WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: +(0(),y) -> y +(s(x),y) -> +(x,s(y)) +(s(x),y) -> s(+(x,y)) - Signature: {+/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {+} 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(s) = {1} Following symbols are considered usable: {+} TcT has computed the following interpretation: p(+) = [3] x1 + [2] x2 + [0] p(0) = [4] p(s) = [1] x1 + [8] Following rules are strictly oriented: +(0(),y) = [2] y + [12] > [1] y + [0] = y +(s(x),y) = [3] x + [2] y + [24] > [3] x + [2] y + [16] = +(x,s(y)) +(s(x),y) = [3] x + [2] y + [24] > [3] x + [2] y + [8] = s(+(x,y)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))