WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: +(0(),y) -> y +(s(x),y) -> s(+(x,y)) -(x,0()) -> x -(0(),y) -> 0() -(s(x),s(y)) -> -(x,y) - Signature: {+/2,-/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(2) x A(1)] -(8)-> A(0) - :: [A(4) x A(0)] -(4)-> A(4) 0 :: [] -(0)-> A(2) 0 :: [] -(0)-> A(0) 0 :: [] -(0)-> A(4) 0 :: [] -(0)-> A(9) s :: [A(2)] -(2)-> A(2) s :: [A(4)] -(4)-> A(4) s :: [A(0)] -(0)-> A(0) Cost-free Signatures used: -------------------------- + :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) - :: [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) -> s(+(x,y)) -(x,0()) -> x -(0(),y) -> 0() -(s(x),s(y)) -> -(x,y) - Signature: {+/2,-/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) -> s(+(x,y)) -(x,0()) -> x -(0(),y) -> 0() -(s(x),s(y)) -> -(x,y) - Signature: {+/2,-/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {+,-} and constructors {0,s} WORST_CASE(?,O(n^1))