WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(x1,0()) -> g(x1,0()) f(y,S(x)) -> f(S(y),x) g(0(),x2) -> x2 g(S(x),y) -> g(x,S(y)) - Signature: {f/2,g/2} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {0,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: {f,g} TcT has computed the following interpretation: p(0) = 4 p(S) = 1 + x1 p(f) = 4*x1 + 5*x2 p(g) = 4*x1 + x2 Following rules are strictly oriented: f(x1,0()) = 20 + 4*x1 > 4 + 4*x1 = g(x1,0()) f(y,S(x)) = 5 + 5*x + 4*y > 4 + 5*x + 4*y = f(S(y),x) g(0(),x2) = 16 + x2 > x2 = x2 g(S(x),y) = 4 + 4*x + y > 1 + 4*x + y = g(x,S(y)) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))