,6) -> 8
g_1(4,6) -> 8
g_1(5,6) -> 3
g_1(6,6) -> 8
g_1(13,6) -> 10
g_2(1,11) -> 9
g_2(1,12) -> 10
g_2(2,12) -> 10
g_2(4,12) -> 10
g_2(6,12) -> 14
g_2(12,12) -> 14
s_0(1) -> 3
s_0(1) -> 4
s_0(2) -> 3
s_0(2) -> 4
s_0(4) -> 3
s_0(4) -> 4
1 -> 3
2 -> 3
4 -> 3
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
g(x,s(y)) -> g(f(x,y),0())
g(0(),f(x,x)) -> x
g(f(x,y),0()) -> f(g(x,0()),g(y,0()))
g(s(x),y) -> g(f(x,y),0())
- Signature:
{g/2} / {0/0,f/2,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {g} and constructors {0,f,s}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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