WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: -(x,0()) -> x -(s(x),s(y)) -> -(x,y) double(0()) -> 0() double(s(x)) -> s(s(double(x))) half(0()) -> 0() half(double(x)) -> x half(s(0())) -> 0() half(s(s(x))) -> s(half(x)) if(0(),y,z) -> y if(s(x),y,z) -> z - Signature: {-/2,double/1,half/1,if/3} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {-,double,half,if} and constructors {0,s} + Applied Processor: Ara {araHeuristics = Heuristics, minDegree = 1, maxDegree = 2, araTimeout = 3, araRuleShifting = Nothing} + Details: Signatures used: ---------------- - :: ["A"(0) x "A"(1)] -(1)-> "A"(0) 0 :: [] -(0)-> "A"(1) 0 :: [] -(0)-> "A"(3) 0 :: [] -(0)-> "A"(0) double :: ["A"(3)] -(1)-> "A"(1) half :: ["A"(1)] -(1)-> "A"(0) if :: ["A"(0) x "A"(0) x "A"(0)] -(1)-> "A"(0) s :: ["A"(0)] -(0)-> "A"(0) s :: ["A"(1)] -(1)-> "A"(1) s :: ["A"(3)] -(3)-> "A"(3) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "0_A" :: [] -(0)-> "A"(0) "s_A" :: ["A"(0)] -(0)-> "A"(0) WORST_CASE(?,O(n^1))