WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: add0(0(),x2) -> x2 add0(S(x),x2) -> +(S(0()),add0(x2,x)) - Weak TRS: +(x,S(0())) -> S(x) +(S(0()),y) -> S(y) - Signature: {+/2,add0/2} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {+,add0} 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: {+,add0} TcT has computed the following interpretation: p(+) = [1] x1 + [1] x2 + [1] p(0) = [6] p(S) = [1] x1 + [8] p(add0) = [2] x1 + [2] x2 + [0] Following rules are strictly oriented: add0(0(),x2) = [2] x2 + [12] > [1] x2 + [0] = x2 add0(S(x),x2) = [2] x + [2] x2 + [16] > [2] x + [2] x2 + [15] = +(S(0()),add0(x2,x)) Following rules are (at-least) weakly oriented: +(x,S(0())) = [1] x + [15] >= [1] x + [8] = S(x) +(S(0()),y) = [1] y + [15] >= [1] y + [8] = S(y) WORST_CASE(?,O(n^1))