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(activate(X)) activate(n__g(X)) -> g(X) c(X) -> d(activate(X)) d(X) -> n__d(X) f(X) -> n__f(X) f(f(X)) -> c(n__f(n__g(n__f(X)))) g(X) -> n__g(X) h(X) -> c(n__d(X)) - Signature: {activate/1,c/1,d/1,f/1,g/1,h/1} / {n__d/1,n__f/1,n__g/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,c,d,f,g,h} and constructors {n__d,n__f,n__g} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = Z3} + Details: Signatures used: ---------------- activate :: [A(11)] -(4)-> A(2) c :: [A(11)] -(8)-> A(2) d :: [A(2)] -(3)-> A(2) f :: [A(2)] -(10)-> A(2) g :: [A(0)] -(3)-> A(11) h :: [A(15)] -(15)-> A(0) n__d :: [A(11)] -(0)-> A(11) n__d :: [A(2)] -(0)-> A(2) n__d :: [A(15)] -(0)-> A(15) n__f :: [A(11)] -(11)-> A(11) n__f :: [A(2)] -(2)-> A(2) n__f :: [A(0)] -(0)-> A(0) n__g :: [A(0)] -(0)-> A(11) n__g :: [A(0)] -(0)-> A(13) 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) n__g :: [A_cf(0)] -(0)-> A_cf(0) Base Constructor Signatures used: --------------------------------- n__d_A :: [A(0)] -(0)-> A(1) n__f_A :: [A(0)] -(1)-> A(1) n__g_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(activate(X)) activate(n__g(X)) -> g(X) c(X) -> d(activate(X)) d(X) -> n__d(X) f(X) -> n__f(X) f(f(X)) -> c(n__f(n__g(n__f(X)))) g(X) -> n__g(X) h(X) -> c(n__d(X)) - Signature: {activate/1,c/1,d/1,f/1,g/1,h/1} / {n__d/1,n__f/1,n__g/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,c,d,f,g,h} and constructors {n__d,n__f,n__g} Following problems could not be solved: - Strict TRS: activate(X) -> X activate(n__d(X)) -> d(X) activate(n__f(X)) -> f(activate(X)) activate(n__g(X)) -> g(X) c(X) -> d(activate(X)) d(X) -> n__d(X) f(X) -> n__f(X) f(f(X)) -> c(n__f(n__g(n__f(X)))) g(X) -> n__g(X) h(X) -> c(n__d(X)) - Signature: {activate/1,c/1,d/1,f/1,g/1,h/1} / {n__d/1,n__f/1,n__g/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,c,d,f,g,h} and constructors {n__d,n__f,n__g} WORST_CASE(?,O(n^1))