WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: activate(X) -> X activate(n__zeros()) -> zeros() tail(cons(X,XS)) -> activate(XS) zeros() -> cons(0(),n__zeros()) zeros() -> n__zeros() - Signature: {activate/1,tail/1,zeros/0} / {0/0,cons/2,n__zeros/0} - Obligation: innermost runtime complexity wrt. defined symbols {activate,tail,zeros} and constructors {0,cons,n__zeros} + Applied Processor: NaturalPI {shape = Linear, restrict = NoRestrict, uargs = UArgs, urules = URules, selector = Nothing} + Details: We apply a polynomial interpretation of kind constructor-based(linear): The following argument positions are considered usable: none Following symbols are considered usable: {activate,tail,zeros} TcT has computed the following interpretation: p(0) = 0 p(activate) = 11 + x1 p(cons) = 2 + x2 p(n__zeros) = 0 p(tail) = 12 + 5*x1 p(zeros) = 3 Following rules are strictly oriented: activate(X) = 11 + X > X = X activate(n__zeros()) = 11 > 3 = zeros() tail(cons(X,XS)) = 22 + 5*XS > 11 + XS = activate(XS) zeros() = 3 > 2 = cons(0(),n__zeros()) zeros() = 3 > 0 = n__zeros() Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))