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