WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: b(X) -> a(X) f(a(g(X))) -> b(X) f(f(X)) -> f(a(b(f(X)))) - Signature: {b/1,f/1} / {a/1,g/1} - Obligation: innermost runtime complexity wrt. defined symbols {b,f} and constructors {a,g} + Applied Processor: NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} + Details: We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 1 non-zero interpretation-entries in the diagonal of the component-wise maxima): The following argument positions are considered usable: uargs(a) = {1}, uargs(f) = {1} Following symbols are considered usable: {b,f} TcT has computed the following interpretation: p(a) = [1 1] x1 + [1] [0 0] [0] p(b) = [1 1] x1 + [3] [0 0] [1] p(f) = [1 4] x1 + [0] [0 0] [3] p(g) = [1 2] x1 + [5] [0 0] [0] Following rules are strictly oriented: b(X) = [1 1] X + [3] [0 0] [1] > [1 1] X + [1] [0 0] [0] = a(X) f(a(g(X))) = [1 2] X + [6] [0 0] [3] > [1 1] X + [3] [0 0] [1] = b(X) f(f(X)) = [1 4] X + [12] [0 0] [3] > [1 4] X + [8] [0 0] [3] = f(a(b(f(X)))) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))