WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: half(0()) -> 0() half(s(s(x))) -> s(half(x)) log(s(0())) -> 0() log(s(s(x))) -> s(log(s(half(x)))) - Signature: {half/1,log/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {half,log} 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(4) 0 :: [] -(0)-> A(5) 0 :: [] -(0)-> A(3) half :: [A(4)] -(1)-> A(5) log :: [A(4)] -(0)-> A(2) s :: [A(4)] -(4)-> A(4) s :: [A(5)] -(5)-> A(5) s :: [A(2)] -(2)-> A(2) Cost-free Signatures used: -------------------------- 0 :: [] -(0)-> A_cf(0) half :: [A_cf(0)] -(0)-> A_cf(0) log :: [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: half(0()) -> 0() half(s(s(x))) -> s(half(x)) log(s(0())) -> 0() log(s(s(x))) -> s(log(s(half(x)))) - Signature: {half/1,log/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {half,log} and constructors {0,s} Following problems could not be solved: - Strict TRS: half(0()) -> 0() half(s(s(x))) -> s(half(x)) log(s(0())) -> 0() log(s(s(x))) -> s(log(s(half(x)))) - Signature: {half/1,log/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {half,log} and constructors {0,s} WORST_CASE(?,O(n^1))