WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(s(x),y,y) -> f(y,x,s(x)) - Signature: {f/3} / {s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {s} + 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) = [2] x1 + [1] x2 + [1] x3 + [8] p(s) = [1] x1 + [8] Following rules are strictly oriented: f(s(x),y,y) = [2] x + [2] y + [24] > [2] x + [2] y + [16] = f(y,x,s(x)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))