WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(a,cons(x,k)) -> f(cons(x,a),k) f(a,empty()) -> g(a,empty()) g(cons(x,k),d) -> g(k,cons(x,d)) g(empty(),d) -> d - Signature: {f/2,g/2} / {cons/2,empty/0} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {cons,empty} + 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: {f,g} TcT has computed the following interpretation: p(cons) = 1 + x2 p(empty) = 1 p(f) = 8 + 8*x1 + 12*x2 p(g) = 11 + 8*x1 + x2 Following rules are strictly oriented: f(a,cons(x,k)) = 20 + 8*a + 12*k > 16 + 8*a + 12*k = f(cons(x,a),k) f(a,empty()) = 20 + 8*a > 12 + 8*a = g(a,empty()) g(cons(x,k),d) = 19 + d + 8*k > 12 + d + 8*k = g(k,cons(x,d)) g(empty(),d) = 19 + d > d = d Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))