WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: append(Cons(x,xs),ys) -> Cons(x,append(xs,ys)) append(Nil(),ys) -> ys goal(x,y) -> append(x,y) - Signature: {append/2,goal/2} / {Cons/2,Nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {append,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: {append,goal} TcT has computed the following interpretation: p(Cons) = [1] x2 + [8] p(Nil) = [3] p(append) = [2] x1 + [2] x2 + [2] p(goal) = [2] x1 + [2] x2 + [6] Following rules are strictly oriented: append(Cons(x,xs),ys) = [2] xs + [2] ys + [18] > [2] xs + [2] ys + [10] = Cons(x,append(xs,ys)) append(Nil(),ys) = [2] ys + [8] > [1] ys + [0] = ys goal(x,y) = [2] x + [2] y + [6] > [2] x + [2] y + [2] = append(x,y) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))