WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: b(r(x)) -> r(b(x)) b(w(x)) -> w(b(x)) w(r(x)) -> r(w(x)) - Signature: {b/1,w/1} / {r/1} - Obligation: innermost runtime complexity wrt. defined symbols {b,w} and constructors {r} + 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(r) = {1}, uargs(w) = {1} Following symbols are considered usable: {b,w} TcT has computed the following interpretation: p(b) = [3] x1 + [1] p(r) = [1] x1 + [2] p(w) = [8] x1 + [6] Following rules are strictly oriented: b(r(x)) = [3] x + [7] > [3] x + [3] = r(b(x)) b(w(x)) = [24] x + [19] > [24] x + [14] = w(b(x)) w(r(x)) = [8] x + [22] > [8] x + [8] = r(w(x)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))