WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: rev(++(x,x)) -> rev(x) rev(++(x,y)) -> ++(rev(y),rev(x)) rev(a()) -> a() rev(b()) -> b() - Signature: {rev/1} / {++/2,a/0,b/0} - Obligation: innermost runtime complexity wrt. defined symbols {rev} and constructors {++,a,b} + 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(++) = {1,2} Following symbols are considered usable: {rev} TcT has computed the following interpretation: p(++) = [1] x1 + [1] x2 + [8] p(a) = [1] p(b) = [5] p(rev) = [2] x1 + [7] Following rules are strictly oriented: rev(++(x,x)) = [4] x + [23] > [2] x + [7] = rev(x) rev(++(x,y)) = [2] x + [2] y + [23] > [2] x + [2] y + [22] = ++(rev(y),rev(x)) rev(a()) = [9] > [1] = a() rev(b()) = [17] > [5] = b() Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))