WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: sum(0()) -> 0() sum(s(x)) -> +(sum(x),s(x)) sum1(0()) -> 0() sum1(s(x)) -> s(+(sum1(x),+(x,x))) - Signature: {sum/1,sum1/1} / {+/2,0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {sum,sum1} 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)] -(0)-> A(0) + :: [A(0) x A(0)] -(0)-> A(4) 0 :: [] -(0)-> A(12) 0 :: [] -(0)-> A(13) 0 :: [] -(0)-> A(14) 0 :: [] -(0)-> A(0) s :: [A(12)] -(12)-> A(12) s :: [A(13)] -(13)-> A(13) s :: [A(0)] -(0)-> A(0) sum :: [A(12)] -(8)-> A(0) sum1 :: [A(13)] -(12)-> 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) sum :: [A_cf(0)] -(0)-> A_cf(0) sum1 :: [A_cf(0)] -(0)-> A_cf(0) Base Constructor Signatures used: --------------------------------- +_A :: [A(0) x A(0)] -(0)-> A(0) 0_A :: [] -(0)-> A(1) s_A :: [A(1)] -(1)-> A(1) * Step 2: Open MAYBE - Strict TRS: sum(0()) -> 0() sum(s(x)) -> +(sum(x),s(x)) sum1(0()) -> 0() sum1(s(x)) -> s(+(sum1(x),+(x,x))) - Signature: {sum/1,sum1/1} / {+/2,0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {sum,sum1} and constructors {+,0,s} Following problems could not be solved: - Strict TRS: sum(0()) -> 0() sum(s(x)) -> +(sum(x),s(x)) sum1(0()) -> 0() sum1(s(x)) -> s(+(sum1(x),+(x,x))) - Signature: {sum/1,sum1/1} / {+/2,0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {sum,sum1} and constructors {+,0,s} WORST_CASE(?,O(n^1))