WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: even(0()) -> S(0()) even(S(x)) -> odd(x) odd(0()) -> 0() odd(S(x)) -> even(x) - Signature: {even/1,odd/1} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {even,odd} 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: none Following symbols are considered usable: {even,odd} TcT has computed the following interpretation: p(0) = [4] p(S) = [1] x1 + [2] p(even) = [4] x1 + [0] p(odd) = [4] x1 + [0] Following rules are strictly oriented: even(0()) = [16] > [6] = S(0()) even(S(x)) = [4] x + [8] > [4] x + [0] = odd(x) odd(0()) = [16] > [4] = 0() odd(S(x)) = [4] x + [8] > [4] x + [0] = even(x) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))