WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: ++(x,nil()) -> x ++(++(x,y),z) -> ++(x,++(y,z)) ++(.(x,y),z) -> .(x,++(y,z)) ++(nil(),y) -> y - Signature: {++/2} / {./2,nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {++} and constructors {.,nil} + 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(.) = {2} Following symbols are considered usable: {++} TcT has computed the following interpretation: p(++) = [2] x1 + [1] x2 + [1] p(.) = [1] x1 + [1] x2 + [8] p(nil) = [9] Following rules are strictly oriented: ++(x,nil()) = [2] x + [10] > [1] x + [0] = x ++(++(x,y),z) = [4] x + [2] y + [1] z + [3] > [2] x + [2] y + [1] z + [2] = ++(x,++(y,z)) ++(.(x,y),z) = [2] x + [2] y + [1] z + [17] > [1] x + [2] y + [1] z + [9] = .(x,++(y,z)) ++(nil(),y) = [1] y + [19] > [1] y + [0] = y Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))