WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: 2nd(cons(X,n__cons(Y,Z))) -> activate(Y) activate(X) -> X activate(n__cons(X1,X2)) -> cons(X1,X2) activate(n__from(X)) -> from(X) cons(X1,X2) -> n__cons(X1,X2) from(X) -> cons(X,n__from(s(X))) from(X) -> n__from(X) - Signature: {2nd/1,activate/1,cons/2,from/1} / {n__cons/2,n__from/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {2nd,activate,cons,from} and constructors {n__cons,n__from ,s} + 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: {2nd,activate,cons,from} TcT has computed the following interpretation: p(2nd) = 9 + 2*x1 p(activate) = 12 + 8*x1 p(cons) = 4 + 6*x1 + 8*x2 p(from) = 8 + 8*x1 p(n__cons) = x1 + x2 p(n__from) = x1 p(s) = 0 Following rules are strictly oriented: 2nd(cons(X,n__cons(Y,Z))) = 17 + 12*X + 16*Y + 16*Z > 12 + 8*Y = activate(Y) activate(X) = 12 + 8*X > X = X activate(n__cons(X1,X2)) = 12 + 8*X1 + 8*X2 > 4 + 6*X1 + 8*X2 = cons(X1,X2) activate(n__from(X)) = 12 + 8*X > 8 + 8*X = from(X) cons(X1,X2) = 4 + 6*X1 + 8*X2 > X1 + X2 = n__cons(X1,X2) from(X) = 8 + 8*X > 4 + 6*X = cons(X,n__from(s(X))) from(X) = 8 + 8*X > X = n__from(X) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))