WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(0()) -> s(0()) f(s(x)) -> s(s(g(x))) g(0()) -> 0() g(s(x)) -> f(x) - Signature: {f/1,g/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {0,s} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = Z3} + Details: Signatures used: ---------------- 0 :: [] -(0)-> A(1) 0 :: [] -(0)-> A(14) 0 :: [] -(0)-> A(0) f :: [A(1)] -(15)-> A(0) g :: [A(1)] -(15)-> A(0) s :: [A(1)] -(1)-> A(1) s :: [A(14)] -(14)-> A(14) s :: [A(0)] -(0)-> A(0) Cost-free Signatures used: -------------------------- 0 :: [] -(0)-> A_cf(0) f :: [A_cf(0)] -(0)-> A_cf(0) g :: [A_cf(0)] -(0)-> A_cf(0) s :: [A_cf(0)] -(0)-> A_cf(0) Base Constructor Signatures used: --------------------------------- 0_A :: [] -(0)-> A(1) s_A :: [A(1)] -(1)-> A(1) * Step 2: Open MAYBE - Strict TRS: f(0()) -> s(0()) f(s(x)) -> s(s(g(x))) g(0()) -> 0() g(s(x)) -> f(x) - Signature: {f/1,g/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {0,s} Following problems could not be solved: - Strict TRS: f(0()) -> s(0()) f(s(x)) -> s(s(g(x))) g(0()) -> 0() g(s(x)) -> f(x) - Signature: {f/1,g/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {0,s} WORST_CASE(?,O(n^1))