WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: activate(X) -> X activate(n__from(X)) -> from(X) after(0(),XS) -> XS after(s(N),cons(X,XS)) -> after(N,activate(XS)) from(X) -> cons(X,n__from(s(X))) from(X) -> n__from(X) - Signature: {activate/1,after/2,from/1} / {0/0,cons/2,n__from/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,after,from} and constructors {0,cons,n__from,s} + 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(after) = {2} Following symbols are considered usable: {activate,after,from} TcT has computed the following interpretation: p(0) = [2] p(activate) = [1] x1 + [11] p(after) = [8] x1 + [2] x2 + [0] p(cons) = [1] x2 + [0] p(from) = [2] p(n__from) = [0] p(s) = [1] x1 + [3] Following rules are strictly oriented: activate(X) = [1] X + [11] > [1] X + [0] = X activate(n__from(X)) = [11] > [2] = from(X) after(0(),XS) = [2] XS + [16] > [1] XS + [0] = XS after(s(N),cons(X,XS)) = [8] N + [2] XS + [24] > [8] N + [2] XS + [22] = after(N,activate(XS)) from(X) = [2] > [0] = cons(X,n__from(s(X))) from(X) = [2] > [0] = n__from(X) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))