WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: +(0(),y) -> y +(s(x),0()) -> s(x) +(s(x),s(y)) -> s(+(s(x),+(y,0()))) - 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(+) = {2}, uargs(s) = {1} Following symbols are considered usable: {+} TcT has computed the following interpretation: p(+) = [1] x1 + [8] x2 + [2] p(0) = [0] p(s) = [1] x1 + [3] Following rules are strictly oriented: +(0(),y) = [8] y + [2] > [1] y + [0] = y +(s(x),0()) = [1] x + [5] > [1] x + [3] = s(x) +(s(x),s(y)) = [1] x + [8] y + [29] > [1] x + [8] y + [24] = s(+(s(x),+(y,0()))) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))