```* Step 1: ToInnermost WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
f(.(.(x,y),z)) -> f(.(x,.(y,z)))
f(.(nil(),y)) -> .(nil(),f(y))
f(nil()) -> nil()
g(.(x,.(y,z))) -> g(.(.(x,y),z))
g(.(x,nil())) -> .(g(x),nil())
g(nil()) -> nil()
- Signature:
{f/1,g/1} / {./2,nil/0}
- Obligation:
runtime complexity wrt. defined symbols {f,g} and constructors {.,nil}
+ 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),z)) -> f(.(x,.(y,z)))
f(.(nil(),y)) -> .(nil(),f(y))
f(nil()) -> nil()
g(.(x,.(y,z))) -> g(.(.(x,y),z))
g(.(x,nil())) -> .(g(x),nil())
g(nil()) -> nil()
- Signature:
{f/1,g/1} / {./2,nil/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {f,g} and constructors {.,nil}
+ Applied Processor:
Bounds {initialAutomaton = perSymbol, enrichment = match}
+ Details:
The problem is match-bounded by 1.
The enriched problem is compatible with follwoing automaton.
._0(1,1) -> 1
._0(1,4) -> 1
._0(4,1) -> 1
._0(4,4) -> 1
._1(1,1) -> 6
._1(1,4) -> 6
._1(1,5) -> 5
._1(1,6) -> 5
._1(4,1) -> 6
._1(4,4) -> 6
._1(4,5) -> 5
._1(4,6) -> 5
._1(6,1) -> 9
._1(6,4) -> 9
._1(7,8) -> 2
._1(9,1) -> 9
._1(9,4) -> 9
._1(10,8) -> 3
._1(10,8) -> 8
._1(10,10) -> 10
f_0(1) -> 2
f_0(4) -> 2
f_1(1) -> 8
f_1(4) -> 8
f_1(5) -> 2
f_1(5) -> 8
f_1(6) -> 8
g_0(1) -> 3
g_0(4) -> 3
g_1(1) -> 10
g_1(4) -> 10
g_1(6) -> 10
g_1(9) -> 3
g_1(9) -> 10
nil_0() -> 4
nil_1() -> 2
nil_1() -> 3
nil_1() -> 7
nil_1() -> 8
nil_1() -> 10
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
f(.(.(x,y),z)) -> f(.(x,.(y,z)))
f(.(nil(),y)) -> .(nil(),f(y))
f(nil()) -> nil()
g(.(x,.(y,z))) -> g(.(.(x,y),z))
g(.(x,nil())) -> .(g(x),nil())
g(nil()) -> nil()
- Signature:
{f/1,g/1} / {./2,nil/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {f,g} and constructors {.,nil}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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