WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: b(u(x)) -> a(e(x)) c(u(x)) -> b(x) d(x) -> e(u(x)) d(u(x)) -> c(x) v(e(x)) -> x - Signature: {b/1,c/1,d/1,v/1} / {a/1,e/1,u/1} - Obligation: innermost runtime complexity wrt. defined symbols {b,c,d,v} and constructors {a,e,u} + 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: none Following symbols are considered usable: {b,c,d,v} TcT has computed the following interpretation: p(a) = [2] p(b) = [6] p(c) = [14] p(d) = [1] x1 + [14] p(e) = [1] x1 + [0] p(u) = [4] p(v) = [4] x1 + [8] Following rules are strictly oriented: b(u(x)) = [6] > [2] = a(e(x)) c(u(x)) = [14] > [6] = b(x) d(x) = [1] x + [14] > [4] = e(u(x)) d(u(x)) = [18] > [14] = c(x) v(e(x)) = [4] x + [8] > [1] x + [0] = x Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))