WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: app(cons(X),YS) -> cons(X) app(nil(),YS) -> YS from(X) -> cons(X) prefix(L) -> cons(nil()) zWadr(XS,nil()) -> nil() zWadr(cons(X),cons(Y)) -> cons(app(Y,cons(X))) zWadr(nil(),YS) -> nil() - Signature: {app/2,from/1,prefix/1,zWadr/2} / {cons/1,nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {app,from,prefix,zWadr} and constructors {cons,nil} + 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: uargs(cons) = {1} Following symbols are considered usable: {app,from,prefix,zWadr} TcT has computed the following interpretation: p(app) = [4] x1 + [4] x2 + [4] p(cons) = [1] x1 + [0] p(from) = [2] x1 + [1] p(nil) = [3] p(prefix) = [15] p(zWadr) = [8] x1 + [7] x2 + [6] Following rules are strictly oriented: app(cons(X),YS) = [4] X + [4] YS + [4] > [1] X + [0] = cons(X) app(nil(),YS) = [4] YS + [16] > [1] YS + [0] = YS from(X) = [2] X + [1] > [1] X + [0] = cons(X) prefix(L) = [15] > [3] = cons(nil()) zWadr(XS,nil()) = [8] XS + [27] > [3] = nil() zWadr(cons(X),cons(Y)) = [8] X + [7] Y + [6] > [4] X + [4] Y + [4] = cons(app(Y,cons(X))) zWadr(nil(),YS) = [7] YS + [30] > [3] = nil() Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))