WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: div2(0()) -> 0() div2(S(0())) -> 0() div2(S(S(x))) -> +(S(0()),div2(x)) - Weak TRS: +(x,S(0())) -> S(x) +(S(0()),y) -> S(y) - Signature: {+/2,div2/1} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {+,div2} 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(+) = {2} Following symbols are considered usable: {+,div2} TcT has computed the following interpretation: p(+) = [2] x1 + [1] x2 + [8] p(0) = [0] p(S) = [1] x1 + [2] p(div2) = [4] x1 + [2] Following rules are strictly oriented: div2(0()) = [2] > [0] = 0() div2(S(0())) = [10] > [0] = 0() div2(S(S(x))) = [4] x + [18] > [4] x + [14] = +(S(0()),div2(x)) Following rules are (at-least) weakly oriented: +(x,S(0())) = [2] x + [10] >= [1] x + [2] = S(x) +(S(0()),y) = [1] y + [12] >= [1] y + [2] = S(y) WORST_CASE(?,O(n^1))