WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: bits(0()) -> 0() bits(s(x)) -> s(bits(half(s(x)))) half(0()) -> 0() half(s(0())) -> 0() half(s(s(x))) -> s(half(x)) - Signature: {bits/1,half/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {bits,half} 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(7) 0 :: [] -(0)-> A(4) 0 :: [] -(0)-> A(13) bits :: [A(7)] -(8)-> A(0) half :: [A(4)] -(1)-> A(7) s :: [A(7)] -(7)-> A(7) s :: [A(4)] -(4)-> A(4) s :: [A(0)] -(0)-> A(0) Cost-free Signatures used: -------------------------- 0 :: [] -(0)-> A_cf(0) bits :: [A_cf(0)] -(0)-> A_cf(0) half :: [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: bits(0()) -> 0() bits(s(x)) -> s(bits(half(s(x)))) half(0()) -> 0() half(s(0())) -> 0() half(s(s(x))) -> s(half(x)) - Signature: {bits/1,half/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {bits,half} and constructors {0,s} Following problems could not be solved: - Strict TRS: bits(0()) -> 0() bits(s(x)) -> s(bits(half(s(x)))) half(0()) -> 0() half(s(0())) -> 0() half(s(s(x))) -> s(half(x)) - Signature: {bits/1,half/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {bits,half} and constructors {0,s} WORST_CASE(?,O(n^1))