WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: 2nd(cons(X,n__cons(Y,Z))) -> activate(Y) activate(X) -> X activate(n__cons(X1,X2)) -> cons(X1,X2) activate(n__from(X)) -> from(X) cons(X1,X2) -> n__cons(X1,X2) from(X) -> cons(X,n__from(s(X))) from(X) -> n__from(X) - Signature: {2nd/1,activate/1,cons/2,from/1} / {n__cons/2,n__from/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {2nd,activate,cons,from} and constructors {n__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: none Following symbols are considered usable: {2nd,activate,cons,from} TcT has computed the following interpretation: p(2nd) = [8] x1 + [1] p(activate) = [4] x1 + [4] p(cons) = [1] x1 + [1] x2 + [1] p(from) = [1] x1 + [2] p(n__cons) = [1] x1 + [1] x2 + [0] p(n__from) = [1] x1 + [0] p(s) = [0] Following rules are strictly oriented: 2nd(cons(X,n__cons(Y,Z))) = [8] X + [8] Y + [8] Z + [9] > [4] Y + [4] = activate(Y) activate(X) = [4] X + [4] > [1] X + [0] = X activate(n__cons(X1,X2)) = [4] X1 + [4] X2 + [4] > [1] X1 + [1] X2 + [1] = cons(X1,X2) activate(n__from(X)) = [4] X + [4] > [1] X + [2] = from(X) cons(X1,X2) = [1] X1 + [1] X2 + [1] > [1] X1 + [1] X2 + [0] = n__cons(X1,X2) from(X) = [1] X + [2] > [1] X + [1] = cons(X,n__from(s(X))) from(X) = [1] X + [2] > [1] X + [0] = n__from(X) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))