WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(x,a()) -> x f(x,g(y)) -> f(g(x),y) - Signature: {f/2} / {a/0,g/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {a,g} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = Z3} + Details: Signatures used: ---------------- a :: [] -(0)-> A(6) f :: [A(0) x A(6)] -(8)-> A(0) g :: [A(6)] -(6)-> A(6) g :: [A(0)] -(0)-> A(0) Cost-free Signatures used: -------------------------- a :: [] -(0)-> A_cf(0) f :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) g :: [A_cf(0)] -(0)-> A_cf(0) Base Constructor Signatures used: --------------------------------- a_A :: [] -(0)-> A(1) g_A :: [A(1)] -(1)-> A(1) * Step 2: Open MAYBE - Strict TRS: f(x,a()) -> x f(x,g(y)) -> f(g(x),y) - Signature: {f/2} / {a/0,g/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {a,g} Following problems could not be solved: - Strict TRS: f(x,a()) -> x f(x,g(y)) -> f(g(x),y) - Signature: {f/2} / {a/0,g/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {a,g} WORST_CASE(?,O(n^1))