WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: a() -> n__a() activate(X) -> X activate(n__a()) -> a() activate(n__f(X)) -> f(activate(X)) activate(n__g(X)) -> g(activate(X)) f(X) -> n__f(X) f(f(a())) -> c(n__f(n__g(n__f(n__a())))) g(X) -> n__g(X) - Signature: {a/0,activate/1,f/1,g/1} / {c/1,n__a/0,n__f/1,n__g/1} - Obligation: innermost runtime complexity wrt. defined symbols {a,activate,f,g} and constructors {c,n__a,n__f,n__g} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = MiniSMT} + Details: Signatures used: ---------------- a :: [] -(1)-> A(0) activate :: [A(4)] -(2)-> A(0) c :: [A(0)] -(0)-> A(0) f :: [A(0)] -(1)-> A(0) g :: [A(0)] -(1)-> A(0) n__a :: [] -(0)-> A(4) n__a :: [] -(0)-> A(8) n__a :: [] -(0)-> A(1) n__f :: [A(4)] -(4)-> A(4) n__f :: [A(0)] -(0)-> A(0) n__g :: [A(4)] -(4)-> A(4) n__g :: [A(0)] -(0)-> A(0) Cost-free Signatures used: -------------------------- a :: [] -(0)-> A_cf(0) activate :: [A_cf(0)] -(0)-> A_cf(0) c :: [A_cf(0)] -(0)-> A_cf(0) f :: [A_cf(0)] -(0)-> A_cf(0) g :: [A_cf(0)] -(0)-> A_cf(0) n__a :: [] -(0)-> A_cf(0) n__f :: [A_cf(0)] -(0)-> A_cf(0) n__g :: [A_cf(0)] -(0)-> A_cf(0) Base Constructor Signatures used: --------------------------------- c_A :: [A(1)] -(0)-> A(1) n__a_A :: [] -(0)-> A(1) n__f_A :: [A(0)] -(1)-> A(1) n__g_A :: [A(0)] -(1)-> A(1) * Step 2: Open MAYBE - Strict TRS: a() -> n__a() activate(X) -> X activate(n__a()) -> a() activate(n__f(X)) -> f(activate(X)) activate(n__g(X)) -> g(activate(X)) f(X) -> n__f(X) f(f(a())) -> c(n__f(n__g(n__f(n__a())))) g(X) -> n__g(X) - Signature: {a/0,activate/1,f/1,g/1} / {c/1,n__a/0,n__f/1,n__g/1} - Obligation: innermost runtime complexity wrt. defined symbols {a,activate,f,g} and constructors {c,n__a,n__f,n__g} Following problems could not be solved: - Strict TRS: a() -> n__a() activate(X) -> X activate(n__a()) -> a() activate(n__f(X)) -> f(activate(X)) activate(n__g(X)) -> g(activate(X)) f(X) -> n__f(X) f(f(a())) -> c(n__f(n__g(n__f(n__a())))) g(X) -> n__g(X) - Signature: {a/0,activate/1,f/1,g/1} / {c/1,n__a/0,n__f/1,n__g/1} - Obligation: innermost runtime complexity wrt. defined symbols {a,activate,f,g} and constructors {c,n__a,n__f,n__g} WORST_CASE(?,O(n^1))