```* Step 1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
-(x,0()) -> x
-(s(x),s(y)) -> -(x,y)
double(0()) -> 0()
double(s(x)) -> s(s(double(x)))
half(0()) -> 0()
half(s(0())) -> 0()
half(s(s(x))) -> s(half(x))
if(0(),y,z) -> y
if(s(x),y,z) -> z
- Signature:
{-/2,double/1,half/1,if/3} / {0/0,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {-,double,half,if} and constructors {0,s}
+ 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
-_1(2,2) -> 1
0_0() -> 1
0_0() -> 2
0_1() -> 1
0_1() -> 3
0_1() -> 4
double_0(2) -> 1
double_1(2) -> 4
half_0(2) -> 1
half_1(2) -> 3
if_0(2,2,2) -> 1
s_0(2) -> 1
s_0(2) -> 2
s_1(3) -> 1
s_1(3) -> 3
s_1(3) -> 4
s_1(4) -> 3
2 -> 1
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
-(x,0()) -> x
-(s(x),s(y)) -> -(x,y)
double(0()) -> 0()
double(s(x)) -> s(s(double(x)))
half(0()) -> 0()
half(s(0())) -> 0()
half(s(s(x))) -> s(half(x))
if(0(),y,z) -> y
if(s(x),y,z) -> z
- Signature:
{-/2,double/1,half/1,if/3} / {0/0,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {-,double,half,if} and constructors {0,s}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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