WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: +(0(),y) -> y +(s(x),y) -> +(x,s(y)) +(s(x),y) -> s(+(x,y)) - Signature: {+/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {+} and constructors {0,s} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = MiniSMT} + Details: Signatures used: ---------------- + :: [A(9) x A(4)] -(2)-> A(1) 0 :: [] -(0)-> A(9) s :: [A(9)] -(9)-> A(9) s :: [A(4)] -(4)-> A(4) s :: [A(1)] -(1)-> A(1) 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) Base Constructor Signatures used: --------------------------------- 0_A :: [] -(0)-> A(1) s_A :: [A(1)] -(1)-> A(1) * Step 2: Open MAYBE - Strict TRS: +(0(),y) -> y +(s(x),y) -> +(x,s(y)) +(s(x),y) -> s(+(x,y)) - Signature: {+/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {+} and constructors {0,s} Following problems could not be solved: - Strict TRS: +(0(),y) -> y +(s(x),y) -> +(x,s(y)) +(s(x),y) -> s(+(x,y)) - Signature: {+/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {+} and constructors {0,s} WORST_CASE(?,O(n^1))