WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: even(0()) -> S(0()) even(S(x)) -> odd(x) odd(0()) -> 0() odd(S(x)) -> even(x) - Signature: {even/1,odd/1} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {even,odd} and constructors {0,S} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = MiniSMT} + Details: Signatures used: ---------------- 0 :: [] -(0)-> A(11) 0 :: [] -(0)-> A(0) S :: [A(11)] -(11)-> A(11) S :: [A(0)] -(0)-> A(0) even :: [A(11)] -(8)-> A(0) odd :: [A(11)] -(8)-> A(0) Cost-free Signatures used: -------------------------- 0 :: [] -(0)-> A_cf(0) S :: [A_cf(0)] -(0)-> A_cf(0) even :: [A_cf(0)] -(0)-> A_cf(0) odd :: [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: even(0()) -> S(0()) even(S(x)) -> odd(x) odd(0()) -> 0() odd(S(x)) -> even(x) - Signature: {even/1,odd/1} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {even,odd} and constructors {0,S} Following problems could not be solved: - Strict TRS: even(0()) -> S(0()) even(S(x)) -> odd(x) odd(0()) -> 0() odd(S(x)) -> even(x) - Signature: {even/1,odd/1} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {even,odd} and constructors {0,S} WORST_CASE(?,O(n^1))