* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: intlookup(e,p) -> intlookup(lookup(e,p),p) lookup(Cons(x',xs'),Cons(x,xs)) -> lookup(xs',xs) lookup(Nil(),Cons(x,xs)) -> x run(e,p) -> intlookup(e,p) - Signature: {intlookup/2,lookup/2,run/2} / {Cons/2,Nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {intlookup,lookup,run} and constructors {Cons,Nil} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: intlookup(e,p) -> intlookup(lookup(e,p),p) lookup(Cons(x',xs'),Cons(x,xs)) -> lookup(xs',xs) lookup(Nil(),Cons(x,xs)) -> x run(e,p) -> intlookup(e,p) - Signature: {intlookup/2,lookup/2,run/2} / {Cons/2,Nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {intlookup,lookup,run} and constructors {Cons,Nil} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: lookup(y,u){y -> Cons(x,y),u -> Cons(z,u)} = lookup(Cons(x,y),Cons(z,u)) ->^+ lookup(y,u) = C[lookup(y,u) = lookup(y,u){}] WORST_CASE(Omega(n^1),?)