WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(x,g(x)) -> x f(x,h(y)) -> f(h(x),y) - Signature: {f/2} / {g/1,h/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {g,h} + 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(f) = [4] x1 + [6] x2 + [1] p(g) = [0] p(h) = [1] x1 + [1] Following rules are strictly oriented: f(x,g(x)) = [4] x + [1] > [1] x + [0] = x f(x,h(y)) = [4] x + [6] y + [7] > [4] x + [6] y + [5] = f(h(x),y) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))