* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
id_inc(x) -> x
id_inc(x) -> s(x)
if(false(),x,y) -> y
if(true(),x,y) -> rand(p(x),id_inc(y))
nonZero(0()) -> false()
nonZero(s(x)) -> true()
p(s(0())) -> 0()
p(s(s(x))) -> s(p(s(x)))
rand(x,y) -> if(nonZero(x),x,y)
random(x) -> rand(x,0())
- Signature:
{id_inc/1,if/3,nonZero/1,p/1,rand/2,random/1} / {0/0,false/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {id_inc,if,nonZero,p,rand,random} 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:
id_inc(x) -> x
id_inc(x) -> s(x)
if(false(),x,y) -> y
if(true(),x,y) -> rand(p(x),id_inc(y))
nonZero(0()) -> false()
nonZero(s(x)) -> true()
p(s(0())) -> 0()
p(s(s(x))) -> s(p(s(x)))
rand(x,y) -> if(nonZero(x),x,y)
random(x) -> rand(x,0())
- Signature:
{id_inc/1,if/3,nonZero/1,p/1,rand/2,random/1} / {0/0,false/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {id_inc,if,nonZero,p,rand,random} and constructors {0
,false,s,true}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
p(s(x)){x -> s(x)} =
p(s(s(x))) ->^+ s(p(s(x)))
= C[p(s(x)) = p(s(x)){}]
WORST_CASE(Omega(n^1),?)