* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
goal(xs) -> subsets(xs)
mapconsapp(x,Nil(),rest) -> rest
mapconsapp(x',Cons(x,xs),rest) -> Cons(Cons(x',x),mapconsapp(x',xs,rest))
notEmpty(Cons(x,xs)) -> True()
notEmpty(Nil()) -> False()
subsets(Cons(x,xs)) -> subsets[Ite][True][Let](Cons(x,xs),subsets(xs))
subsets(Nil()) -> Cons(Nil(),Nil())
- Weak TRS:
subsets[Ite][True][Let](Cons(x,xs),subs) -> mapconsapp(x,subs,subs)
- Signature:
{goal/1,mapconsapp/3,notEmpty/1,subsets/1,subsets[Ite][True][Let]/2} / {Cons/2,False/0,Nil/0,True/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {goal,mapconsapp,notEmpty,subsets
,subsets[Ite][True][Let]} and constructors {Cons,False,Nil,True}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
goal(xs) -> subsets(xs)
mapconsapp(x,Nil(),rest) -> rest
mapconsapp(x',Cons(x,xs),rest) -> Cons(Cons(x',x),mapconsapp(x',xs,rest))
notEmpty(Cons(x,xs)) -> True()
notEmpty(Nil()) -> False()
subsets(Cons(x,xs)) -> subsets[Ite][True][Let](Cons(x,xs),subsets(xs))
subsets(Nil()) -> Cons(Nil(),Nil())
- Weak TRS:
subsets[Ite][True][Let](Cons(x,xs),subs) -> mapconsapp(x,subs,subs)
- Signature:
{goal/1,mapconsapp/3,notEmpty/1,subsets/1,subsets[Ite][True][Let]/2} / {Cons/2,False/0,Nil/0,True/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {goal,mapconsapp,notEmpty,subsets
,subsets[Ite][True][Let]} and constructors {Cons,False,Nil,True}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
mapconsapp(x,z,u){z -> Cons(y,z)} =
mapconsapp(x,Cons(y,z),u) ->^+ Cons(Cons(x,y),mapconsapp(x,z,u))
= C[mapconsapp(x,z,u) = mapconsapp(x,z,u){}]
WORST_CASE(Omega(n^1),?)