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(activate(X)) activate(n__h(X)) -> h(activate(X)) f(X) -> g(n__h(n__f(X))) f(X) -> n__f(X) h(X) -> n__h(X) - Signature: {activate/1,f/1,h/1} / {g/1,n__f/1,n__h/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,f,h} and constructors {g,n__f,n__h} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = Z3} + Details: Signatures used: ---------------- activate :: [A(15)] -(9)-> A(0) f :: [A(0)] -(4)-> A(0) g :: [A(0)] -(0)-> A(2) h :: [A(0)] -(3)-> A(0) n__f :: [A(15)] -(15)-> A(15) n__f :: [A(0)] -(0)-> A(0) n__h :: [A(15)] -(15)-> A(15) n__h :: [A(0)] -(0)-> A(0) Cost-free Signatures used: -------------------------- activate :: [A_cf(0)] -(0)-> A_cf(0) f :: [A_cf(0)] -(0)-> A_cf(0) g :: [A_cf(0)] -(0)-> A_cf(0) h :: [A_cf(0)] -(0)-> A_cf(0) n__f :: [A_cf(0)] -(0)-> A_cf(0) n__h :: [A_cf(0)] -(0)-> A_cf(0) Base Constructor Signatures used: --------------------------------- g_A :: [A(0)] -(0)-> A(1) n__f_A :: [A(0)] -(1)-> A(1) n__h_A :: [A(0)] -(1)-> A(1) * Step 2: Open MAYBE - Strict TRS: activate(X) -> X activate(n__f(X)) -> f(activate(X)) activate(n__h(X)) -> h(activate(X)) f(X) -> g(n__h(n__f(X))) f(X) -> n__f(X) h(X) -> n__h(X) - Signature: {activate/1,f/1,h/1} / {g/1,n__f/1,n__h/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,f,h} and constructors {g,n__f,n__h} Following problems could not be solved: - Strict TRS: activate(X) -> X activate(n__f(X)) -> f(activate(X)) activate(n__h(X)) -> h(activate(X)) f(X) -> g(n__h(n__f(X))) f(X) -> n__f(X) h(X) -> n__h(X) - Signature: {activate/1,f/1,h/1} / {g/1,n__f/1,n__h/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,f,h} and constructors {g,n__f,n__h} WORST_CASE(?,O(n^1))