WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: add(0(),X) -> X add(s(),Y) -> s() from(X) -> cons(X) fst(0(),Z) -> nil() fst(s(),cons(Y)) -> cons(Y) len(cons(X)) -> s() len(nil()) -> 0() - Signature: {add/2,from/1,fst/2,len/1} / {0/0,cons/1,nil/0,s/0} - Obligation: innermost runtime complexity wrt. defined symbols {add,from,fst,len} 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: {add,from,fst,len} TcT has computed the following interpretation: p(0) = [6] p(add) = [3] x1 + [2] x2 + [2] p(cons) = [1] x1 + [0] p(from) = [8] x1 + [2] p(fst) = [2] x1 + [1] x2 + [5] p(len) = [10] p(nil) = [4] p(s) = [8] Following rules are strictly oriented: add(0(),X) = [2] X + [20] > [1] X + [0] = X add(s(),Y) = [2] Y + [26] > [8] = s() from(X) = [8] X + [2] > [1] X + [0] = cons(X) fst(0(),Z) = [1] Z + [17] > [4] = nil() fst(s(),cons(Y)) = [1] Y + [21] > [1] Y + [0] = cons(Y) len(cons(X)) = [10] > [8] = s() len(nil()) = [10] > [6] = 0() Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))