WORST_CASE(?,O(n^1)) * Step 1: NaturalMI 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: NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} + Details: We apply a matrix interpretation of kind constructor based matrix interpretation: 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) = [1] x1 + [1] x2 + [8] p(Nil) = [8] p(duplicate) = [3] x1 + [0] p(goal) = [3] x1 + [2] Following rules are strictly oriented: duplicate(Cons(x,xs)) = [3] x + [3] xs + [24] > [2] x + [3] xs + [16] = Cons(x,Cons(x,duplicate(xs))) duplicate(Nil()) = [24] > [8] = Nil() goal(x) = [3] x + [2] > [3] x + [0] = duplicate(x) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))