WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(x,a()) -> x f(x,g(y)) -> f(g(x),y) - Signature: {f/2} / {a/0,g/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {a,g} + 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: none Following symbols are considered usable: {f} TcT has computed the following interpretation: p(a) = [6] p(f) = [1] x1 + [2] x2 + [0] p(g) = [1] x1 + [1] Following rules are strictly oriented: f(x,a()) = [1] x + [12] > [1] x + [0] = x f(x,g(y)) = [1] x + [2] y + [2] > [1] x + [2] y + [1] = f(g(x),y) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))