WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f0(x1,0(),x3,x4,x5) -> 0() f0(x1,S(x),x3,0(),x5) -> 0() f0(x1,S(x'),x3,S(x),x5) -> f1(x',S(x'),x,S(x),S(x)) f1(x1,x2,x3,x4,0()) -> 0() f1(x1,x2,x3,x4,S(x)) -> f2(x2,x1,x3,x4,x) f2(x1,x2,0(),x4,x5) -> 0() f2(x1,x2,S(x),0(),0()) -> 0() f2(x1,x2,S(x'),0(),S(x)) -> f3(x1,x2,x',0(),x) f2(x1,x2,S(x'),S(x),0()) -> 0() f2(x1,x2,S(x''),S(x'),S(x)) -> f5(x1,x2,S(x''),x',x) f3(x1,x2,x3,x4,0()) -> 0() f3(x1,x2,x3,x4,S(x)) -> f4(x1,x2,x4,x3,x) f4(0(),x2,x3,x4,x5) -> 0() f4(S(x),0(),x3,x4,0()) -> 0() f4(S(x'),0(),x3,x4,S(x)) -> f3(x',0(),x3,x4,x) f4(S(x'),S(x),x3,x4,0()) -> 0() f4(S(x''),S(x'),x3,x4,S(x)) -> f2(S(x''),x',x3,x4,x) f5(x1,x2,x3,x4,0()) -> 0() f5(x1,x2,x3,x4,S(x)) -> f6(x2,x1,x3,x4,x) f6(x1,x2,x3,x4,0()) -> 0() f6(x1,x2,x3,x4,S(x)) -> f0(x1,x2,x4,x3,x) - Signature: {f0/5,f1/5,f2/5,f3/5,f4/5,f5/5,f6/5} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {f0,f1,f2,f3,f4,f5,f6} and constructors {0,S} + Applied Processor: Ara {araHeuristics = Heuristics, minDegree = 1, maxDegree = 2, araTimeout = 3, araRuleShifting = Nothing} + Details: Signatures used: ---------------- 0 :: [] -(0)-> "A"(2) 0 :: [] -(0)-> "A"(5) 0 :: [] -(0)-> "A"(0) S :: ["A"(2)] -(2)-> "A"(2) S :: ["A"(5)] -(5)-> "A"(5) S :: ["A"(0)] -(0)-> "A"(0) f0 :: ["A"(0) x "A"(2) x "A"(0) x "A"(5) x "A"(0)] -(1)-> "A"(0) f1 :: ["A"(0) x "A"(2) x "A"(5) x "A"(0) x "A"(0)] -(5)-> "A"(0) f2 :: ["A"(2) x "A"(0) x "A"(5) x "A"(0) x "A"(0)] -(4)-> "A"(0) f3 :: ["A"(2) x "A"(0) x "A"(5) x "A"(5) x "A"(0)] -(6)-> "A"(0) f4 :: ["A"(2) x "A"(0) x "A"(5) x "A"(5) x "A"(0)] -(5)-> "A"(0) f5 :: ["A"(2) x "A"(0) x "A"(5) x "A"(0) x "A"(0)] -(3)-> "A"(0) f6 :: ["A"(0) x "A"(2) x "A"(5) x "A"(0) x "A"(0)] -(2)-> "A"(0) 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))