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