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