WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: half(0()) -> 0() half(s(s(x))) -> s(half(x)) log(s(0())) -> 0() log(s(s(x))) -> s(log(s(half(x)))) - Signature: {half/1,log/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {half,log} and constructors {0,s} + 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(log) = {1}, uargs(s) = {1} Following symbols are considered usable: {half,log} TcT has computed the following interpretation: p(0) = [0] p(half) = [1] x1 + [2] p(log) = [3] x1 + [0] p(s) = [1] x1 + [4] Following rules are strictly oriented: half(0()) = [2] > [0] = 0() half(s(s(x))) = [1] x + [10] > [1] x + [6] = s(half(x)) log(s(0())) = [12] > [0] = 0() log(s(s(x))) = [3] x + [24] > [3] x + [22] = s(log(s(half(x)))) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))