WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(0()) -> s(0()) f(s(0())) -> s(0()) f(s(s(x))) -> f(f(s(x))) - Signature: {f/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {0,s} + 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(f) = {1} Following symbols are considered usable: {f} TcT has computed the following interpretation: p(0) = [2] [0] p(f) = [1 2] x1 + [0] [0 0] [4] p(s) = [0 1] x1 + [0] [0 1] [4] Following rules are strictly oriented: f(0()) = [2] [4] > [0] [4] = s(0()) f(s(0())) = [8] [4] > [0] [4] = s(0()) f(s(s(x))) = [0 3] x + [20] [0 0] [4] > [0 3] x + [16] [0 0] [4] = f(f(s(x))) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))