WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: minus(x,0()) -> x minus(s(x),s(y)) -> minus(x,y) quot(0(),s(y)) -> 0() quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) - Signature: {minus/2,quot/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {minus,quot} 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(0) 0 :: [] -(0)-> A(9) 0 :: [] -(0)-> A(5) minus :: [A(9) x A(0)] -(1)-> A(9) quot :: [A(9) x A(1)] -(12)-> A(3) s :: [A(9)] -(9)-> A(9) s :: [A(0)] -(0)-> A(0) s :: [A(1)] -(1)-> A(1) s :: [A(3)] -(3)-> A(3) Cost-free Signatures used: -------------------------- 0 :: [] -(0)-> A_cf(0) minus :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) quot :: [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: minus(x,0()) -> x minus(s(x),s(y)) -> minus(x,y) quot(0(),s(y)) -> 0() quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) - Signature: {minus/2,quot/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {minus,quot} and constructors {0,s} Following problems could not be solved: - Strict TRS: minus(x,0()) -> x minus(s(x),s(y)) -> minus(x,y) quot(0(),s(y)) -> 0() quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) - Signature: {minus/2,quot/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {minus,quot} and constructors {0,s} WORST_CASE(?,O(n^1))