WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: div2(0()) -> 0() div2(S(0())) -> 0() div2(S(S(x))) -> +(S(0()),div2(x)) - Weak TRS: +(x,S(0())) -> S(x) +(S(0()),y) -> S(y) - Signature: {+/2,div2/1} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {+,div2} and constructors {0,S} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = MiniSMT} + Details: Signatures used: ---------------- + :: [A(0) x A(0)] -(2)-> A(0) 0 :: [] -(0)-> A(7) 0 :: [] -(0)-> A(0) 0 :: [] -(0)-> A(6) S :: [A(7)] -(7)-> A(7) S :: [A(0)] -(0)-> A(0) div2 :: [A(7)] -(8)-> A(0) Cost-free Signatures used: -------------------------- + :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) 0 :: [] -(0)-> A_cf(0) S :: [A_cf(0)] -(0)-> A_cf(0) div2 :: [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: div2(0()) -> 0() div2(S(0())) -> 0() div2(S(S(x))) -> +(S(0()),div2(x)) - Weak TRS: +(x,S(0())) -> S(x) +(S(0()),y) -> S(y) - Signature: {+/2,div2/1} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {+,div2} and constructors {0,S} Following problems could not be solved: - Strict TRS: div2(0()) -> 0() div2(S(0())) -> 0() div2(S(S(x))) -> +(S(0()),div2(x)) - Weak TRS: +(x,S(0())) -> S(x) +(S(0()),y) -> S(y) - Signature: {+/2,div2/1} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {+,div2} and constructors {0,S} WORST_CASE(?,O(n^1))