WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: activate(X) -> X activate(n__zeros()) -> zeros() tail(cons(X,XS)) -> activate(XS) zeros() -> cons(0(),n__zeros()) zeros() -> n__zeros() - Signature: {activate/1,tail/1,zeros/0} / {0/0,cons/2,n__zeros/0} - Obligation: innermost runtime complexity wrt. defined symbols {activate,tail,zeros} and constructors {0,cons,n__zeros} + 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: {activate,tail,zeros} TcT has computed the following interpretation: p(0) = [0] p(activate) = [8] x1 + [1] p(cons) = [1] x1 + [1] x2 + [0] p(n__zeros) = [1] p(tail) = [8] x1 + [9] p(zeros) = [8] Following rules are strictly oriented: activate(X) = [8] X + [1] > [1] X + [0] = X activate(n__zeros()) = [9] > [8] = zeros() tail(cons(X,XS)) = [8] X + [8] XS + [9] > [8] XS + [1] = activate(XS) zeros() = [8] > [1] = cons(0(),n__zeros()) zeros() = [8] > [1] = n__zeros() Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))