WORST_CASE(?,O(n^2)) * Step 1: Ara WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: fac(0()) -> s(0()) fac(s(x)) -> times(s(x),fac(p(s(x)))) p(s(x)) -> x - Signature: {fac/1,p/1} / {0/0,s/1,times/2} - Obligation: innermost runtime complexity wrt. defined symbols {fac,p} and constructors {0,s,times} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = MiniSMT} + Details: Signatures used: ---------------- 0 :: [] -(0)-> A(4, 4) 0 :: [] -(0)-> A(2, 2) fac :: [A(4, 4)] -(2)-> A(0, 0) p :: [A(0, 4)] -(1)-> A(4, 4) s :: [A(4, 4)] -(4)-> A(4, 4) s :: [A(4, 4)] -(0)-> A(0, 4) s :: [A(0, 0)] -(0)-> A(0, 0) s :: [A(0, 0)] -(2)-> A(2, 0) times :: [A(0, 0) x A(0, 0)] -(0)-> A(4, 0) Cost-free Signatures used: -------------------------- 0 :: [] -(0)-> A_cf(0, 0) fac :: [A_cf(0, 0)] -(0)-> A_cf(0, 0) p :: [A_cf(0, 0)] -(0)-> A_cf(0, 0) s :: [A_cf(0, 0)] -(0)-> A_cf(0, 0) times :: [A_cf(0, 0) x A_cf(0, 0)] -(0)-> A_cf(0, 0) Base Constructor Signatures used: --------------------------------- 0_A :: [] -(0)-> A(1, 0) 0_A :: [] -(0)-> A(0, 1) s_A :: [A(0, 0)] -(1)-> A(1, 0) s_A :: [A(1, 1)] -(0)-> A(0, 1) times_A :: [A(0, 0) x A(0, 0)] -(0)-> A(1, 0) times_A :: [A(0, 1) x A(0, 0)] -(1)-> A(0, 1) * Step 2: Open MAYBE - Strict TRS: fac(0()) -> s(0()) fac(s(x)) -> times(s(x),fac(p(s(x)))) p(s(x)) -> x - Signature: {fac/1,p/1} / {0/0,s/1,times/2} - Obligation: innermost runtime complexity wrt. defined symbols {fac,p} and constructors {0,s,times} Following problems could not be solved: - Strict TRS: fac(0()) -> s(0()) fac(s(x)) -> times(s(x),fac(p(s(x)))) p(s(x)) -> x - Signature: {fac/1,p/1} / {0/0,s/1,times/2} - Obligation: innermost runtime complexity wrt. defined symbols {fac,p} and constructors {0,s,times} WORST_CASE(?,O(n^2))