* 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),?)