WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: plus(plus(X,Y),Z) -> plus(X,plus(Y,Z)) times(X,s(Y)) -> plus(X,times(Y,X)) - Signature: {plus/2,times/2} / {s/1} - Obligation: innermost runtime complexity wrt. defined symbols {plus,times} and constructors {s} + Applied Processor: NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} + Details: We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 1 non-zero interpretation-entries in the diagonal of the component-wise maxima): The following argument positions are considered usable: uargs(plus) = {2} Following symbols are considered usable: {plus,times} TcT has computed the following interpretation: p(plus) = [0 2] x1 + [1 0] x2 + [1] [0 1] [0 1] [4] p(s) = [1 4] x1 + [2] [0 0] [2] p(times) = [1 4] x1 + [1 2] x2 + [5] [3 1] [3 0] [2] Following rules are strictly oriented: plus(plus(X,Y),Z) = [0 2] X + [0 2] Y + [1 0] Z + [9] [0 1] [0 1] [0 1] [8] > [0 2] X + [0 2] Y + [1 0] Z + [2] [0 1] [0 1] [0 1] [8] = plus(X,plus(Y,Z)) times(X,s(Y)) = [1 4] X + [1 4] Y + [11] [3 1] [3 12] [8] > [1 4] X + [1 4] Y + [6] [3 1] [3 1] [6] = plus(X,times(Y,X)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))