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