* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: goal(xs) -> permute(xs) mapconsapp(x,Nil(),rest) -> rest mapconsapp(x',Cons(x,xs),rest) -> Cons(Cons(x',x),mapconsapp(x',xs,rest)) permute(Cons(x,xs)) -> select(x,Nil(),xs) permute(Nil()) -> Cons(Nil(),Nil()) revapp(Cons(x,xs),rest) -> revapp(xs,Cons(x,rest)) revapp(Nil(),rest) -> rest select(x,revprefix,Nil()) -> mapconsapp(x,permute(revapp(revprefix,Nil())),Nil()) select(x',revprefix,Cons(x,xs)) -> mapconsapp(x' ,permute(revapp(revprefix,Cons(x,xs))) ,select(x,Cons(x',revprefix),xs)) - Signature: {goal/1,mapconsapp/3,permute/1,revapp/2,select/3} / {Cons/2,Nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {goal,mapconsapp,permute,revapp ,select} and constructors {Cons,Nil} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: goal(xs) -> permute(xs) mapconsapp(x,Nil(),rest) -> rest mapconsapp(x',Cons(x,xs),rest) -> Cons(Cons(x',x),mapconsapp(x',xs,rest)) permute(Cons(x,xs)) -> select(x,Nil(),xs) permute(Nil()) -> Cons(Nil(),Nil()) revapp(Cons(x,xs),rest) -> revapp(xs,Cons(x,rest)) revapp(Nil(),rest) -> rest select(x,revprefix,Nil()) -> mapconsapp(x,permute(revapp(revprefix,Nil())),Nil()) select(x',revprefix,Cons(x,xs)) -> mapconsapp(x' ,permute(revapp(revprefix,Cons(x,xs))) ,select(x,Cons(x',revprefix),xs)) - Signature: {goal/1,mapconsapp/3,permute/1,revapp/2,select/3} / {Cons/2,Nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {goal,mapconsapp,permute,revapp ,select} and constructors {Cons,Nil} + 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),?)