```* Step 1: ToInnermost WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
merge(x,nil()) -> x
merge(++(x,y),++(u(),v())) -> ++(x,merge(y,++(u(),v())))
merge(++(x,y),++(u(),v())) -> ++(u(),merge(++(x,y),v()))
merge(nil(),y) -> y
- Signature:
{merge/2} / {++/2,nil/0,u/0,v/0}
- Obligation:
runtime complexity wrt. defined symbols {merge} and constructors {++,nil,u,v}
+ 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:
merge(x,nil()) -> x
merge(++(x,y),++(u(),v())) -> ++(x,merge(y,++(u(),v())))
merge(++(x,y),++(u(),v())) -> ++(u(),merge(++(x,y),v()))
merge(nil(),y) -> y
- Signature:
{merge/2} / {++/2,nil/0,u/0,v/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {merge} and constructors {++,nil,u,v}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 1.
The enriched problem is compatible with follwoing automaton.
++_0(2,2) -> 1
++_0(2,2) -> 2
++_1(2,2) -> 8
++_1(2,3) -> 1
++_1(2,3) -> 3
++_1(5,6) -> 3
++_1(5,6) -> 4
++_1(5,7) -> 1
++_1(5,7) -> 3
merge_0(2,2) -> 1
merge_1(2,4) -> 3
merge_1(8,6) -> 7
nil_0() -> 1
nil_0() -> 2
u_0() -> 1
u_0() -> 2
u_1() -> 5
v_0() -> 1
v_0() -> 2
v_1() -> 6
2 -> 1
4 -> 3
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
merge(x,nil()) -> x
merge(++(x,y),++(u(),v())) -> ++(x,merge(y,++(u(),v())))
merge(++(x,y),++(u(),v())) -> ++(u(),merge(++(x,y),v()))
merge(nil(),y) -> y
- Signature:
{merge/2} / {++/2,nil/0,u/0,v/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {merge} and constructors {++,nil,u,v}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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