WORST_CASE(?,O(1)) * Step 1: NaturalMI WORST_CASE(?,O(1)) + Considered Problem: - Strict TRS: first(0(),X) -> nil() first(s(X),cons(Y)) -> cons(Y) from(X) -> cons(X) - Signature: {first/2,from/1} / {0/0,cons/1,nil/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {first,from} and constructors {0,cons,nil,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: {first,from} TcT has computed the following interpretation: p(0) = [0] p(cons) = [0] p(first) = [1] p(from) = [8] p(nil) = [0] p(s) = [0] Following rules are strictly oriented: first(0(),X) = [1] > [0] = nil() first(s(X),cons(Y)) = [1] > [0] = cons(Y) from(X) = [8] > [0] = cons(X) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(1))