* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
10() -> double(s(double(s(s(0())))))
1024() -> 1024_1(0())
1024_1(x) -> if(lt(x,10()),x)
double(0()) -> 0()
double(s(x)) -> s(s(double(x)))
if(false(),x) -> s(0())
if(true(),x) -> double(1024_1(s(x)))
lt(x,0()) -> false()
lt(0(),s(y)) -> true()
lt(s(x),s(y)) -> lt(x,y)
- Signature:
{10/0,1024/0,1024_1/1,double/1,if/2,lt/2} / {0/0,false/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {10,1024,1024_1,double,if,lt} and constructors {0,false,s
,true}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
10() -> double(s(double(s(s(0())))))
1024() -> 1024_1(0())
1024_1(x) -> if(lt(x,10()),x)
double(0()) -> 0()
double(s(x)) -> s(s(double(x)))
if(false(),x) -> s(0())
if(true(),x) -> double(1024_1(s(x)))
lt(x,0()) -> false()
lt(0(),s(y)) -> true()
lt(s(x),s(y)) -> lt(x,y)
- Signature:
{10/0,1024/0,1024_1/1,double/1,if/2,lt/2} / {0/0,false/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {10,1024,1024_1,double,if,lt} and constructors {0,false,s
,true}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
double(x){x -> s(x)} =
double(s(x)) ->^+ s(s(double(x)))
= C[double(x) = double(x){}]
WORST_CASE(Omega(n^1),?)