WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(x1,0()) -> g(x1,0()) f(y,S(x)) -> f(S(y),x) g(0(),x2) -> x2 g(S(x),y) -> g(x,S(y)) - Signature: {f/2,g/2} / {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(13) 0 :: [] -(0)-> A(9) 0 :: [] -(0)-> A(14) S :: [A(13)] -(13)-> A(13) S :: [A(9)] -(9)-> A(9) S :: [A(0)] -(0)-> A(0) f :: [A(9) x A(13)] -(13)-> A(0) g :: [A(9) x A(0)] -(1)-> A(0) Cost-free Signatures used: -------------------------- 0 :: [] -(0)-> A_cf(0) S :: [A_cf(0)] -(0)-> A_cf(0) f :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) g :: [A_cf(0) x 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(x1,0()) -> g(x1,0()) f(y,S(x)) -> f(S(y),x) g(0(),x2) -> x2 g(S(x),y) -> g(x,S(y)) - Signature: {f/2,g/2} / {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(x1,0()) -> g(x1,0()) f(y,S(x)) -> f(S(y),x) g(0(),x2) -> x2 g(S(x),y) -> g(x,S(y)) - Signature: {f/2,g/2} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {0,S} WORST_CASE(?,O(n^1))