WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: activate(X) -> X and(tt(),X) -> activate(X) plus(N,0()) -> N plus(N,s(M)) -> s(plus(N,M)) - Signature: {activate/1,and/2,plus/2} / {0/0,s/1,tt/0} - Obligation: innermost runtime complexity wrt. defined symbols {activate,and,plus} and constructors {0,s,tt} + 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: uargs(s) = {1} Following symbols are considered usable: {activate,and,plus} TcT has computed the following interpretation: p(0) = 8 p(activate) = 6 + x1 p(and) = 1 + 4*x1 + 8*x2 p(plus) = 2 + 8*x1 + 2*x2 p(s) = 8 + x1 p(tt) = 4 Following rules are strictly oriented: activate(X) = 6 + X > X = X and(tt(),X) = 17 + 8*X > 6 + X = activate(X) plus(N,0()) = 18 + 8*N > N = N plus(N,s(M)) = 18 + 2*M + 8*N > 10 + 2*M + 8*N = s(plus(N,M)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))