WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X) u21(ackout(X),Y) -> u22(ackin(Y,X)) - Signature: {ackin/2,u21/2} / {ackout/1,s/1,u22/1} - Obligation: innermost runtime complexity wrt. defined symbols {ackin,u21} and constructors {ackout,s,u22} + 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(u21) = {1}, uargs(u22) = {1} Following symbols are considered usable: {ackin,u21} TcT has computed the following interpretation: p(ackin) = [1] x2 + [0] p(ackout) = [1] x1 + [14] p(s) = [1] x1 + [1] p(u21) = [1] x1 + [0] p(u22) = [1] x1 + [4] Following rules are strictly oriented: ackin(s(X),s(Y)) = [1] Y + [1] > [1] Y + [0] = u21(ackin(s(X),Y),X) u21(ackout(X),Y) = [1] X + [14] > [1] X + [4] = u22(ackin(Y,X)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))