WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(x,y,s(z)) -> s(f(0(),1(),z)) f(0(),1(),x) -> f(s(x),x,x) - Signature: {f/3} / {0/0,1/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {0,1,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(s) = {1} Following symbols are considered usable: {f} TcT has computed the following interpretation: p(0) = [0] [5] p(1) = [1] [0] p(f) = [0 2] x1 + [4 4] x3 + [0] [0 0] [0 3] [1] p(s) = [1 4] x1 + [0] [0 0] [4] Following rules are strictly oriented: f(x,y,s(z)) = [0 2] x + [4 16] z + [16] [0 0] [0 0] [13] > [4 16] z + [14] [0 0] [4] = s(f(0(),1(),z)) f(0(),1(),x) = [4 4] x + [10] [0 3] [1] > [4 4] x + [8] [0 3] [1] = f(s(x),x,x) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))