WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: activate(X) -> X activate(n__d(X)) -> d(X) activate(n__f(X)) -> f(X) c(X) -> d(activate(X)) d(X) -> n__d(X) f(X) -> n__f(X) f(f(X)) -> c(n__f(g(n__f(X)))) h(X) -> c(n__d(X)) - Signature: {activate/1,c/1,d/1,f/1,h/1} / {g/1,n__d/1,n__f/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,c,d,f,h} and constructors {g,n__d,n__f} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = MiniSMT} + Details: Signatures used: ---------------- activate :: [A(1)] -(12)-> A(0) c :: [A(1)] -(14)-> A(0) d :: [A(0)] -(1)-> A(4) f :: [A(0)] -(8)-> A(0) g :: [A(0)] -(0)-> A(0) h :: [A(0)] -(15)-> A(0) n__d :: [A(0)] -(0)-> A(1) n__d :: [A(0)] -(0)-> A(4) n__f :: [A(0)] -(0)-> A(1) n__f :: [A(0)] -(0)-> A(0) Cost-free Signatures used: -------------------------- activate :: [A_cf(0)] -(0)-> A_cf(0) c :: [A_cf(0)] -(0)-> A_cf(0) d :: [A_cf(0)] -(0)-> A_cf(0) f :: [A_cf(0)] -(0)-> A_cf(0) g :: [A_cf(0)] -(0)-> A_cf(0) n__d :: [A_cf(0)] -(0)-> A_cf(0) n__f :: [A_cf(0)] -(0)-> A_cf(0) Base Constructor Signatures used: --------------------------------- g_A :: [A(0)] -(0)-> A(1) n__d_A :: [A(0)] -(0)-> A(1) n__f_A :: [A(0)] -(0)-> A(1) * Step 2: Open MAYBE - Strict TRS: activate(X) -> X activate(n__d(X)) -> d(X) activate(n__f(X)) -> f(X) c(X) -> d(activate(X)) d(X) -> n__d(X) f(X) -> n__f(X) f(f(X)) -> c(n__f(g(n__f(X)))) h(X) -> c(n__d(X)) - Signature: {activate/1,c/1,d/1,f/1,h/1} / {g/1,n__d/1,n__f/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,c,d,f,h} and constructors {g,n__d,n__f} Following problems could not be solved: - Strict TRS: activate(X) -> X activate(n__d(X)) -> d(X) activate(n__f(X)) -> f(X) c(X) -> d(activate(X)) d(X) -> n__d(X) f(X) -> n__f(X) f(f(X)) -> c(n__f(g(n__f(X)))) h(X) -> c(n__d(X)) - Signature: {activate/1,c/1,d/1,f/1,h/1} / {g/1,n__d/1,n__f/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,c,d,f,h} and constructors {g,n__d,n__f} WORST_CASE(?,O(n^1))