WORST_CASE(?,O(n^1)) * Step 1: NaturalPI 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: 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: uargs(cons) = {1} Following symbols are considered usable: {app,from,prefix,zWadr} TcT has computed the following interpretation: p(app) = 4 + x1 + x2 p(cons) = x1 p(from) = 5 + x1 p(nil) = 0 p(prefix) = 10 + x1 p(zWadr) = 9 + x1 + x2 Following rules are strictly oriented: app(cons(X),YS) = 4 + X + YS > X = cons(X) app(nil(),YS) = 4 + YS > YS = YS from(X) = 5 + X > X = cons(X) prefix(L) = 10 + L > 0 = cons(nil()) zWadr(XS,nil()) = 9 + XS > 0 = nil() zWadr(cons(X),cons(Y)) = 9 + X + Y > 4 + X + Y = cons(app(Y,cons(X))) zWadr(nil(),YS) = 9 + YS > 0 = nil() Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))