* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
conv(x) -> conviter(x,cons(0(),nil()))
conviter(x,l) -> if(zero(x),x,l)
half(0()) -> 0()
half(s(0())) -> 0()
half(s(s(x))) -> s(half(x))
if(false(),x,l) -> conviter(half(x),cons(lastbit(x),l))
if(true(),x,l) -> l
lastbit(0()) -> 0()
lastbit(s(0())) -> s(0())
lastbit(s(s(x))) -> lastbit(x)
zero(0()) -> true()
zero(s(x)) -> false()
- Signature:
{conv/1,conviter/2,half/1,if/3,lastbit/1,zero/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {conv,conviter,half,if,lastbit,zero} and constructors {0
,cons,false,nil,s,true}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
conv(x) -> conviter(x,cons(0(),nil()))
conviter(x,l) -> if(zero(x),x,l)
half(0()) -> 0()
half(s(0())) -> 0()
half(s(s(x))) -> s(half(x))
if(false(),x,l) -> conviter(half(x),cons(lastbit(x),l))
if(true(),x,l) -> l
lastbit(0()) -> 0()
lastbit(s(0())) -> s(0())
lastbit(s(s(x))) -> lastbit(x)
zero(0()) -> true()
zero(s(x)) -> false()
- Signature:
{conv/1,conviter/2,half/1,if/3,lastbit/1,zero/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {conv,conviter,half,if,lastbit,zero} and constructors {0
,cons,false,nil,s,true}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
half(x){x -> s(s(x))} =
half(s(s(x))) ->^+ s(half(x))
= C[half(x) = half(x){}]
WORST_CASE(Omega(n^1),?)