WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(x,x,y) -> x f(x,y,y) -> y f(x,y,g(y)) -> x f(f(x,y,z),u,f(x,y,v)) -> f(x,y,f(z,u,v)) f(g(x),x,y) -> y - Signature: {f/3} / {g/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {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: uargs(f) = {3} Following symbols are considered usable: {f} TcT has computed the following interpretation: p(f) = [2] x1 + [2] x3 + [2] p(g) = [1] x1 + [4] Following rules are strictly oriented: f(x,x,y) = [2] x + [2] y + [2] > [1] x + [0] = x f(x,y,y) = [2] x + [2] y + [2] > [1] y + [0] = y f(x,y,g(y)) = [2] x + [2] y + [10] > [1] x + [0] = x f(f(x,y,z),u,f(x,y,v)) = [4] v + [8] x + [4] z + [10] > [4] v + [2] x + [4] z + [6] = f(x,y,f(z,u,v)) f(g(x),x,y) = [2] x + [2] y + [10] > [1] y + [0] = y Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))