WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: average(x,s(s(s(y)))) -> s(average(s(x),y)) average(0(),0()) -> 0() average(0(),s(0())) -> 0() average(0(),s(s(0()))) -> s(0()) average(s(x),y) -> average(x,s(y)) - Signature: {average/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {average} and constructors {0,s} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = Z3} + Details: Signatures used: ---------------- 0 :: [] -(0)-> A(2) 0 :: [] -(0)-> A(1) 0 :: [] -(0)-> A(7) 0 :: [] -(0)-> A(13) average :: [A(2) x A(1)] -(4)-> A(0) s :: [A(1)] -(1)-> A(1) s :: [A(2)] -(2)-> A(2) s :: [A(0)] -(0)-> A(0) Cost-free Signatures used: -------------------------- 0 :: [] -(0)-> A_cf(0) average :: [A_cf(0) x A_cf(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: average(x,s(s(s(y)))) -> s(average(s(x),y)) average(0(),0()) -> 0() average(0(),s(0())) -> 0() average(0(),s(s(0()))) -> s(0()) average(s(x),y) -> average(x,s(y)) - Signature: {average/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {average} and constructors {0,s} Following problems could not be solved: - Strict TRS: average(x,s(s(s(y)))) -> s(average(s(x),y)) average(0(),0()) -> 0() average(0(),s(0())) -> 0() average(0(),s(s(0()))) -> s(0()) average(s(x),y) -> average(x,s(y)) - Signature: {average/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {average} and constructors {0,s} WORST_CASE(?,O(n^1))