WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^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: NaturalPI {shape = StronglyLinear, restrict = NoRestrict, uargs = UArgs, urules = URules, selector = Nothing} + Details: We apply a polynomial interpretation of kind constructor-based(stronglyLinear): The following argument positions are considered usable: none Following symbols are considered usable: {first,from} TcT has computed the following interpretation: p(0) = 2 p(cons) = 2 + x1 p(first) = 14 + x1 + x2 p(from) = 11 + x1 p(nil) = 5 p(s) = 12 Following rules are strictly oriented: first(0(),X) = 16 + X > 5 = nil() first(s(X),cons(Y)) = 28 + Y > 2 + Y = cons(Y) from(X) = 11 + X > 2 + X = cons(X) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))