* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
cond(false(),n,l) -> tail(nthtail(s(n),l))
cond(true(),n,l) -> l
ge(u,0()) -> true()
ge(0(),s(v)) -> false()
ge(s(u),s(v)) -> ge(u,v)
length(cons(x,l)) -> s(length(l))
length(nil()) -> 0()
nthtail(n,l) -> cond(ge(n,length(l)),n,l)
tail(cons(x,l)) -> l
tail(nil()) -> nil()
- Signature:
{cond/3,ge/2,length/1,nthtail/2,tail/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {cond,ge,length,nthtail,tail} 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:
cond(false(),n,l) -> tail(nthtail(s(n),l))
cond(true(),n,l) -> l
ge(u,0()) -> true()
ge(0(),s(v)) -> false()
ge(s(u),s(v)) -> ge(u,v)
length(cons(x,l)) -> s(length(l))
length(nil()) -> 0()
nthtail(n,l) -> cond(ge(n,length(l)),n,l)
tail(cons(x,l)) -> l
tail(nil()) -> nil()
- Signature:
{cond/3,ge/2,length/1,nthtail/2,tail/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {cond,ge,length,nthtail,tail} and constructors {0,cons
,false,nil,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),?)