WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: activate(X) -> X and(tt(),X) -> activate(X) plus(N,0()) -> N plus(N,s(M)) -> s(plus(N,M)) - Signature: {activate/1,and/2,plus/2} / {0/0,s/1,tt/0} - Obligation: innermost runtime complexity wrt. defined symbols {activate,and,plus} and constructors {0,s,tt} + 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(s) = {1} Following symbols are considered usable: {activate,and,plus} TcT has computed the following interpretation: p(0) = [5] p(activate) = [2] x1 + [14] p(and) = [4] x1 + [3] x2 + [12] p(plus) = [1] x1 + [5] x2 + [0] p(s) = [1] x1 + [4] p(tt) = [1] Following rules are strictly oriented: activate(X) = [2] X + [14] > [1] X + [0] = X and(tt(),X) = [3] X + [16] > [2] X + [14] = activate(X) plus(N,0()) = [1] N + [25] > [1] N + [0] = N plus(N,s(M)) = [5] M + [1] N + [20] > [5] M + [1] N + [4] = s(plus(N,M)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))