WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: duplicate(Cons(x,xs)) -> Cons(x,Cons(x,duplicate(xs))) duplicate(Nil()) -> Nil() goal(x) -> duplicate(x) - Signature: {duplicate/1,goal/1} / {Cons/2,Nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {duplicate,goal} and constructors {Cons,Nil} + Applied Processor: NaturalPI {shape = Linear, restrict = NoRestrict, uargs = UArgs, urules = URules, selector = Nothing} + Details: We apply a polynomial interpretation of kind constructor-based(linear): The following argument positions are considered usable: uargs(Cons) = {2} Following symbols are considered usable: {duplicate,goal} TcT has computed the following interpretation: p(Cons) = 4 + x2 p(Nil) = 6 p(duplicate) = 4*x1 p(goal) = 2 + 8*x1 Following rules are strictly oriented: duplicate(Cons(x,xs)) = 16 + 4*xs > 8 + 4*xs = Cons(x,Cons(x,duplicate(xs))) duplicate(Nil()) = 24 > 6 = Nil() goal(x) = 2 + 8*x > 4*x = duplicate(x) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))