WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(0()) -> cons(0()) f(s(0())) -> f(p(s(0()))) p(s(X)) -> X - Signature: {f/1,p/1} / {0/0,cons/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,p} and constructors {0,cons,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,p} TcT has computed the following interpretation: p(0) = [1] [0] p(cons) = [0] [0] p(f) = [2 1] x1 + [0] [0 0] [0] p(p) = [1 0] x1 + [1] [1 0] [0] p(s) = [1 1] x1 + [0] [0 0] [5] Following rules are strictly oriented: f(0()) = [2] [0] > [0] [0] = cons(0()) f(s(0())) = [7] [0] > [5] [0] = f(p(s(0()))) p(s(X)) = [1 1] X + [1] [1 1] [0] > [1 0] X + [0] [0 1] [0] = X Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))