```* Step 1: ToInnermost WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
f(a,cons(x,k)) -> f(cons(x,a),k)
f(a,empty()) -> g(a,empty())
g(cons(x,k),d) -> g(k,cons(x,d))
g(empty(),d) -> d
- Signature:
{f/2,g/2} / {cons/2,empty/0}
- Obligation:
runtime complexity wrt. defined symbols {f,g} and constructors {cons,empty}
+ 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(a,cons(x,k)) -> f(cons(x,a),k)
f(a,empty()) -> g(a,empty())
g(cons(x,k),d) -> g(k,cons(x,d))
g(empty(),d) -> d
- Signature:
{f/2,g/2} / {cons/2,empty/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {f,g} and constructors {cons,empty}
+ Applied Processor:
Bounds {initialAutomaton = perSymbol, enrichment = match}
+ Details:
The problem is match-bounded by 2.
The enriched problem is compatible with follwoing automaton.
cons_0(1,1) -> 1
cons_0(1,1) -> 4
cons_0(1,2) -> 1
cons_0(1,2) -> 4
cons_0(2,1) -> 1
cons_0(2,1) -> 4
cons_0(2,2) -> 1
cons_0(2,2) -> 4
cons_1(1,1) -> 4
cons_1(1,1) -> 5
cons_1(1,2) -> 4
cons_1(1,2) -> 5
cons_1(1,5) -> 4
cons_1(1,5) -> 5
cons_1(1,6) -> 3
cons_1(1,6) -> 6
cons_1(1,7) -> 3
cons_1(1,7) -> 6
cons_1(2,1) -> 4
cons_1(2,1) -> 5
cons_1(2,2) -> 4
cons_1(2,2) -> 5
cons_1(2,5) -> 4
cons_1(2,5) -> 5
cons_1(2,6) -> 3
cons_1(2,6) -> 6
cons_1(2,7) -> 3
cons_1(2,7) -> 6
cons_2(1,6) -> 3
cons_2(1,6) -> 7
cons_2(1,7) -> 3
cons_2(1,7) -> 7
cons_2(2,6) -> 3
cons_2(2,6) -> 7
cons_2(2,7) -> 3
cons_2(2,7) -> 7
empty_0() -> 2
empty_0() -> 4
empty_1() -> 3
empty_1() -> 6
f_0(1,1) -> 3
f_0(1,2) -> 3
f_0(2,1) -> 3
f_0(2,2) -> 3
f_1(5,1) -> 3
f_1(5,2) -> 3
g_0(1,1) -> 4
g_0(1,2) -> 4
g_0(2,1) -> 4
g_0(2,2) -> 4
g_1(1,5) -> 4
g_1(1,6) -> 3
g_1(2,5) -> 4
g_1(2,6) -> 3
g_1(5,6) -> 3
g_2(1,7) -> 3
g_2(2,7) -> 3
g_2(5,7) -> 3
1 -> 4
2 -> 4
5 -> 4
6 -> 3
7 -> 3
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
f(a,cons(x,k)) -> f(cons(x,a),k)
f(a,empty()) -> g(a,empty())
g(cons(x,k),d) -> g(k,cons(x,d))
g(empty(),d) -> d
- Signature:
{f/2,g/2} / {cons/2,empty/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {f,g} and constructors {cons,empty}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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