WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: a(b(x)) -> b(a(x)) a(c(x)) -> x - Signature: {a/1} / {b/1,c/1} - Obligation: innermost runtime complexity wrt. defined symbols {a} and constructors {b,c} + 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(b) = {1} Following symbols are considered usable: {a} TcT has computed the following interpretation: p(a) = [8] x1 + [4] p(b) = [1] x1 + [3] p(c) = [1] x1 + [0] Following rules are strictly oriented: a(b(x)) = [8] x + [28] > [8] x + [7] = b(a(x)) a(c(x)) = [8] x + [4] > [1] x + [0] = x Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))