WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: minus(f(x,y)) -> f(minus(y),minus(x)) minus(h(x)) -> h(minus(x)) minus(minus(x)) -> x - Signature: {minus/1} / {f/2,h/1} - Obligation: innermost runtime complexity wrt. defined symbols {minus} and constructors {f,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: uargs(f) = {1,2}, uargs(h) = {1} Following symbols are considered usable: {minus} TcT has computed the following interpretation: p(f) = [1] x1 + [1] x2 + [4] p(h) = [1] x1 + [4] p(minus) = [4] x1 + [1] Following rules are strictly oriented: minus(f(x,y)) = [4] x + [4] y + [17] > [4] x + [4] y + [6] = f(minus(y),minus(x)) minus(h(x)) = [4] x + [17] > [4] x + [5] = h(minus(x)) minus(minus(x)) = [16] x + [5] > [1] x + [0] = x Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))